0 Research

# Only YOU Can Make IEEE VIS Environmentally Sustainable

Elsie Lee-Robbins
University of Michigan  e-mail<EMAIL_ADDRESS>Andrew McNutt
University of Chicago e-mail<EMAIL_ADDRESS>
###### Abstract

The IEEE VIS Conference (or VIS) hosts more than 1000 people annually. It
brings together visualization researchers and practitioners from across the
world to share new research and knowledge. Behind the scenes, a team of
volunteers puts together the entire conference and makes sure it runs
smoothly. Organizing involves logistics of the conference, ensuring that the
attendees have an enjoyable time, allocating rooms to multiple concurrent
tracks, and keeping the conference within budget. In recent years, the
COVID-19 pandemic has abruptly disrupted plans, forcing organizers to switch
to virtual, hybrid, and satellite formats. These alternatives offer many
benefits: fewer costs (e.g., travel, venue, institutional), greater
accessibility (who can physically travel, who can get visas, who can get child
care), and a lower carbon footprint (as people do not need to fly to attend).
As many conferences begin to revert to the pre-pandemic status quo of
primarily in-person conferences, we suggest that it is an opportune moment to
reflect on the benefits and drawbacks of lower-carbon conference formats. To
learn more about the logistics of conference organizing, we talked to 6 senior
executive-level VIS organizers. We review some of the many considerations that
go into planning, particularly with regard to how they influence decisions
about alternative formats. We aim to start a discussion about the
sustainability of VIS—including sustainability for finance, volunteers, and,
central to this work, the environment—for the next three years and the next
three hundred years.

###### keywords:

Environmental Sustainability, Conference Organization

Introduction

What is the environmental impact of academic travel? What are ways to reduce a
conference’s carbon footprint? Do we even care to make these changes?

Climate change is an important and urgent issue. As we write this paper, we
are experiencing the hottest day in recorded history (July 4, 2023) [36]—a
title that day will not hold for long. The Intergovernmental Panel on Climate
Change (IPCC) stated that: “Climate change is a threat to human well-being and
planetary health. There is a rapidly closing window of opportunity to secure a
liveable and sustainable future for all” [17]. Action needs to be taken this
decade (and as soon as possible) to ensure that life on Earth is at least
livable for everyone on it. Unfortunately, due to the slow and global scale of
environmental change, it is easy to dismiss climate change as a distant
problem that is someone else’s responsibility [12], or as something
individuals are exempt from as it can only be dealt with on a governmental or
institutional scale. Just as U.S. Forest Service mascot Smokey Bear advises
that “Only YOU can prevent wildfires,” we believe it is every VIS participant
and organizer’s responsibility to make VIS environmentally sustainable (Fig.
1).

Institutional-scale behaviors are made up of individual actions. Global air
travel makes up $\approx$2.5% of total global CO2 emissions and $\approx$3.5%
of global warming [32]. Consider a provocative calculation: a round-trip
flight from Seattle to Melbourne (the location of IEEE VIS 2023) is
$\approx$2.7 tons of CO2 emissions [22]. For scale, that is a bit more than
“driving from Boston to New Delhi in India and back (assuming you have a car
that can drive on water)” [39]. An international flight could easily be your
largest carbon emission for an entire year: more than your car emissions, the
food you eat, or the things you buy.

For better or worse, Computer Science has primarily tied publications to
conference attendance in a way that is unlike other research areas. Other
disciplines also share research at conferences, but as works-in-progress and
not as the final, archival publication. Computer Science conferences are, as
Vardi describes it, a “journal that meets in a hotel” [40]. This causes our
conferences to have large carbon footprints, as scholars from across the world
are asked to fly to a wide variety of (often not nearby) locations as a key
part of their work [5], sometimes multiple times per year.

However, a large carbon footprint is not unavoidable. As a result of the
pandemic, alternative conference formats (such as remote and hybrid) were
briefly widespread, significantly reducing the conference carbon footprint and
making those conferences more accessible (as a visa or physical accommodation
was not required to attend). As pre-COVID practices return, it seems likely
that such affordances will end, with venues such as UIST, VIS, and CHI
electing to offer no or limited hybrid options.

It is easy (and enjoyable) to return to the status quo [27], as the benefits
of in-person experiences are visible and visceral, but we are also offered an
opportunity to reflect and consider what is essential about VIS. Should the
conference strive to consider its environmental impacts? How much should we
value alternative conference formats as a way to lower our carbon footprint?
As IEEE VIS is the “premier forum for advances in visualization and visual
analytics” [16], and hence an institution with the power and impact that comes
with spending millions of dollars and involving thousands of people, how do we
wish to exert that power?

In this paper, we explore the benefits and drawbacks of alternative conference
formats that would lead to a lower carbon footprint. We center this discussion
around the considerations that go into the immense task of organizing a
1200-person event [6]. To learn more about how VIS is organized, we conduct an
interview study with ($N=6$) executive-level organizers of the IEEE VIS
conference. We uncover a variety of trade-offs and perspectives, and find
there is no perfect solution for how we should engage with sustainability. Our
goal in this work is to raise the issue of environmental sustainability in our
community. To support this dialog, we sketch a variety of ways to make VIS
more sustainable, such as via remote, hybrid, and regional conferences. As
ours are just two voices, we do not aim to give a recommendation of which
conference format is the best, but rather to start a conversation about the
sustainability of IEEE VIS.

Figure 1: Smokey (the) bear is a mascot of the U.S. Forest Service that
advocates personal responsibility in preventing wild fires. Here he has
graciously changed his message to urge you to take ownership over making IEEE
VIS environmentally sustainable.

##  1 IEEE VIS and Climate Change

This paper is far from the first time VIS has interacted with the climate. For
instance, the Viz4Climate workshop [15] brought together visualization
researchers and climate scientists. Visualizations can be used to educate the
public on how to be more sustainable (e.g., Fig. 2, [34]) and inspire
conversations about climate change (e.g., [13]). Instead, we turn this
question and ask how are we contributing to climate change?

Academic travel is, if not essential to, a large part of career development.
Publish (and present) or perish. However, conferences can be far from where
many live. Reductionist accounts can make the premise of presenting seem
absurd: many will have to fly for more than 30 hours merely to make a 10
minute talk at this year’s VIS—although this obviously precludes extrinsic
benefits.111 We do not mean to attack the decision to host the conference in
Australia. There are good reasons to have the conference there: the Victorian
state government has helped cover costs in a difficult time, and it is the
first time the conference will be held in the southern hemisphere (and
shockingly only the 4th outside the US). Yet, the distance from many VIS geo-
centers offers an extrema for reflection.  Networking at conferences can grow
the community of people familiar with your work, foster collaborations, and
gain personal connections. Academic travel is also seen as a job perk: it is
fun to be paid to travel to new places around the world multiple times a year.

More quantitatively, Jacques [18] studied the CO2 emissions from CHI, finding
that the total emissions are generally increasing. Berne et al. [5] found that
flying to conferences was positively correlated with h-index. They concluded
that “flying is a means for early-career scientists to obtain scientific
visibility, and for senior scientists to maintain this visibility.” Wynes et
al. found that academic travel was correlated with salary (but not h-index)
[42]. This suggests that common academic metrics of success encourage us to
travel to conferences. Is visibility and an h-index bump worth significant
negative climate contributions?

There are efforts by academics to fly less on a personal level [19, 11], but
in this paper we focus on activism at the organization level. Institutional-
wide changes mitigate some of the negative impacts that would be felt on a
personal level (i.e., deciding not to fly to a conference that everyone else
is going to). Moreover, an organizational decision would affect many more
people than advocating for individual choices.

##  2 IEEE VIS Organizing Considerations

Organizing the VIS conference is an immense effort undertaken by community
volunteers. Many considerations go into how to choose the next location and
format of the conference, many of which are not visible or widely discussed.
To better understand these deliberations, we interviewed executive-level
organizers of the IEEE VIS conference about their views on conference
sustainability.

Current and recent members of the VIS Executive Committee (VEC) and the VIS
Steering Community (VSC) were invited via email to discuss conference
logistics and to elicit their thoughts on conference sustainability. 6
organizers participated. Participants had a total of $\approx$110 years of
attending and $\approx$90 years of organizing the VIS conference. We quote
participants “like so.”222To maintain anonymity of this small population, we
do not release demographics or associate quotes to ids. Our Zoom-based
interviews lasted $\approx$30 minutes and were automatically transcribed. No
formal qualitative analysis was conducted. The set of interview questions can
be found in the appendix.

While our sample size represents a third of the VEC and VSC, it is still
small. As such, we do not claim to present a comprehensive view of the
concerns of all VIS organizers. Instead, we offer a starting point for
subsequent considerations and discussions. Participants discussed a variety of
concerns about the sustainability of organizing the conference, which we
discuss here.

Figure 2: The carbon footprint of different modes of travel. How might
consideration of how attendees travel to the conference influence how we
organize it? Chart created by Hannah Ritchie from Our World in Data [34].

Financial Risks. The financial feasibility of the conference was seen as an
important aspect of organizing. One participant described it as a
“precondition,” and that “without it, you can’t do it.” If the costs are too
high or if the number of registrations is too low, the organizers run the risk
of a budget deficit. One question that arose was “how to predict how many
attendees will you have?” This logistical estimation is difficult, given that
the number of attendees has grown over time, there is variation from year to
year, and the prediction has to happen $\approx$2 years in advance. Another
consideration is that “IEEE takes on that financial risk,” with VGTC also
handling some of the financial aspects.

The goal is not to have the most cost-effective conference, but rather spend
money where we want to support our values. One participant mentioned the
VISKids Child Care available at VIS22, saying that the organizers paid for
child care to support parents. Another participant echoed this idea, saying,
“if there’s extra money, part of that stays at the VGTC. So the VGTC can
reinvest this in… diversity scholarships… [and] accessibility.” It was
unanimously agreed that diversity and accessibility are valued at IEEE VIS,
and time and money are dedicated to support these goals. How much money are we
willing to dedicate towards environmental sustainability?

Networking. Some participants described networking as one of the essential
conference goals. This can encompass attendees’ opportunities “to create new
ideas, also to plan about careers, next steps, invites, joint proposals.” This
is reflected in the conference schedule: coffee breaks are built into the
program to facilitate conversation. One participant strongly valued such in-
person interactions, saying, “I don’t think you get the mentoring and the
education without the interpersonal interaction.”

However, not all participants saw in-person networking as essential. One
questioned “Is in-person networking required for an academic career? That’s
probably the fundamental question.” Prior work [5, 14] suggests that academic
networks are necessary for career success, however it is unclear if physical
co-location is necessary to support the formation of those networks [41]. What
aspects of in-person networking are lost in virtual contexts? Are there ways
to maintain some benefits of networking in other formats?

Volunteer Labor. VIS is primarily organized by volunteers from the community.
One participant cited the availability of volunteers for general chairs as the
biggest constraint, noting that recruiting them can be especially difficult,
as they only “get anywhere from 1–4 bids in a year.”333One reviewer noted that
the opposite is true for non-leadership positions. For example, VIS often has
more applicants than it needs for student volunteer roles. They went on to
describe location selection as boiling down to “we want to have VIS at Place
X, because Person X said they will do it, and we’re happy that somebody said
they would do it.”

Another participant discussed volunteer labor in the context of organizational
sustainability: “What I find very interesting are the incentive structures.
Why people engage in organizing conferences like VIS, and how we can keep up a
healthy community in the sense that people volunteer to take on roles in VIS…
That’s a question also for sustainability.” Volunteer labor may potentially be
an obstacle for conference formats that require more volunteers or effort.
What are the benefits and incentives for volunteering? How can we encourage
more volunteers to ensure the organizational sustainability of VIS?

Environmental Sustainability. Participants did not prioritize environmental
sustainability over other values (such as diversity and accessibility). Some
saw it as “a nice to have,” and another noted “I don’t know that
environmentally friendly has entered into it much at all.” However, some
participants were more enthusiastic: “sustainable and environmental friendly.
Of course. Yeah, that’s for the long term. We also need that.”

As a provocative question, we asked participants about the carbon footprint of
an academic conference. Most participants asked, “Relative to what?” Relative
to other computer science conferences and industry conferences, VIS is small
at only $\approx$1000 people. Other related conferences—such as “NeurIPs” (13k
[23]) or “CHI” (3–4k [37])—have many more participants than VIS and so our
impact relative to them is small. However, the carbon cost of a round-trip
international flight is immense, relative to an individual’s entire footprint.
One participant suggested that “academics have 3 times the carbon footprint of
other people.” Some organizers mentioned the impact of air travel. One
commented, “VIS has a big footprint, I would say, due to the international
flights” and another commented on the location for 2023, “if it is like this
year in Melbourne, where it’s a long haul for people in the Americas and
Europe, that’s a much larger footprint.”

As another provocative question, we asked our participants if VIS has a
responsibility to be sustainable. Some participants agreed with this, with one
saying, “every conference, including VIS, has the responsibility to become
more sustainable than they already are.” Understandably, some participants
commented that VIS alone does not carry the responsibility, arguing that
governments and other higher-level institutions (e.g., “IEEE”) should also
address climate change. One participant noted, “Every conference has a
responsibility to uphold reasonable standards of sustainability, right?… If
you’re choosing food containers… those should be compostable or reusable
plates or whatever, as opposed to lots of plastic garbage.” This participant
advocated for “easy choices for environmentalism,” which can include reducing
food waste, not printing out conference programs, or excluding meat-based food
options [33]. We agree that these are good choices, but we argue that now is
the time for difficult choices. Should we exchange how enjoyable the
conference is or limit in-person networking to make VIS more sustainable?
Should we dedicate resources to have a less ecologically harmful conference?

Figure 3: Speculative rankings for several conference formats on various
logistical considerations. Some rankings are more uncertain than others:
hybrid may be more or less environmentally sustainable depending on location
and virtual attendance.

##  3 Discussion

Next, we consider alternatives to the single-venue global meeting status quo.
The pandemic prompted a natural experiment in which three different formats
were explored (remote at VIS20, regional satellites at VIS21, and hybrid at
VIS22), each of which come with competing trade-offs. We sketch these trade-
offs in Fig. 3.

Remote conferences. One of the most extreme approaches to reducing our carbon
footprint would be to switch to an entirely online format. Without taking a
formal poll, we expect that this might be unpopular. One participant went so
far as to say, “I’m not going to participate in the virtual conferences.” The
remote option leaves no opportunity for in-person networking, and many feel
like they are less engaging than in-person conferences. Many attendees did not
feel driven (or were unable) to block off the time to become immersed in the
conference in the way in-person conferences demand. One participant said, “I
still think we haven’t found a replacement for on site or co-located
networking that is satisfying.” But, a more radical reorganization of a remote
conference could be explored, such as at Info+ 2021’s, wherein presenter
videos were posted to the open internet prior to the conference and then
conference time was used for extended discussions.

Remote conferences are substantially more accessible and equitable than in-
person events. Those who cannot afford or get visas to attend would not be
excluded by their circumstances. Attending an in-person conference can be
prohibitively expensive for academics from lower-income countries and industry
practitioners who do not have job-provided funding to attend. Remote (and
hybrid) formats are also friendlier to immunocompromised attendees. One
participant mentioned, “there’s plenty of academics that have told the VEC
that they’re not willing to travel to conferences now, because they don’t want
to risk their health.” A remote conference would also cut costs, as renting
space, filling hotels, and feeding attendees would no longer be concerns.
Finally, being remote would be the most effective at reducing our carbon
footprint, as travel and hosting carbon costs would be essentially eliminated.

Hybrid conferences. Hybrid offers compromise formats between virtual and
physical. These typically (at VIS22, CHI21, and others) involve a smaller
physical conference for in-person attendees and a Discord server with video
streaming for remote attendees. Hybrid options would seem to offer the best of
both worlds, but this can leave those online supported only superficially
while magnifying the cost and logistic burden of the conference for the
organizers.

Hybrid formats were divisive. One participant did not like the hybrid format,
saying “we haven’t got the technology right yet to make it a good experience
for everybody.” Another participant had quite the opposite feeling about
hybrid, saying that VIS22 was “a huge success” and “in my view,… probably one
of the best conferences.” Similarly, in personal communications, we have heard
from those on the virtual end of that hybrid both that it was wonderful and
that it was disastrous. Perhaps this is an area where more software innovation
is needed444Some non-academic conferences have successfully explored mediums
beyond the _pandemic standard_ of Zoom + Discord + Gathertown. For instance,
the indie-games conference Roguelike Celebration [24] matched the ostensible
theme of the venue by presenting the conference in a multi-user dungeon or
MUD. MUDs are an early form of virtual world whose retro origins are similar
to the game Rogue, from which Roguelike Celebration gets its name. While far
from becoming a conventional approach, it shows that there is more space yet
to explore., however it may also be necessary to rethink conference
organization (such as is being explored by ICER [20]).

Hybrid also necessitates substantial extra labor compared to physical or
remote. One participant highlighted the volunteer burden: “it’s hard to find a
general chair, and if you want to add a hybrid option. Now, I’m basically
asking you as the general chair to run 2 conferences.” Furthermore, hybrid
options cost more than completely in-person or completely remote experiences.
The reduction in conference emissions depends on how many people opt to attend
virtually compared to in-person. A hybrid conference with few virtual
attendees may not be more environmentally friendly than just having a single
global meeting.

Regional conferences. An alternative compromise to a single global location is
to have regional or satellite conferences (also known as multi-hub conferences
[30]). VIS21 orchestrated 8 informal regional events to accompany an
overarching virtual edition.555However, these were quite unevenly distributed.
For instance, the state of Illinois had two events (in Chicago and Urbana)
while the entirety of Europe had two (in Norrköping and Copenhagen). One
participant said their experience attending a satellite event “was good. It
was a nice event, but I think it could be more formalized.” One approach would
be to have 2–5 official locations around the world without having one central
location—an idea which has also been explored by the American Association for
Geographers (AAG) [2]. Regional conferences have proved to worked well, with
FOSS4G:UK Local 2022 hosting regional events across nine venues, which was so
well-received by the participants that they are planning on continuing the
same format for 2023 [29]. Regional events make it more feasible for people to
travel semi-locally and still enjoy the in-person experience, however this
limits networking to the people in your regional area.

Complicating matters is that more locations would require even more volunteers
to operate. One participant mentioned this as a factor in VIS21, that “they
were up to volunteers to start”, while another participant saw it as a major
obstacle for this format. Another participant noted that “it’s too much work.
Somebody’s got to organize that and who’s gonna want to organize an event that
is just a watching party?” This view of a ‘watching party’ may be overly
specific to the VIS21 satellite model, however this is far from the only
conceivable method of regionalization. Like FOSS4G:UK Local 2022, a regional
conference could be a combination of streamed content and locally in-person
content. Like Info+ 2021, in-person aspects of the conference could focus more
on conversations and discussions. Incentives other than tenure service
requirements may be useful for prompting OC-participation (or just
alternatives for those not on the tenure-track)—such as awards or money. Some
sticks may usefully match such carrots: analogous to Ko’s [21] sustainable
reviewing marketplace proposal (in which authors cannot submit papers if they
have not done a corresponding amount of reviewing), service requirements could
be placed on institutions to balance their usage of community resources. There
are many open questions about the logistics. For instance, how would time
zones be navigated? One participant suggested a schedule similar to the hybrid
“Outlier Conference,” which ran from 9am to 1am local time to accommodate
other locales. How would spreading out VIS’s financial “tight margins” to
multiple locations work? What do “legal obligations” like insurance look like
for satellites? Would organizing bodies like IEEE still support the logistics,
overhead, and risk of such a reorganization? Would this negatively silo
regional communities?

An alternative cadence. One idea that has emerged in other conferences
(particularly CHI [35]) is to limit, but not stop, the rate at which we hold
international conferences. In particular, the conference cadence could involve
an international “full” VIS every three years, while the other two years would
be coordinated regional events (or online events [7]). One participant also
mentioned this idea, suggesting a global conference “every N numbers of years…
it becomes almost like an Olympics, like every 4 years, you have a big event,
and in between you have several almost like qualifying type of events.” In
this model, presenters in the ‘non-global years’ could be invited to share
their work as a poster presentation in person at the global event. Our
participant noted that UIST has implemented something similar this year (as
has PLDI [9]), by inviting presenters who presented their work virtually in
the past three years to present again as a poster. Such a cadence could be
matched with the length of a typical Ph.D. program to allow every student the
opportunity to present their work at one global conference. We could consider
a timeline of every 3 years, to account for shorter Ph.D programs (such as in
the UK), compared to longer Ph.D programs (such as in the US). This timeline
could still disadvantage students without a paper ready in their first year,
but could be worked around through low stakes submission formats like first
year consortium’s.

(At least briefly) Consider the environmental impact of site selection.
Finding and selecting a venue for an international conference is an obviously
difficult and technical process full of complex moving pieces. Still, the
environmental impact of the site could be a more central consideration in the
decision-making process for VIS. Additionally, VIS could publish the factors
that go into the decision-making process for site selection, similar to CHI
[26].

However, optimizing location for emissions may negatively affect global
equity. Hosting VIS23 in Australia will likely bring local participants that
would not have joined North America-based events. Similarly: “If you look at
Berlin and then look at let’s say 2017 in Phoenix, you’ll see a big shift
between Europeans and Americans.” One participant contrasted optimized
locations with accessibility, noting that if we “make the conference central
to the majority of participants” by minimizing travel distance, we impede “the
people with limited travel budgets, [who] lose accessibility to attend the in-
person part.” One option that we could consider is to provide travel grants
for academics that live in locations disadvantaged by site selection. Offering
these travel grants might increase the amount of carbon emissions, but the
goal is to view sustainability holistically among all considerations. In this
way, we are increasing equity for geographical diversity, while still hosting
the conference in a place that minimizes travel distance for most other
attendees, and thus overall lowering the total carbon emissions. No matter
where or how we decide to host VIS, there seems to be no universal winning
strategy for this “multi-pronged objective function”.

Drastic Measures. A more drastic solution might be to decouple publishing from
conferences, so that attendees are not pushed across the globe on a clockwork
cadence to present their work, but rather can present when ready at global
venues (like VIS) or more local venues (like EuroVIS or PacificVIS). This
could be supported by a stronger embrace of the journal-style publishing found
in every other scientific field, rather than our current conference
style666While venues like TVCG and JOVI exist, subjectively, they are not the
primary way in which visualization papers are published.. Decoupling
publications from conferences would allow researchers to publish papers
without requiring them to also physically travel to present their work in-
person. Some recent initiatives (such as that of SIGCOMM [8]) explore this
idea, however it has yet to reach the mainstream. An even more avant-garde
proposal explores removing the synchronous component of the conference
entirely by mediating presentations through the mail in the form of zines
[31].

Other Opportunities for Sustainability. Interest in sustainability and
environmental concerns has not been seen as essential to VIS organizing. One
faulty measure to this end, is that in the years since VEC/VSC became elected
positions, only one candidate has made any allusion to sustainability in their
bios and statements. It may be useful to form a sustainability committee as
part of the VIS OC, so as to give environmental sustainability a seat at the
table. This would be akin to the recently added Open Practices chairs. Similar
organizing bodies are present at other venues (e.g., CHI and UIST).

Reviewers of this paper questioned why conference sustainability
considerations are presented as an alt.vis paper rather than a meetup, (as one
participant suggested) a VIS panel discussion, a question at the VIS town
hall, or a Visualization for Social Good paper. We believe that these forms of
engagement would be welcome and likely useful. We focused on this venue
because we wanted to reach a broader swath of the community than those who
might opt in to attending a more sustainability-focused event (as those
attending such an event are likely to already think sustainability is
valuable)—although we recognize that this venue has its own selection biases.

Several participants compared VIS to other conferences, sometimes pointing out
how much bigger they are, or their offerings and formats. In interviews, VIS’s
small size was seen as a downside, leaving us with fewer volunteers, and the
feeling that our actions are only a drop in the bucket. We suggest that rather
than making our actions inconsequential, it allows us to be nimble and able to
explore new formats more easily. Just as we compare ourselves to others,
others look to us. If we make an effort to lower our emissions, we can be an
example and an inspiration for other communities.

Another means of decreasing the size of our footprint is via carbon offsets.
These offsets are ostensibly a way to purchase “negative” carbon emissions,
such as by funding systems that capture carbon (e.g., forests).777 As noted
above, flying from Seattle to Melbourne generates about 2.7 tons of CO2 [22].
To capture that much carbon, one must grow around 110 trees for a year
(notably, to be effective those trees need must not have already been growing
[38]). To “offset” the carbon emissions for the next full pre-pandemic size
VIS, we must plant approximately 130k trees for a year [10]. This is about a
fifth of the trees in New York City [28]. There is some nuance here: carbon
offsets are known to sometimes be ineffective [4, 38] and increase the
financial cost of the conference, but at least they would be more than
nothing888The well-known mantra reduce-reuse-recycle is commonly misunderstood
[1] as putting recycling on an equal foot with use reduction and the reuse of
extant goods, when in fact, it is a hierarchy where reducing is more effective
than reusing, which is more effective than recycling. We suggest that offsets
have a similarly tertiary place in a different hierarchy: Offload (don’t do
things that aren’t necessary), Optimize (make them less resource intensive as
possible), and Offset (pay your way out of having done them). . We suggest
that, at a bare minimum, VIS could include offsets as part of conference
registration. There exists precedence to this effect: ACM [3] has begun
pushing its conferences to include a means for attendees to purchase offsets
as part of registration.

##  4 Conclusion

Many of these observations have been made before [25, 5, 41], but we use this
paper to bring the discussion to our community. The best time to make VIS
sustainable was 20 years ago. The second best time is now. We recognize that a
lot of us have taken a lot of flights in our lives to publish our work and
advance our careers. Rather than focus on our past decisions, we can push our
community to take sustainable steps forward. Our world is crumbling into
rising oceans and forest wildfires. But there is hope: it has not crumbled
yet. Pandemic-era innovations illuminated ways for us to be more sustainable,
but we are slowly slinking back to the status quo of in-person conferences. As
a community, we can choose not to forget these lessons, we can embrace
environmental sustainability as a value, and work towards making VIS more
sustainable.

##  5 Acknowledgments

Thank you to Eytan Adar, Cliff Lampe, Kentaro Toyama, and all of our VEC and
VSC participants for sharing their thoughts on conference organizing.

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##  Appendix A Interview instrument

Here we provide the questions involved in our interview. A pdf of the specific
Qualtrics form used is available at osf.io/u2eps/.

  1. 1.

How many times have you attended the VIS conference (approximately)?

  2. 2.

How many times have you helped with organizing the VIS conference?

  3. 3.

Please rank the following items by how important they are when planning the
logistical aspects of the VIS conference.

     * •

The event should be financially responsible.

     * •

The event should be accessible for people with disabilities.

     * •

The event should allow for networking opportunities and support professional
connections.

     * •

The event should be an enjoyable and engaging conference experience.

     * •

The event should be sustainable and environmentally friendly.

     * •

The event should support diversity and inclusion.

  4. 4.

What are other logistical considerations for planning VIS that are important
to you? (Verbal response)

  5. 5.

Please explain why you ranked those items in that way (verbal response).

  6. 6.

The carbon footprint of an academic conference is (multiple choice)

     * •

Immense

     * •

Large

     * •

Medium

     * •

Small

     * •

Tiny

  7. 7.

Please explain your previous answer (verbal response).

  8. 8.

Please rate your agreement with the following statement: VIS has a
responsibility to be a sustainable conference

     * •

Strongly disagree

     * •

Disagree

     * •

Slightly disagree

     * •

Neither agree nor disagree

     * •

Slightly agree

     * •

Agree

     * •

Strongly agree

  9. 9.

Please explain your reasoning for the previous question (verbal response).

  10. 10.

Is there anything else that you wanted to mention? (verbal response)


  * May 2023

# Efficient cooling of high-angular-momentum atoms

Logan E. Hillberry1, Dmitry Budker2,3, Simon M. Rochester4, Mark G. Raizen1 1
Department of Physics, The University of Texas at Austin, Austin, Texas,
78712, USA  2Johannes Gutenberg-Universität Mainz, Helmholtz-Institut Mainz,
GSI Helmholtzzentrum für Schwerionenforschung, 55128 Mainz, Germany  3
Department of Physics, University of California, Berkeley, California 94720,
USA  4Rochester Scientific, LLC, El Cerrito, California 94530, USA
<EMAIL_ADDRESS>
###### Abstract

We propose a highly efficient and fast method of translational cooling for
high-angular-momentum atoms. Optical pumping and stimulated transitions,
combined with magnetic forces, can be used to compress phase-space density,
and the efficiency of each compression step increases with the angular
momentum. Entropy is removed by spontaneously emitted photons, and particle
number is conserved. This method may be an attractive alternative to
evaporative cooling of atoms and possibly molecules in order to produce
quantum degenerate gases.

††: J. Phys. B: At. Mol. Opt. Phys.

Keywords: atomic physics, cold atoms, phase-space compression

##  1 Introduction

Laser cooling, first proposed almost half a century ago, remains the standard
approach for producing ultracold atoms [1, 2]. This method relies on momentum
transfer from light to atoms as photons are repeatedly scattered, enabling the
production and study of ultracold atomic gases. Many improvements on basic
laser cooling have advanced the state of the art, including sub-Doppler
Sisyphus cooling [3, 4, 5, 6, 7], and sub-recoil degenerate Raman sideband
cooling cooling [8, 9].

While laser cooling works extremely well, the requirement of a closed, two-
level transition has limited the applicability of the method to a subset of
elements in the periodic table. For those atoms, after many years of
refinement, laser cooling has reached saturation in its performance due to
multiple scattering of resonant photons which create an effective repulsive
interaction between the atoms, pushing them apart. An important figure-of-
merit is the phase-space density, a dimensionless parameter which is the
product of number density and the third power of the average de Broglie
wavelength. Laser cooling typically produces a phase-space density of 10-6.
This is also the starting point for creating quantum degenerate gasses with
order-unity phase-space density through evaporative cooling in a trap [10,
11], and the creation of the so-called atom laser [12, 13, 14]. Evaporative
cooling is even more restrictive than laser cooling, as it relies on elastic
collisions between atoms to maintain thermal equilibrium as the hottest atoms
are ejected. Inelastic channels create unwanted losses and often make
evaporative cooling impossible. Even when working optimally, evaporative
cooling is a slow process and results in a significant loss of atom number.

Figure 1: A schematic depiction of the MOP-cooling sequence for ensembles with
angular momentum $J=1$. The colored circles represent atoms, initially trapped
in a flat, hard-wall potential. The colors represent the atom’s magnetic state
(orange: $m_{J}=-1$, purple: $m_{J}=0$, teal: $m_{J}=+1$). A cycle begins with
optically pumping all atoms to the same state. Then, a sequence of stimulated
transitions correlate the magnetic states with position along the direction of
compression. A sequence of one-dimensional magnetic kicks pushes atoms of
oppositely-signed magnetic states together. The cycle is closed by optically
pumping the compressed atoms back into the same magnetic state. A cycle’s
compression factor increases with the number of available magnetic states.

In recent years, alternative approaches to producing cold atoms and molecules
were developed (see [15] and references therein). The starting point for much
of this work is a supersonic molecular beam where desired atoms or molecules
can be entrained in the flow and stopped in a series of pulsed magnetic or
electric fields. Alternatively, cold atoms and molecules are produced by
buffer-gas cooling [16]. After stopping, these atoms and molecules can be
trapped, typically in a magnetic field configuration that confines the low-
field seekers to the center of the trap. In parallel, cooling of atoms with a
one-way wall was proposed and demonstrated [17, 18, 19], and relies on photon
entropy, not momentum as in laser cooling. The one-way wall is the first
practical realization of Maxwell’s demon for an ensemble of atoms. While one-
way-wall cooling demonstrated a large increase in phase-space density, it did
not conserve atom number. To address this limitation, we proposed [20] a
variation which we called magneto-optical (MOP) cooling, relying on cycles of
state preparation and magnetic kicks.

In this paper, we present a generalized and highly efficient version of MOP
cooling that can work for high-angular-momentum atoms and offers an attractive
alternative to laser cooling and evaporative cooling. Quantum gases of atoms
with high angular momentum have become of increasing scientific interest over
the last 20 years [21] making our method timely and relevant to a growing
community. As depicted schematically in Fig. 1, and described in detail below,
the larger internal-state space of high-angular-momentum atoms may be
leveraged to yield a greater compression of an ensemble in real space. This is
in contrast to our original proposal [20] that focused on spin-1/2 systems.
Our method will help bridge the existing gap of approximately six orders of
magnitude between the phase-space density limits of standard sub-Doppler
cooling and evaporative cooling, thereby promising larger ultracold samples.

In the following section, our simulation methodology is described, followed by
a brief review of MOP cooling for a spin-1/2 system. Then MOP cooling is
generalized for high-angular-momentum atoms. We conclude the paper with a
discussion of possible limitations to our new method, how those limitations
may be overcome, and the significance of MOP cooling in the atomic physics
toolbox. The subsequent appendix presents a one-dimensional model of MOP
cooling as an alternative to the detailed simulations that follow.

##  2 MOP cooling

MOP cooling is a conceptually new method that does not rely on the momentum of
the photon, making it completely different from laser cooling. The key benefit
of this approach is its universality and simplicity, since it relies only on
internal magnetic state preparation and magnetic forces from pulsed coils. MOP
cooling may be interpreted as a technique that transforms the cooling of
internal degrees of freedom via optical pumping [22] to external degrees of
freedom. Through numeric simulations, we will evaluate the efficacy of MOP
cooling for atoms with different numbers of internal states.

Our MOP-cooling simulations track the three-dimensional positions ${\bf x}$,
velocities ${\bf v}$, and magnetic states $m_{J}\in\\{-2J,-2J+1,\ldots,2J\\}$
of a sample of $N=10^{5}$ atoms, each with total angular-momentum quantum
number $J$. The internal magnetic state of each atom is initialized in
accordance with the MOP-cooling cycle (discussed further below). Positions are
initialized from a flat distribution of a 0.5 cm width. Velocities are
initialized from the Maxwell-Boltzmann distribution corresponding to a
temperature of $25\times T_{\rm rec}$ where $T_{\rm rec}=h^{2}/Mk_{\rm
B}\lambda^{2}$ is the recoil temperature imposed by, e.g., a magneto-optical
trap operating at wavelength $\lambda$ to trap a species of mass $M$. Here,
$h$ is Planck’s constant and $k_{\rm B}$ is Boltzmann’s constant.

A fourth-order Runge-Kutta algorithm updates the position and velocity of each
atom subject to the force ${\bf F}(t)=-m_{J}g_{J}\mu_{\rm B}\nabla\left|{\bf
B}({\bf x},t)\right|$ where $g_{J}$ is the Landé $g$-factor of the atom’s
ground state, $\mu_{\rm B}$ is the Bohr magneton, and ${\bf B}$ is the pulsed
magnetic field arranged to provide the one-dimensional kick. The simulation
time step is one microsecond. Table 1 reports the atomic properties used in
this study.

Table 1: Atomic properties used for simulation purposes. The Ref. column provides an example of magneto-optical trap operation for each species with a corresponding recoil temperature $T_{\rm rec}$. Values for $g_{J}$ are provided in [23], except for Li for which we adopt the electron’s value. Atom | $M$ | $J$ | $g_{J}$ | $T_{\rm rec}$ | Ref.
---|---|---|---|---|---
($10^{-26}$ kg) | $({\rm\upmu K})$
Li | $1.15$ | 1/2 | $2.002\,32$ | $6.1$ | [24]
Cr | $8.63$ | 3 | $2.001\,83$ | $2.0$ | [25]
Er | $27.83$ | 6 | $1.163\,81$ | $0.3$ | [26]
Dy | $26.98$ | 8 | $1.241\,59$ | $0.3$ | [27]

The magnetic field is modeled as two sets of coaxial coil pairs, one in the
Maxwell configuration to provide a strong gradient [28] and the other in the
Helmholtz configuration to shift the zero-crossing of the field away from the
ensemble’s center, thereby providing a nearly-one-dimensional kick. We use
superposition of the exact solution for a current-carrying loop to model the
full coil geometry. ${\bf B}$ is evaluated on a dense grid for unit current.
Vector interpolation allows us to evaluate $\nabla\left|{\bf B}({\bf
x})\right|$ at arbitrary positions. Time-dependent current pulses are modeled
by scaling the field gradient interpolation result by
$I(t)=I_{0}\sin[\pi(t-t_{0})/\tau]$ for $t\in[t_{0},t_{0}+\tau]$ and $I(t)=0$
otherwise, where $I_{0}$ is the peak current, $t_{0}$ is the pulse delay, and
$\tau$ is the pulse width. In this paper, we set $\tau=300~{}{\rm\upmu s}$.

The simulated coil parameters are as follows. There are 7 turns $\times$ 2
layers, or 14 loops per Helmholtz coil, each with a nominal radius of $R_{\rm
HH}=3.5\,\rm{cm}$, axially-separated by $R_{\rm HH}$, and carrying
identically-oriented currents . There are 5 turns $\times$ 2 layers, or 10
loops per Maxwell coil, each with a nominal radius of $R_{\rm HH}/\sqrt{3}$,
separated by $R_{\rm HH}$, and carrying oppositely-oriented currents. The peak
currents are $I_{0,{\rm HH}}=1000$ A for the Helmholtz coils and $I_{0,{\rm
M}}=800$ A for the Maxwell coils. The shared midpoint between the coil pairs
is displaced by 0.2 cm in the positive $z$-direction from the initial center
of mass of the atomic sample (taken as the origin of the coordinate system).
We find that this region provides a more uniform and one-dimensional kick.
With these coil parameters, the peak field gradients are approximately 1520
G/cm along the kick direction and 45 G/cm in the transverse directions. Two-
dimensional slices of the magnetic field gradient used in our simulations are
shown in Figure 2.

Figure 2: Two-dimensional slices of the magnetic field gradient used for MOP
cooling simulations, evaluated at peak current, and shown (a) transverse-to
and (b) along the kicking direction. The black-and-white dashed line marks the
initial extent of the atomic cloud. The magnitude of the total field $|{\bf
B}|$ varies primarily along $z$ in a nearly-linear fashion.  Figure 3:  MOP
cooling simulations for Li (a-d) and Dy (e-h) visualized in phase-space. Each
column of plots represents a snapshot during the magnetic kicks required for a
cycle. Initially, the magnetic states are correlated with position along the
$z$-axis through optical pumping followed by spatially-resolved coherent
population transfer via stimulated transitions. The vertical dashed black
lines in panels (a) and (e) mark the ideal boundary between different magnetic
states. In panels (b) and (f), a one-dimensional magnetic kick accelerates
atoms to a velocity that is proportional to their magnetic state. After
waiting an optimized delay time the phase-space distribution has been
compressed in real space but remains extended in velocity space, as shown in
panels (c) and (g). In panels (d) and (f), we show a reverse kick returning
the atom’s velocity distribution to near its original extent while preserving
the spatial compression. More precisely, we find the relative difference
between standard deviations of the ensembles’ initial and final velocity
distribution is below 0.2% for all coordinates and all four species simulated.

For a specific example, consider atomic lithium (Li) trapped using standard
techniques [24]. At sufficient magnetic fields, the electronic spin decouples
from the nuclear spin yielding a total angular momentum of $J=1/2$; the two
electronic $m_{J}$ states are denoted $\left|1/2\right\rangle$ and
$\left|-1/2\right\rangle$ and it is in this high-field regime that Li may be
MOP-cooled as originally discussed in [20]. The cooling sequence starts with
suddenly turning off the trap so that the atoms are free. In step (1) of MOP
cooling, all of the atoms are optically pumped to the $\left|1/2\right\rangle$
state. Then, half of the cloud is transferred to the $\left|-1/2\right\rangle$
state by stimulated transitions, i.e., stimulated Raman adiabatic passage
(STIRAP) sequences [29, 30], thereby creating two spatially-distinct
populations [see Fig. 3 (a)]. In step (2), a magnetic-field-gradient kick is
applied to the cloud, thereby causing the two halves to merge [Fig. 3 (b-c)],
and then a reverse kick returns the atoms to their original velocity
distribution [Fig. 3 (d)]. As demonstrated experimentally in [31], such
magnetic kicks can be applied along a single axis while minimally affecting
the other two dimensions. In step (3), all atoms are optically-pumped back to
the $\left|1/2\right\rangle$ state, thereby completing the cooling cycle. In
principle, a factor of $2\times$ in phase-space compression is possible.

Figure 4: Optimizing the wait time between the MOP cooling kick and unkick
according to the compression factor. The open circle marks the optimal delay
time for each species subject to the initial conditions and magnetic forces
described in the text. The inset shows the peak compression factor vs the
species’ angular momentum $J$, compared to the geometric limit $2J+1$ (black
line).

We now generalize the method to a system with an arbitrary total angular
momentum $J$. There are $2J+1$ states in this case, and we assume that the
atoms are trapped in a hard-walled flat potential. Just as in the case of Li
above, we turn off the trap to start the cooling sequence. Using optical
pumping and stimulated transitions in step (1), the cloud is divided into
$2J+1$ equally-sized components, where the leftmost section is prepared in
state $\left|J,-J\right\rangle$, then $\left|J,-J+1\right\rangle$, and so on,
to the rightmost section in state $\left|J,J\right\rangle$. In step (2), a
magnetic field gradient kick is applied to the cloud, causing each sub-section
to move at a velocity that is proportional to its distance from the center-
plane. Thus, the stretched states $\left|J,\pm J\right\rangle$ will move the
fastest towards the center, and lower magnetic-quantum-numbered sections will
move slower. The cloud will collapse to a single section after an optimal
delay time, and a reverse magnetic kick will restore the original velocity
distributions. Finally, in step (3), all atoms are optically pumped to the
$\left|J,J\right\rangle$ state, and the cloud can be re-trapped. Ideally, the
cloud has been compressed by a factor of $2J+1$.

Figures 3 (e \- h) show snapshots of the simulated phase-space for MOP cooling
of Dy atoms ($J=8$) after state preparation (step 1) and during magnetic
kicking (step 2). Comparing the final spatial distribution of Li [Fig. 3 (d)]
to that of Dy [Fig. 3 (h)] clearly demonstrates how MOP cooling may leverage
high-angular-momentum atoms for efficient phase-space compression.

The delay time between kicks is optimized in our numeric simulations and the
results are shown for a variety of atoms in Fig. 4. As a figure of merit, we
compute the compression factor as the ratio of standard deviations between the
initial and final $z$-coordinate distributions of the cloud. The inset of Fig.
4 shows the peak compression factor for each species is bound by the geometric
limit $2J+1$. In the following section we consider some limitations of MOP
cooling and how they may be overcome in an experiment.

##  3 Discussion

In MOP cooling, a maximum compression factor of $2J+1$ per cycle may be
approached. However, in practice, the efficiency will be lower due to thermal
expansion, deviations from a flat density distribution, imperfect kicking
fields, and photon-recoil heating during the optical pumping stage.

To better understand the influence of thermal expansion and the initial
density profile, we have developed a one-dimensional analytic model of MOP
cooling that is reported in the Appendix. A few key conclusions derived from
our model are now summarized. While the MOP cooling sequence progresses, the
atomic ensemble’s initial standard deviation $\sigma_{0}$ grows according to
$\sigma(t)=\sqrt{\sigma_{0}^{2}+t^{2}v_{\rm th}^{2}}$ where $v_{\rm
th}=\sqrt{k_{\rm B}T/M}$ is the thermal velocity. Thus, after a MOP cooling
sequence, the ensemble has collapsed to a single section, but the sections
have grown from their initial size. The total time for one sequence is
$t_{0}+\tau$ and for simplicity let us assume $t_{0}\gg 2\tau$, i.e. the delay
time between kicks is much longer than the kicks’ combined pulse length.
Additionally, a flat distribution of width $2s$ has a standard deviation
$\sigma=2s/\sqrt{12}$, so the thermally-limited compression factor is
approximately $(2J+1)/\sqrt{1+12v_{\rm th}^{2}/\Delta v^{2}}$ where $\Delta
v=2g_{J}\mu_{\rm B}G\tau/M\pi$ is the relative kick velocity of adjacent
sections and $G$ is the peak field gradient. Thus, the geometric limit $2J+1$
is only achieved for $\Delta v\gg\sqrt{12}v_{\rm th}$.

The flat-density initial condition is quite different from that usually
encountered with laser cooled atoms in a magneto-optical trap, but turns out
to be important for the gains in efficiency that are predicted (details in the
Appendix). For example, we predict a compression factor of 1.8 for Li
initialized with with a flat density or 1.5 for a Gaussian distribution. For
Dy initialized with a flat density, a peak compression factor of 14.4 is
observed, while for an initially-Gaussian distribution the factor reduces to
8.6. To obtain a flat “boxlike” distribution in an experiment, the atoms can
first be confined in a magnetic quadrupole trap. An optical box can be created
around the atoms using a time-averaged optical dipole potential from beams
that are moving rapidly in two dimensions. Such potentials were created in the
past to study optical billiards [32, 33] and BECs in painted potentials [34].
After trapping, the box can be adiabatically expanded in three dimensions to a
desired size, which will result in a nearly flat density profile of atoms. The
optical setup for state preparation of each segment would enable multiple
cycles of cooling in each dimension. Adiabatic expansion would lower the
kinetic energy and MOP cooling would compress the cloud spatially. The process
can be dynamically controlled with motorized zoom lenses [35].

Ideally, a complete cycle of MOP cooling leaves the velocity distribution of
the atomic sample unchanged. This means that the momentum imparted on the
atoms in the kick phase must be nulled in the reverse-kick phase.
Inhomogeneities in the kicking field will result in a nonzero mean velocity
for the cloud. Such inhomogeneities are noticeable in Fig. 2 (b) that shows
the peak magnetic field gradient in the $x=0$ plane. For instance, atoms near
$z=0.25$ will be kicked downward with slightly less force than their upward
motion-arresting kick that is applied once they are near $z=0$. Our
simulations suggest this effect is negligible for the chosen field and cloud
parameters, but it becomes relevant for larger clouds or less uniform field
gradients. Moreover, there exist advanced wiring-design-optimization
techniques to generate uniform bias or gradient fields with minimal inductance
[36, 28]. Though originally developed for magnetic resonance imaging, MOP
cooling could benefit from such analyses to improve switching times of the
pulsed magnetic fields and increase the uniformity of the required biased
gradients, thereby enabling MOP cooling of larger ensembles. A possibly more
significant mean velocity is incurred due to free fall in the Earth’s
gravitational field. For example, in the $\sim 3.5$ ms of delay time required
for MOP cooling of Cr, the cloud accelerates to nearly 3.5 cm/s and displaces
0.67 mm. Such velocities and displacements are within typical capture ranges
of atomic traps, though some loss upon re-trapping should be expected. To
mitigate the free fall effects, one could use the MOP cooling setup to apply
an additional uniform kicks against gravity.

In general, optically pumping the cloud to the same magnetic state is a lossy
step due to, for instance, atoms decaying to unobserved trap states.
Fortunately, there exist efficient techniques for optical pumping as discussed
in [37], where it is shown that it is possible to perform optical pumping with
only one spontaneous photon emitted per atom. The same physics lets us
understand MOP cooling’s high phase-space compression efficiency in terms of
the photon entropy carried away from the ensemble by spontaneous emission
[38].

The entropy associated with the motional degrees of freedom is given by
$S_{\rm mo.}=k_{\rm B}\ln(V/V_{\rm Q})$, where $V$ is the phase-space volume
and $V_{\rm Q}$ is a reference volume. The ensemble’s volume is reduced by a
factor of (at most) $2J+1$ at each cooling step, so the maximum entropy
reduction per step is $\Delta S_{\rm mo.}=k_{\rm B}\ln{(2J+1)}$. The magnetic
kicks are reversible evolution, so they do not produce a net change in
entropy. Therefore the entropy change must occur during the optical pumping
step. Optical pumping of an unpolarized ensemble to produce a pure state
reduces the polarization entropy by $\Delta S_{\text{pol.}}=k_{\rm
B}\ln{(2J+1)}$. Thus for each step, (1) optical pumping takes unpolarized
state to pure state, reducing polarization entropy by $k_{\rm B}\ln{(2J+1)}$;
(2) magnetic kicks take the pure state to an unpolarized one by overlapping
the sub-ensembles, increasing polarization entropy by $k_{\rm B}\ln{(2J+1)}$
and reducing motional entropy by the same amount. The cooling must ultimately
be limited by recoil heating. If single-photon optical pumping efficiency is
achieved and spatial compression converted to temperature reduction through
adiabatic expansion, the temperature limit will correspond to the recoil
temperature $T_{\rm rec}$. For less efficient optical pumping the temperature
limit will be higher.

The conceptual significance of MOP cooling is two-fold. First, in species that
have already reached quantum degeneracy with the aid of laser cooling, MOP
cooling can reduce losses induced by the typical final step of evaporation.
Alternative all-optical approaches have produced degenerate ${}^{87}{\rm Rb}$
samples while avoiding evaporation: Raman cooling in combination with either
optical compression cycles [39] or far-off-resonant optical pumping [40] have
reached degeneracy within 300 ms or 1.4 s, respectively. The present
simulations predict that a single cycle of MOP cooling for Dy will compress
the extent of the ensemble along one dimension by a factor of 14.4 within just
3 ms. This compression increases the number density, and therefore also the
phase-space density, by the same factor. Hence, if initially laser cooled to a
phase-space density of $\sim 10^{-6}$, MOP cooling may bring Dy to degeneracy
within six cycles or about 20 ms. Second, in species lacking a sufficiently-
closed two-level cycling transition, MOP cooling provides an alternative
technique that only requires optical pumping, coherent population transfer,
and pulsed magnetic fields. Here, we have shown that the efficiency of MOP
cooling can be increased by leveraging larger internal state spaces.
Therefore, a particularly enticing possibility for future work is the
application of MOP cooling to ultracold molecules [41, 42]. A rich internal-
state structure makes laser cooling prohibitively challenging for most, though
not all [43], molecular species. On the other hand, molecules may be cooled
quite generally to the single-kelvin regime via buffer-gas collisions or
supersonic expansion [16], and perhaps MOP cooling could push molecular
ensembles to yet-higher phase-space densities.

##  4 Conclusion

In this paper, we proposed a highly efficient method for phase-space
compression of high-angular-momentum atoms. This work extends an earlier MOP-
cooling proposal from Li to general high-angular-momentum atoms. We
numerically tested our new MOP-cooling protocol on four atomic species of
increasing angular momenta that have each already been cooled using
traditional techniques. We find, for example, an impressive compression factor
of 14.4 is conceivably attainable in less than 3 ms for the case of Dy.

The work of MGR was supported by the Sid W. Richardson Foundation. The work of
DB was supported by the Deutsche Forschungsgemeinschaft (DFG) - Project ID
423116110 and by the Cluster of Excellence Precision Physics, Fundamental
Interactions, and Structure of Matter (PRISMA+ EXC 2118/1) funded by the DFG
within the German Excellence Strategy (Project ID 39083149).

## Appendix: One-dimensional model

In this appendix, we develop a one-dimensional model for MOP cooling. We
consider the compression limits imposed by 1) geometry of the initial spatial
distribution of atoms and 2) thermal free expansion during the required time-
of-flight to complete a MOP cooling cycle. To this end, we begin with the more
complicated case of an initially-Gaussian spatial distribution. Ignoring free
expansion, we determine an optimal partitioning scheme that splits the initial
distribution into $2J+1$ sections. Then, we consider how the shape of each
Gaussian partition changes over the time of flight required to merge the
sections. Finally, we repeat the analysis for an initially flat distribution.

###  A.1 General setup

Consider a one-dimensional, classical, non-interacting gas composed of a
constant number of atoms with mass $M$ trapped in a potential $V(x)$ and in
thermal equilibrium at temperature $T$. The energy of an atom is
$Mv^{2}/2+V(x)$ when it is at position $x$ with velocity $v$. The probability
for an atom to be found in the phasespace area $(x+dx)\times(v+dv)$ is
$\rho(x,v)dxdv$ where the probability density is given by the Boltzmann factor

$\rho(x,v)=\rho_{0}e^{-[Mv^{2}/2+V(x)]/k_{\rm B}T},$ (1)

where the constant $\rho_{0}$ normalizes the density such that it integrates
to unity. Therefore, the real-space probability density is given by the
marginal

$\mathcal{P}(x)=\int_{-\infty}^{\infty}{\rm d}v\rho(x,v)=\rho_{0}\sqrt{2\pi
v_{\rm th}^{2}}e^{-V(x)/k_{\rm B}T},$ (2)

where we have defined the thermal velocity $v_{\rm th}=\sqrt{k_{\rm B}T/M}$.

In MOP cooling we imagine slicing the initial density distribution
$\mathcal{P}(x)$ into $2J+1$ sections, where the left-most section is labeled
by $m_{J}=-J$, followed by $-J+1$, and so on to the right most section labeled
$m_{J}=J$. Then, each section is kicked to a velocity $v_{0}\propto-m_{J}$
such that the distribution is compressed. Our goal is to develop a model
allowing us to optimize the MOP cooling protocol for maximum compression. As a
figure of merit, we compute the compression factor as the initial-to-final
ratio $\mathcal{R}$ of the spatial distribution’s standard deviation. We
restrict our attention to cases in which $\mathcal{P}$ remains symmetric
around $x=0$ so that the distribution’s standard deviation is the square-root
of its second moment. Therefore, the compression factor is
$\mathcal{R}\equiv\sqrt{\langle x^{2}\rangle_{\mathcal{P}_{\rm
initial}}/\langle x^{2}\rangle_{\mathcal{P}_{\rm final}}}$ where

$\langle x^{2}\rangle_{\mathcal{P}}=\int_{-\infty}^{\infty}{\rm
d}x\,x^{2}\mathcal{P}(x).$ (3)

Note that maximizing $\mathcal{R}$ is equivalent to minimizing
$\mathcal{R}^{-2}$, i.e. the ratio of the distribution’s final-to-initial
variance.

Figure 5: The initially Gaussian (a-b) and final (c-d) distributions for MOP
cooling of with $J=1$ [(a) and (c)] and $J=2$ [(b) and (d)]. Colors correspond
to $m_{J}$ sections, as labeled in panels (a) and (b), and the black lines
mark the total distribution. Here, $\delta$ was chosen according to Equation
(11).

###  A.2 Compression limits for a Gaussian distribution

When trapped in a harmonic potential $V(x)=M\omega_{0}^{2}x^{2}/2$, the real-
space probability density is Gaussian

$\mathcal{P}_{\rm
G}(x)=\frac{1}{\sqrt{2\pi\sigma_{0}^{2}}}e^{-x^{2}/2\sigma_{0}^{2}},$ (4)

where we have evaluated the phase-space normalization constant
$\rho_{0}=1/2\pi v_{\rm th}\sigma_{0}$ and defined the density’s variance
$\sigma_{0}^{2}=k_{\rm B}T/M\omega_{0}^{2}$. The initial standard deviation in
this case is simply $\sigma_{0}=v_{\rm th}/\omega_{0}$.

Define the the intervals $(a,b)_{m_{J}}$ that specify the partitioning of the
initial distribution as

$(a,b)_{m_{J}}=\delta\sigma_{0}\cases{(-\infty,\,-(2J+1)]&$m_{J}=-J$\\\
((2m_{J}-1),\,(2m_{J}+1)]&$|m_{J}|<J$\\\ ((2J-1),\,\infty)&$m_{J}=J$\\\ }$ (5)

where $2\delta>0$ represents the distance between adjacent sections in units
of $\sigma_{0}$. At the end of a MOP cooling cycle, these sections have
collapsed. Figure 5 depicts examples of the initial and final distributions
for $J=1,2$.

####  A.2.1 Geometric limit

If the section collapse occurs much faster than thermal free expansion, then
the observed compression is limited by the initial distribution’s shape.
Typographically, we will use a hat over functions and optimized variables to
distinguish this _geometric limit_ from the more general results presented
later, which account for thermal free expansion. In the present case of an
initially-Gaussian distribution, the final distribution is

$\hat{\mathcal{P}}(x)=\cases{\mathcal{P}_{\rm
G}(x-2J\delta\sigma_{0})&$x<-\delta\sigma_{0}$\\\
\sum\limits_{m_{J}=-J}^{J}\mathcal{P}_{\rm
G}(x-2m_{J}\delta\sigma_{0})&$|x|<\delta\sigma_{0}$\\\ \mathcal{P}_{\rm
G}(x+2J\delta\sigma_{0})&$x>\delta\sigma_{0}$ .}$ (6)

Figure 6: (a) The compression factor for various ways of splitting and merging
a Gaussian distribution, as given by Equation (7). We numerically extract the
peak compression factor $\hat{\mathcal{R}}_{\rm opt}$ and corresponding
relative half-width $\hat{\delta}_{\rm opt.}$ and show their $J$-scaling in
panels (b) and (c), respectively. The solid lines in (b) and (c) result from
the simultaneous fit to Equations (10) and (11), respectively.

As for the compression factor $\hat{\mathcal{R}}$, the required integral (3)
may be evaluated to give

$\hat{\mathcal{R}}^{-2}(\delta,J)=1-2\delta
S_{1}(\delta,J)+4\delta^{2}\left[J^{2}-S_{2}(\delta,J)\right],$ (7)

which is valid for both integer and half-integer $J$ and where we have defined
the two parameterized summations

$\displaystyle
S_{1}(\delta,J)=\sqrt{\frac{2}{\pi}}\sum_{m_{J}=-J}^{J-1}\exp\left[\frac{-\delta^{2}(2m_{J}+1)^{2}}{2}\right]$
(8) $\displaystyle
S_{2}(\delta,J)=\frac{1}{2}\sum_{m_{J}=-J}^{J-1}(2m_{J}+1){\rm
Erf}\left[\frac{\delta(2m_{J}+1)}{\sqrt{2}}\right].$ (9)

In Figure 6 (a) we show $\hat{\mathcal{R}}$ as a function of $\delta$ for
various $J$.

Equation (7) provides a way to optimize $\delta$ for a given $J$ by solving
$\partial\hat{\mathcal{R}}^{-2}/\partial\delta=0$ for
$\delta\equiv\hat{\delta}_{\rm opt}$. Using the identity
$S_{1}^{\prime}(\delta,J)/S_{2}^{\prime}(\delta,J)=-2\delta$, where the prime
denotes a derivative with respect to $\delta$, we deduce $4\hat{\delta}_{\rm
opt.}[J^{2}-S_{2}(\hat{\delta}_{\rm opt.},J)]-S_{1}(\hat{\delta}_{\rm
opt.},J)=0$. Thus, the corresponding optimal compression factor
$\hat{\mathcal{R}}_{\rm opt.}(J)=\hat{\mathcal{R}}(\delta_{\rm opt.},J)$ is
given by $\hat{\mathcal{R}}^{-2}_{\rm opt.}=1-\hat{\delta}_{\rm
opt.}S_{1}(\hat{\delta}_{\rm opt.},J)$. The transcendental form of the above
optimization equations precludes a closed form solution. Fortunately, numeric
root finding allows us to quickly and accurately obtain $\hat{\delta}_{\rm
opt.}$. Empirically, we find that the numerically-optimized $\hat{\delta}_{\rm
opt.}(J)$ and the corresponding $\hat{\mathcal{R}}_{\rm opt.}(J)$ are well
fit, simultaneously, to the models,

$\displaystyle\hat{\mathcal{R}}_{\rm opt.}(J)\approx A_{1}(2J+1)^{B}$ (10)
$\displaystyle\hat{\delta}_{\rm opt.}(J)\approx A_{2}(2J+A_{3})^{-B}\,,$ (11)

as shown in Figure 6 (b-c). Our fit yields $A_{1}=0.89$, $A_{2}=1.82$,
$A_{3}=1.61$, and $B=0.85$. The fitted functions and numeric optimizations
agree with an average relative error of 0.33% for $\hat{\mathcal{R}}_{\rm
opt.}$ and 0.08% for $\hat{\delta}_{\rm opt.}$ for integer $1\leq J\leq 10$.

####  A.2.2 Thermal limit

Due to finite magnetic kick strengths, MOP cooling requires a finite time-of-
flight to reach peak compression. Due to the ensemble’s finite temperature,
the spatial and velocity distributions correlate via free expansion, meaning
each section becomes more Gaussian-like over the required time-of-flight.
Towards a model of MOP cooling including these effects, let us compute the
time-dependence of an initially-Gaussian spatial distribution subject to
thermal free expansion and translation at a constant kicking velocity $v_{0}$.
We are particularly interested in the time dependence of a subsection of such
a distribution that initially occupies the interval $(a,b)$, denoted
$\mathcal{P}_{\rm sec.}\left[x,t;v_{0},(a,b)\right]$. Microscopically, the
atom trajectories obey $\dot{v}=0$ and $\dot{x}=v+v_{0}$, so, by Liouville’s
theorem, we may write the time-dependent phase-space density as
$\rho(x-(v+v_{0})t,v)$. The real-space marginal is

$\displaystyle\mathcal{P}_{\rm
sec.}\left[x,t;v_{0},(a,b)\right]=\frac{1}{2\pi\sigma_{0}v_{\rm
th}}\int_{\frac{x-b}{t}-v_{0}}^{\frac{x-a}{t}-v_{0}}{\rm d}v\,$ (12)
$\displaystyle\qquad\times\exp\left(-\frac{v^{2}}{2v_{\rm
th}^{2}}-\frac{[x-t(v+v_{0})]^{2}}{2\sigma_{0}^{2}}\right)$
$\displaystyle=\frac{1}{2\sqrt{2\pi\sigma_{0}^{2}f^{2}_{t}}}\exp\left(\frac{-[x-tv_{0}]^{2}}{2\sigma^{2}_{0}f^{2}_{t}}\right)$
$\displaystyle\qquad\times\left[{\rm
Erf}\left(\frac{bf_{t}^{2}+tv_{0}-x}{\sqrt{2}f_{t}v_{\rm th}t}\right)-{\rm
Erf}\left(\frac{af_{t}^{2}+tv_{0}-x}{\sqrt{2}f_{t}v_{\rm th}t}\right)\right]$

where we have defined $f^{2}_{t}=1+t^{2}v_{\rm th}^{2}/\sigma_{0}^{2}$ and
${\rm Erf}$ is the error function. When $(a,b)=(-\infty,\,\infty)$, then the
factor in square brackets becomes $2$, and the result is familiar from time-
of-flight analysis of harmonically trapped ensembles. To model MOP cooling, we
set the kicking velocity to $v_{0}=-m_{J}\gamma v_{\rm th}$, where $\gamma>0$
measures the kicking strength in units of the thermal velocity, and then sum
the distribution sections over the intervals given in Equation (5):

$\mathcal{P}(x,t)=\sum_{m_{J}=-J}^{J}\mathcal{P}_{\rm
sec.}\left[x,t;-m_{J}\gamma v_{\rm th},(a,b)_{m_{J}}\right].$ (13)

Figure 7: Time-dependent MOP cooling model for a kicking strength of
$\gamma=5$ and including effects of free expansion. The initial distributions
are shown for (a) $J=1$ and (b) $J=2$. Similarly, panels (c) and (d) show this
distributions after a time $t_{\rm opt.}/4$ for $J=1$ and $J=2$, respectively.
After a time $t_{\rm opt.}$ the distributions have minimal variance and are
shown shown for (e) $J=1$ and (f) $J=2$.

Figure 7 shows the time-dependent, real-space probability density for $J=1,2$
and $\gamma=5$ at times $t=0$, $t=t_{\rm opt.}/4$, and $t=t_{\rm opt.}$ where
$t_{\rm opt.}\approx 2\delta\sigma_{0}/\gamma v_{\rm th}$ is the optimal delay
time after which the sections have collapsed.

From the probability density (13) we may evaluate the compression factor
$\mathcal{R}$. It is convenient to introduce the non-dimensional time $\tau$
such that $t=\tau\sigma_{0}/v_{\rm th}$. Then, the final result reads

$\displaystyle\mathcal{R}^{-2}(\tau,\delta,\gamma,J)=1$
$\displaystyle-\tau\gamma S_{1}(\delta,J)$
$\displaystyle+\tau^{2}\left[1+\gamma^{2}J^{2}-\gamma^{2}S_{2}(\delta,J)\right].$

The geometric limit (7) is recovered from (A.2.2) for $\gamma\to\infty$ and
$\tau\to 0$ such that $\tau\gamma\to 2\delta$.

From (A.2.2), the optimal delay time $t_{\rm opt.}=\tau_{\rm opt.}v_{\rm
th}/\sigma_{0}$ may be expressed in closed form upon solving
$\partial\mathcal{R}^{-2}/\partial\tau=0$ for $\tau\equiv\tau_{\rm opt.}$,
yielding

$\tau_{\rm
opt.}(\delta,\gamma,J)=\frac{\gamma}{2}\frac{S_{1}(\delta,J)}{1+\gamma^{2}J^{2}-\gamma^{2}S_{2}(\delta,J)}.$
(15)

On the other hand, optimizing $\mathcal{R}$ with respect to the relative half-
width $\delta_{\rm opt.}$ for given angular momentum $J$ and kick strength
$\gamma$ requires numeric minimization of equation (A.2.2). Similarly to the
geometric-limit case, analytic optimization implies $4\delta_{\rm
opt.}[1+\gamma^{2}J^{2}-\gamma^{2}S_{2}(\delta_{\rm
opt.},J)]-\gamma^{2}S_{1}(\delta_{\rm opt.},J)=0$ and ${\mathcal{R}}^{-2}_{\rm
opt.}(\gamma,J)=1-\delta_{\rm opt.}S_{1}(\delta_{\rm opt.},J)$ where
$\mathcal{R}_{\rm opt.}(\gamma,J)=\mathcal{R}(\tau_{\rm opt},\delta_{\rm
opt.},\gamma,J)$.

###  A.3 Compression limits for a flat distribution

When trapped in a box-like potential of width $2s_{0}$, $V(|x|>s_{0})=\infty$
and $V(|x|\leq s_{0})=0$, the ensemble’s spatial distribution
$\mathcal{P}_{\rm F}(|x|<s_{0})=1/2s_{0}$ is flat and has a standard deviation
$\sigma_{0}=s_{0}/\sqrt{3}$. For a flat distribution, deciding how to
partition the $(2J+1)$ sections for MOP cooling is simpler than in the
Gaussian case. The flat distribution only has support over the interval
$(-s_{0},\,s_{0})$, so it is intuitive to split the initial distribution into
a number $2J+1$ of equally sized sections such that each section contains an
equal number of atoms. That is, the intervals of each section are finite and
given by

$(a,b)_{m_{J}}=\left(s_{0}\frac{2m_{J}-1}{2J+1},\,s_{0}\frac{2m_{J}+1}{2J+1}\right).$
(16)

In the geometric limit, all sections remain flat and merge to a single section
of width $2s_{0}/(2J+1)$ and hence the geometrically-limited compression
factor is $\hat{\mathcal{R}}_{\rm opt.}(J)=2J+1$.

Including the effects of thermal and mean velocity, we find the time-dependent
spatial distribution of a section initially occupying the interval $(a,b)$ is

$\displaystyle\mathcal{P}_{\rm
sec.}[x,t;v_{0},(a,b)]=\frac{1}{4s_{0}}\bigg{[}$ $\displaystyle{\rm
Erf}\left(\frac{b-x+tv_{0}}{\sqrt{2}tv_{\rm th}}\right)$ $\displaystyle-{\rm
Erf}\left(\frac{a-x+tv_{0}}{\sqrt{2}tv_{\rm th}}\right)\bigg{]}.$

As in Equation (13), the kicking velocities for each section are
$v_{0}=-m_{J}\gamma v_{\rm th}$ and the total distribution is the sum of each
section’s distribution. The initial variance is given by
$\sigma^{2}_{0}=s_{0}^{2}/3$. Introducing the non-dimensional time
$\tau=tv_{\rm th}/s_{0}$ allows us to express the compression factor as

$\displaystyle\mathcal{R}^{-2}(\tau,\gamma,J)=1$
$\displaystyle-\tau\gamma\frac{4J(J+1)}{(2J+1)}$
$\displaystyle+\tau^{2}\left[3+\gamma^{2}J(J+1)\right].$

Equation (A.3) connects to the simulations discussed in the main text. In
Figure 8 we compare Equation (A.3) to the simulation results presented in
Figure 4. We have set $T=25T_{\rm rec}$ and $\gamma=\Delta v/v_{\rm th}$ where
$\Delta v=2g_{J}\mu_{\rm B}G\tau/M\pi$ is the relative kick velocity of
adjacent sections and $G$ is the peak field gradient. With no remaining free
parameters our one-dimensional model and simulations, which include realistic
kicking profiles, are in excellent agreement.

Figure 8: The data points are reproduced from Figure 4 of the main text and
the dashed lines correspond to Equation (A.3), to the minus-one-half power,
with $\gamma$ and $v_{\rm th}$ set in accordance with the simulations, i.e.,
no free parameters.

For large enough $\gamma$, we expect the time at which $\mathcal{R}$ is
maximized is when all sections have merged at $t_{\rm opt.}\approx
2s_{0}/\gamma v_{\rm th}(2J+1)$. At this time, the compression factor
according to Equation (A.3) evaluates to

$\mathcal{R}_{\rm
opt.}(\gamma,J)\approx\frac{(2J+1)}{\sqrt{1+12/\gamma^{2}}}.$ (19)

Equation (19) is identical to that given in the discussion section of the main
text. More precisely, solving $\partial\mathcal{R}^{-2}/\partial\tau=0$ for
$\tau\equiv\tau_{\rm opt.}$ gives

$\displaystyle\tau_{\rm opt.}(\gamma,J)=\frac{2\gamma
J(J+1)}{(2J+1)\left[3+\gamma^{2}J(J+1)\right]}$ (20)
$\displaystyle=\frac{2}{\gamma(2J+1)}+\mathcal{O}(\gamma^{-2})$
$\displaystyle\mathcal{R}_{\rm
opt.}(\gamma,J)=(2J+1)\left[\frac{3+\gamma^{2}J(J+1)}{3+J(J+1)(\gamma^{2}+12)}\right]^{1/2}.$
(21)

The second equality in (20) comes from a first order expansion in
$\gamma^{-1}$ and recovers our $\gamma\to\infty$ expectation. Approximation
(19) is accurate to better than 10% (1%) of Equation (21) when $\gamma\geq 2$
and $J=1$ ($J=5$), and accuracy improves monotonically with increasing
$\gamma$ and $J$.

The one-dimensional models defined in this appendix are useful to understand
the scaling properties of MOP cooling for both Gaussian and flat density
profiles. We have outlined techniques for optimization that provide
engineering specifications and enable sensitivity analyses for the design of
real experimental systems. In the main text, we focused on atomic simulations
rather than the models defined here because they not only include thermal free
expansion effects, but also three-dimensional, time-dependent kicking forces.
In the future, it may be possible to extend our models to include effects like
kicking inhomogeneities and finite kicking duration as well as quantum-
statistical effects and state preparation details ignored by the main-text
simulations.

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