# Quasi one-dimensional diffuse laser cooling of atoms

Jin-Yin Wan  Laboratory of Space Laser Engineering and Technology, Shanghai
Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai
201800, China  Xin Wang  Key Laboratory of Quantum Optics and Center of Cold
Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy
of Sciences, Shanghai 201800, China  Xiao Zhang  Key Laboratory of Quantum
Optics and Center of Cold Atom Physics, Shanghai Institute of Optics and Fine
Mechanics, Chinese Academy of Sciences, Shanghai 201800, China  Yan-Ling Meng
Laboratory of Space Laser Engineering and Technology, Shanghai Institute of
Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
Wen-Li Wang  Laboratory of Space Laser Engineering and Technology, Shanghai
Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai
201800, China  Yuan Sun<EMAIL_ADDRESS>Key Laboratory of Quantum Optics
and Center of Cold Atom Physics, Shanghai Institute of Optics and Fine
Mechanics, Chinese Academy of Sciences, Shanghai 201800, China  Liang Liu
<EMAIL_ADDRESS>Laboratory of Space Laser Engineering and Technology,
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences,
Shanghai 201800, China  Key Laboratory of Quantum Optics and Center of Cold
Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy
of Sciences, Shanghai 201800, China

###### Abstract

We demonstrate experimentally the generation of one-dimensional cold gases of
87Rb atoms by diffuse laser cooling (DLC). A horizontal slender vacuum glass
tube with length of 105 cm and diameter of 2 cm is used in our experiment. The
diffuse laser light inside the tube, which is generated by multi-reflection of
injected lasers, cools the background vapor atoms. With 250 mW of cooling
light and 50 mW of repumping light, an evenly distributed meter-long profile
of atom cloud is obtained. We observe a factor 4 improvement on the atomic OD
for a typical cooling duration of 170 ms and a sub-Doppler atomic temperature
of 25 $\mu$k. The maximum number of detected cold atoms remain constant for a
free-fall duration of 30 ms. Such samples are ideal for many quantum optical
experiments involving electromagnetically induced transparency, electronically
highly excited (Rydberg) atoms and quantum precision measurements.

##  I INTRODUCTION

Laser cooling techniques have revolutionized experimental research on cold
atom physics and become a standard tool for precision measurement, quantum
optics, and quantum simulation, quantum computation and quantum information
[1]. One typical laser cooling apparatus is the six-beam magneto-optical trap
(MOT) requiring careful alignment of cooling laser beams and magnetic gradient
field, which makes the development of precise metrological devices based on
cold atoms such as atomic clocks, gravimeters and gyroscopes difficult and
complex. Diffuse laser cooling (DLC) scheme is proposed to ease these
problems, where the diffuse light field is generated in a tube or a sphere
whose inner surface reflect laser light diffusely [2, 3, 4, 5]. Then the 3D
diffuse light cooling configurations have been realised on Cs and Rb vapors in
spherical cells [6, 7]. It shows a Sisyphus-like cooling mechanism since the
cold atoms can reach a sub-Doppler temperature as low as 3.5 $\mu$k [6, 8, 9].
DLC technique is easy and robust since it needs no alignments of lasers and is
not sensitive to magnetic field. DLC has been widely applied to compact
microwave atomic clocks for ground operation and on-board applications in
microgravity environment. [10, 11, 12, 13, 14]. Moreover, compact cold atom
platform provides exciting possibilities for portable, robust and accessible
quantum sensors. Therefore, neutral cold atom ensemble by DLC technique is
also a potential candidate for space applications [15, 16, 17].

DLC technique has been studied both in slowing an atomic beam and in cooling
of atoms from vapor background [2, 3, 4, 5, 6, 7]. Many efforts have been made
on the properties of cold atoms captured by DLC including temperature, atomic
density, localization, scale and spectroscopic effects [18, 19, 20, 21, 22,
23, 24, 25]. However, much less attention was paid to one-dimensional
configuration. In this work, we demonstrate a meter-long diffuse laser cooling
apparatus in which 87Rb atoms were cooled in a nearly one dimensional shape by
DLC. Different from the conventional DLC setups [6, 7, 25], we employ a
horizontal slender glass tube whose outside surface is covered by a reflective
material. Atoms are cooled by diffuse light inside the tube homogeneously.

The paper is organized as follows: In Sec. II, the experimental configuration
for the DLC of 87Rb atoms in the horizontal slender glass tube and the
corresponding time sequence are presented. In Sec. III, as a key parameter to
determine the performance of the captured cold atoms, the dependence of the
atomic OD on a variety of experimental parameters, including the cooling light
power, the repumping light power, the detuning of cooling and probe light are
measured. The cooling time and temperature measurement of the cold atoms are
also described. The atomic density distributions of the cold atoms in the
longitudinal direction is detected through a pair of moving Helmholtz coils.
Finally, the paper is concluded in Sec. IV.

##  II EXPERIMENTAL CONFIGURATION

Figure 1 gives the experimental scheme. Two extended-cavity diode lasers
(ECDL) tuned at 780.24 nm of Rubidium D2 line are used, both of which are
frequency locked by saturation absorption spectra. One is used as both cooling
and the probe, the other is used as the repumping, as shown in Fig. 1 (a).
Each laser frequency is individually controlled by acousto-optic modulators
(AOMs).

Similar to traditional optical molasses, there are 4 energy levels involved of
87Rb atoms in our DLC experiment. The cooling light is red detuned by around
-17 MHz ($\sim$2.8$\Gamma$, where $\Gamma$ = 6.056 MHz denotes the natural
linewidth of 87Rb) to the transition $5^{2}S_{1/2},F=2\rightarrow
5^{2}P_{3/2},F^{\prime}=3$. The repumping light is resonant with the
transition $5^{2}S_{1/2},F=1\rightarrow 5^{2}P_{3/2},F^{\prime}=2$ to prevent
87Rb atoms from accumulating in the $5^{2}S_{1/2},F=1$ energy level. The probe
light is nearly resonant with the transition $5^{2}S_{1/2},F=2\rightarrow
5^{2}P_{3/2},F^{\prime}=3$.

---
Figure 1: DLC measurement scheme. (a) Relevant energy levels of 87Rb D2 line
for diffuse light cooling. (b) Schematic of the experimental setup. ECDL 1,
extended-cavity diode laser 1, cooling and probe laser. ECDL 2, repumping
laser. TA, tapered amplifier. ISO, isolator. PBS, polarization beam splitter.
$\lambda/2$, half-wave plate. $\lambda/4$, quarter-wave plate. HR, high-
reflection mirror. PD, photo detector. AOM, acoustic optical modulator. (c)
DLC and atomic density distribution measurement timing sequence. In our case,
the cooling time $t_{c}$ is 170 ms, the probe time $t_{p}$ is 100 ms, the
distribution magnetic field time $t_{b}$ is 50 ms, and the cycle time T is 270
ms.
---
Figure 2: (a) Normalized cold atom number along the optical detection axis
versus the cooling time $t_{c}$, where the atom number has been normalized to
a factor of 8 $\times$ 109. For cooling time more than about 0.17 s,
saturation behavior occurs where the capturing and loss are almost balanced.
(b) The measured OD at different probe time delays. A significant result of
the maximum OD remains unchanged for a free-fall duration 30 ms, as indicated
by the arrow (c). And arrow (d) indicates that it decreases exponentially with
a theoretical fitting, where a temperature 25 $\mu$k is obtained.

A sketch of the experimental setup is shown in Fig. 1(b), the main physical
part is a horizontal cylindrical glass vacuum tube with its length of 105 cm
and the inner cross section diameter of 2 cm, whose vacuum is maintained at
$3\times 10^{-8}$ Pa by an ion pump. Its outside surface is covered with a
coating whose diffuse reflectance is more than 98% at the optical wavelength
of 780 nm. Sizable holes are scratched for the transmission of light beams.
Homogeneous diffuse light inside the tube is formed from diffuse multi-
reflection of lasers which are injected through 8 holes. The vacuum tube is
filled with natural rubidium (Rb) vapor which is composed of 87Rb (27.8%) and
85Rb (72.2%). The Rb vapor is obtained by heating the Rb source to 70
${}^{\texttt{o}}$C to release gaseous atoms. The source is then cooled down
slowly to room temperature ($\sim$25oC).

The optical system mainly consists of two extended-cavity diode lasers (ECDL),
both of which are frequency locked by saturated absorption technique. One ECDL
is locked at the transition $5^{2}S_{1/2},F=2$ to the cross peak of
$5^{2}P_{3/2},F^{\prime}=1$ and $5^{2}P_{3/2},F^{\prime}=3$. It is followed by
a tapered amplifier (TA) which can emit the maximum light power of 2 W. The
output beam is then divided into two beams via a polarizing beam splitter
(PBS). One beam serves as the cooling light, and the other beam serves as the
probe light. Each beam is switched and frequency shifted from a certain
transition by using an acousto-optic modulator (AOM) in the double-pass
configuration. The other ECDL is frequency locked at the transition
$5^{2}S_{1/2},F=1$ to the cross peak of $5^{2}P_{3/2},F^{\prime}=1$ and
$5^{2}P_{3/2},F^{\prime}=2$. It serves as the repumping light which is
controlled by an AOM in the single-pass configuration. Firstly, the cooling
beam and repumping beam are combined by a PBS. Secondly, the two combined
beams are divided to four balanced beams by another two PBSs. Thirdly, each
beam is coupled into an One-to-Two multi-mode optical fiber, and eight
intensity balanced divergent lights are generated. Finally, the fiber coupling
heads are injected into the tube from the eight evenly distributed holes on
the side surface, the injection angles can be between 30 and 60 degrees from
the side section, thus there is no need to optimize the alignment of these
beams. Compared with the well-designed optical alignments, this robust optical
injection mode reduces the difficulty of the optical adjustment.

Fig. 1(c) shows the experimental sequence of the DLC process. The cooling and
repumping lights are applied for 170 ms, this process will cool a large
population of 87Rb atoms down from the background Rb vapor, the internal state
of such 87Rb atoms is prepared to the energy level of $5^{2}S_{1/2},F=2$. And
then the probe light is applied for 100 ms to detect the captured cold atoms.
In the first 50 ms of the probe time, a weak static magnetic field is applied
to measure the atomic density distribution. The total cycle time is 270 ms.

##  III RESULTS AND DISCUSSIONS

Atoms cooled by DLC in the tube are detected by measuring absorption of a
resonant probe laser in the direction of the tube’s axis, as shown in Fig.
1(b). The The diameter of Gaussian probe beam is 1 mm with intensity around
100 $\mu$W/cm2. Generally, OD of the cold atoms is given by the relation
$I=I_{0}e^{-OD}$, here $I_{0}$ and $I$ are the incident and the output
intensity, respectively. The number of cold atoms $N$ obeys the relation
$OD=\sigma N$, where $\sigma$ is the cross section of the atom-light
interaction. The maximum number of cold atoms can be reached at the balance
between capture and loss of laser-cooled atoms . A straightforward
phenomenological model may be given as $dN/dt=-\kappa N+\alpha$, where
$\kappa$ describes the loss and $\alpha$ describes the replenishing rate of
the newly captured cold atoms [1]. Therefore
$N(t)=\alpha/\kappa(1-e^{-\kappa(t-t_{0})})$, and $N(\infty)=\alpha/\kappa$
when $t$ is long enough.

Fig. 2(a) shows the normalized cold atom number versus the cooling time
$t_{c}$. Simulation, shown in the solid line in Fig.. 2(a) , gives the loss
rate $\kappa$ as 17.6 s-1. When the cooling time lasts more than 0.17 s, the
number of cold atoms reaches saturation, which is about 6 times less than the
previous typical DLC schemes [25]. The fast banance comes from the quick loss
of cooled atoms due to the small diameter of the tube which is horizontally
placed in the gravity.

In order to determine the temperature of the captured cold atoms, we use a
recently developed nearly nondestructive thermometry of labeled cold atoms. In
this work, we roughly regard that all the detected atoms after the cooling
process are at the energy level of $5^{2}S_{1/2},F=2$, neglecting the
polarization degree of freedoms. The number of cold atoms within the beam size
of the probe light will decrease over probe time caused by spatial expansion
and gravity. The effect of gravity is neglected for simplicity since the
expansion time of the labeled atoms is rather short. The temperature of the
cold atom ensemble can be evaluated by the detection of the probe light over
time. Moreover, dynamics along the axis of the slender cavity rarely affect
the signal. Therefore the process can be considered under a 2D setting in the
transverse plane. And the velocity distribution of the cold atoms is well
described by the Maxwell-Boltzmann distribution
$f(v)dv=(\frac{m}{2\pi\kappa_{B}T})2\pi
v\exp(-\frac{mv^{2}}{2\kappa_{B}T})dv$, the cold atom number detected in the
range of the probe beam with radius of $r$ is proportional to [25]:

$s(r,t)=1-\exp(-\frac{m(r/t)^{2}}{2k_{B}T}).$ (1)

The experimental results and fitting are shown in Fig. 2(b). Arrow (c)
indicates that the measured OD almost keeps at the maximum for the free-fall
duration of 30 ms, since the density distribution of the targeted cold atoms
on the optical detection axis remain unchanged. It is the first observation of
a nearly fixed maximum cold atom number in a tens of milliseconds time range
once the cooling light is switched off. Generally, the captured cold atoms
starts to decrease immediately when there is no cooling light [7], which would
be limited by the gravity and thermal expansion of the cloud. Arrow (d)
indicates the thermal expansion process of addressed atoms with the
theoretical fitting curve according to Eq. (1), where the temperature is
deduced to be 25 $\mu$k. It demonstrates that a sub-Doppler cooling like
mechanism exists which is caused by the disordered gradient forces formed in
the diffuse light field.

---
Figure 3: The measured OD as a function of various cooling parameters. (a) OD
versus cooling light power when the cooling light is red detuned at 12 MHz and
the repumpming light power is fixed at 50 mW. (b) OD versus repumping light
power when the when the cooling light is red detuned at 12 MHz and the cooling
light power is fixed at 250 mW. (c) OD versus cooling light detuning when the
the cooling light power is 250 mW and the repumpming light power is fixed at
50 mW. (d) OD versus probe light detuning when the cooling light is red
detuned at 17 MHz, the the cooling light power is 250 mW and the repumpming
light power is fixed at 50 mW.

We measured the OD vs the total power of lasers injected into the vacuum tube
with fixed detuning of -12 MHz, cooling time $t_{c}$ is 0.17 s, the probe time
is 0.1 s, and the repumping power at 50 mW. As shown in Fig. 3(a), the OD
increases linearly with the cooling light power, and it reaches a saturation
value as the cooling light power is more than 250 mW.

Then we set the cooling light power at 250 mW and vary the repumping light
power. Fig. 3(b) indicates that the OD increases with the repumping light
power in the lower power region, and it reaches saturation at the value of 50
mW. However, a slight decrease is monitored in the higher power region, which
is caused by the heating effect. As a result, we obtain the atomic OD greater
than 4 with the cooling light power of only 250 mW, such low laser power
reduces the complicity of the laser system.

Fig. 3(c) shows the measured OD as a function of cooling laser detuning. The
measured OD almost maintains at a maximum value of 4.3for the detuning
rangeing between -20 and -8.8 MHz (about -3.3$\Gamma$ to -1.4$\Gamma$).
Different from a MOT or optical molasses, the velocity capture range of DLC is
$\mid\Delta\mid\leq kv\leq 2\mid\Delta\mid$ [2], where $\Delta$ denotes the
detuning of the cooling light, $k$ is the wave vector, and $v$ is the atomic
velocity. Such a wide capture range allows capturing atoms with large range of
velocities.

We measured the atomic OD versus the probe light detuning as shown in Fig.
3(d). The measured OD reaches the largest value of 4.4 when the probe light is
resonant with the atomic transition, and therefore all measurements keep the
probe light resonant for the estimation of number of cold atoms.

---
Figure 4: The atomic density measurement scheme. (a) The atomic density
measurement setup. A pair of Helmholtz coils is used to measure the
longitudinal atomic density distribution. (b) The measured atomic density
distribution along the longitudinal direction of the cavity.

To measure the atomic density distribution along the probe direction, we apply
a weak uniform static magnetic field ($\sim$2.3 mT) perpendicular to the
tube’s longitudinal axis as shown in Fig. 4(a). The magnetic field is
generated by a pair of Helmholtz coils which are distributed on both sides of
the tube perpendicularly and equidistantly. Generally, the resonant probe
light measures the atoms at the $5^{2}S_{1/2},F=2$ energy level. When the
atoms’ energy level is shifted from resonance by 30 MHz through a static
magnetic field as shown in Fig. 3(d), the part of cold atoms in the magnetic
field region would not be detected by the probe light. The data of these cold
atoms can be directly obtained when it is subtracted by the total signal
detected without magnetic field, the data of cold atoms in the magnetic field
region can be obtained. Therefore, we measured the cold atom density
distribution by moving the helmholtz coils from one end of the tube to the
other. In the first 30 ms after the cooling light is switched off, the atomic
distribution signal is too small to be detected precisely since the cold atom
number keeps the maximum and stable in this time region as shown in Fig. 2(b).
Thus the atomic density distribution is measured at the probe time delay of 40
ms as shown in Fig. 4(b). The cold atom number distribution lies in a
horizontal line along the longitudinal direction of the tube, thus a meter-
long nearly one dimensional cold atom cloud is prepared. Since the tube is
slender, the light emitted by the multi-mode optical fibers travels very short
distance before touching the wall and then is diffusely reflected at a high
rate immediately. The isotropic lights in the horizontal chamber forms a quasi
one-dimensional field which is more evenly distributed than that in the
spherical or vertical configurations [21], and it homogenizes the atomic
density.

##  IV CONCLUSION

In conclusion, we have experimentally demostrated nearly one dimensional cold
87Rb atom cloud with a length of 105 cm and a diameter of 2 cm by DLC in a
horizontally-placed slender glass tube. We have systematically studied the
dependence of atomic OD on several control parameters. With a total cooling
power of 250 mW, repumping power of 50 mW and a cooling time of 0.17 s, we
obtain a horizontally uniform distributed cold 87Rb atom ensemble with the
atomic OD more than 4 and the temperature about 25 $\mu$k. We first observe
that the maximum atomic OD almost remain unchanged for a free-fall duration 30
ms.

We have also shown the simplicity and robustness of the DLC. In fact, the DLC
depends only on the interaction between diffuse light and vapor atoms,
regardless of scale, shape, polarization, propagation direction of laser
field, magnetic field and etc. Such characters make the DLC easy to construct
different kind of geometries of cold atom cloud [22] which are not possible by
MOT or optical molasses, for example, the cold atom cloud in meter-long tube
in this work can be easily extended to km-long or even longer, and also to 2D
shape.

Our results give a new method to generate cold atoms especially in some
geometries, which are useful in quantum sensing.

###### Acknowledgements.

We thank Weibin Li for helpful suggestions in the preparation of the
manuscript. This work is supported by the National Natural Science Foundation
of China (Grant No. 61727821).

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benefits of RSMA for joint communications and jamming in a MIMO CR network
with imperfect and statistical CSIT.

Challenges and future work: The spectrum sharing between SUs and PUs gives
rise to security concerns in CR as SUs and PUs may wiretap each others’
information. The secrecy performance of RSMA in such scenario, however,
remains an open problem.

####  VII.A16 Massive machine-type communication

IoT is essential for 5G and beyond as it provides advanced solutions for smart
cities via a massive number of IoT devices. mMTC, which is tailored for
massive IoT applications, has been included in 3GPP Release 13 [198] as an
instrumental usage scenario for ultimately realizing massive connectivity
among IoT devices with low complexity and low power. How to serve massive
devices with lean control signaling and receiver complexity has become the
major challenge in massive IoT.

Existing studies of RSMA have shown that RSMA is capable of achieving higher
SE, reducing receiver complexities, and enhancing robustness with respect to
CSIT inaccuracy and network loads, which therefore makes RSMA an appealing MA
scheme for mMTC. The authors of [57] first showed from an information-
theoretic perspective that RSMA-aided power partitioning achieves the optimal
DoF region in an overloaded MISO BC, where the BS has partial CSIT of some
high-end users and statistical CSIT of some low-end IoT users. The DoF gain of
the proposed RSMA-aided power partitioning approach in the high SNR regime
motivates the study of its achievable sum-rate in the finite SNR regime, where
RSMA also facilitates significant SE enhancement [83].

Challenges and future work: IoT users in 6G are envisioned to have hybrid
requirements, such as simultaneously enhancing the throughput and reducing the
transmission delay. Such hybrid service is known as enhanced eMBB-URLLC-mMTC
in 6G and has been identified as one of the core services in 6G. Whether RSMA
is a promising MA technique to accommodate the hybrid requirements of massive
IoT users is not known, yet.

####  VII.A17 Visible light communication

VLC, which employs the visible light spectrum between 400 and 789 THz for
communication, is emerging as a compelling technique to complement the RF-
based mobile communication networks for high speed communications, especially
in indoor environments. To further enhance the data rate of VLC, MU-MIMO VLC,
which allows multiple light emitting diodes (LEDs) to simultaneously serve
multiple users, has been developed and widely studied in the VLC literature
[121]. However, multi-user interference is still a major bottleneck in MU-MIMO
VLC.

Motivated by the strong interference management capability of RSMA in RF
communications and the high operating SNR offered by VLC, the application of
RSMA in MU-MIMO VLC is promising as RSMA achieves high DoF and SE gains over
existing MA schemes. The authors of [120] and [121] were the first to study
RSMA for MU-MIMO VLC. Both papers show clear sum-rate gains of RSMA over
conventional MA schemes even when the user channels are highly correlated.
Therefore, RSMA is a suitable MA scheme for VLC networks. Both [120] and [121]
use the Shannon formula to calculate the sum-rate, which may thus not be
achievable due to the unique characteristics of VLC. This motivated the
authors of [142] to derive the achievable rate for RSMA-aided VLC networks.
Reference [142] was also the first work that studied RSMA-aided VLC for
imperfect CSIT.

Challenges and future work: Open issues for RSMA in VLC systems have been
thoroughly discussed in [121]. For example, practical limitations, such as
imperfect CSIT, merit further investigation for RSMA-aided VLC.

####  VII.A18 Intelligent reconfigurable surface-aided communications

IRS (a.k.a. reconfigurable intelligent surface–RIS, holographic MIMO
surface–HMIMOS, software controlled metasurface) has emerged as a tempting
technology for 6G. IRSs consist of a number of meta-atoms or passive
scatterers that are configurable and programmable in software. By dynamically
tuning the reflection coefficients of the meta-atoms for an incoming signal,
IRSs have the potential to control the propagation environment, thus changing
the design of wireless networks. IRSs have shown their benefits in improving
PHY layer security, suppressing interference, improving wireless power
transmission efficiency, improving PHY layer security, extending the cell
coverage, etc.

The merits of RSMA in multi-antenna networks have motivated the study of RSMA
in IRS-aided communication [126, 127, 134, 199, 200]. The authors of [126]
were the first to study RSMA for the MISO BC with multiple IRSs cooperatively
assisting the downlink transmission from a BS to multiple users. By jointly
optimizing the precoders, the message splits of 1-layer RS, and the phase
shifts of the IRS to maximize EE, RSMA was shown to achieve a better EE
performance than NOMA and OFDMA in the IRS aided MISO BC. 2-layer HRS and IRS-
aided transmission strategies are further studied in [134, 199, 200], where
the transmission from the BS to the users in each HRS user group is assisted
by one independent IRS. RSMA was shown to improve the WSR and outage
performance compared to 1-layer RS/MU–LP/NOMA-based IRS transmission
strategies.

Challenges and future work: Due to the absence of RF chains, it is challenging
to acquire the CSI at the IRS. An alternative approach is to estimate the
concatenated channel at the BS based on certain IRS reflection patterns, which
however, may result in imperfect CSIT due to limited channel training
resources [201, 202]. The integration of RSMA and IRS has a great potential to
compensate such limitations of IRS and boost the system performance. However,
issues such as joint passive and active beamforming design, user scheduling,
and IRS allocation have not been studied for RSMA based IRS-aided networks
with imperfect CSIT, which thus merits investigation.

####  VII.A19 Other open issues

The aforementioned 6G enabling technologies are not always independent from
each other. Some of them are complementary and the combination of those
techniques may introduce new research directions for RSMA. For example, both
cooperative user relaying and NOUM have the capability of enhancing the SE.
However, the performance of the multicast message in NOUM is restricted by the
worst-case rate among the users. By integrating CRS and NOUM, the system
performance of NOUM could be potentially improved as both the common parts of
the unicast messages and the multicast message are transmitted in the
cooperative transmission phase. The second hop/phase of CRS is therefore used
for the dual functions of improving the rate of the multicast message and
enhancing the interference management among the unicast messages.

In addition to the aforementioned research directions for RSMA, there are many
other unplumbed and timely areas for RSMA research, such as space-air-ground
integrated networks, vehicle-to-everything communications, 3D eMBB-URLLC-mMTC
services, etc. More research efforts are needed in each of these fields and
the underlying motivation is discussed in the following:

  * •

Space-air-ground integrated networks (SAGIN): 6G is envisioned to be an all-
coverage network that seamlessly integrates space, air, and ground
communications. The concept of SAGIN has therefore been developed and has
received considerable research attention recently. By offloading traffic among
space, air, and ground network segments, the network load in each part could
be balanced and alleviated. However, due to the spectrum sharing among the
above segments, interference becomes one of the major challenges in SAGIN that
significantly impacts the entire ecosystem of satellite-aerial-terrestrial
communications. Motivated by the powerful interference management capability
of RSMA demonstrated for satellite, air, and terrestrial cellular networks,
RSMA has great potential to successfully address the interference in SAGIN.

  * •

Vehicle-to-everything (V2X) communications: V2X, which includes vehicle-to-
network (V2N), vehicle-to-infrastructure (V2I), vehicle-to-pedestrian (V2P),
and vehicle-to-vehicle (V2V) communications, has been considered as one
platform for achieving intelligent transportation and is included in 3GPP
release 14 as LTE-based V2X services [203, 204]. Though appealing in its
concept, V2X communication is susceptible to user mobility and there are
rigorous requirements on transmission latency and reliability. Recent studies
of RSMA have shown that RSMA makes MU-MIMO systems robust against interference
resulting from user mobility and feedback delay [88], and it outperforms
existing MA schemes for finite block length coding [89]. It is therefore a
promising option for V2X communication.

  * •

3D eMBB-URLLC-mMTC services: NR defines three core services for 5G, namely
URLLC, mMTC, and eMBB. It is envisioned that 6G needs to provide three-
dimensional services for satisfying the mixed demands of the new use cases.
All possible combinations of the three core services in NR, such as the
enhanced eMBB-URLLC-mMTC service, enhanced eMBB-URLLC service, enhanced eMBB-
mMTC service, and enhanced mMTC-URLLC service, have been identified as hybrid
core services in 6G. As discussed in [144], RSMA provides a unified solution
for facilitating the aforementioned hybrid core services in 6G thanks to its
enhanced performance in terms of the 6G KPIs, i.e., data rate, mobility,
network density and dynamic topology, latency and reliability, and EE. There
are numerous open research topics in 6G that merit investigation in the
context of RSMA.

###  VII.B Standardization and Implementation of RSMA

Figure 33: Pathways to 3GPP

The standardization of RSMA has not been considered by 3GPP yet, but the key
technologies required for the implementation of RSMA, such as, multi-antenna
broadcasting, NOUM, SC at the transmitter, and SIC at the receivers have been
studied in 3GPP. As illustrated in Fig. 33, the four important study items in
5G, namely, multi-user superposition transmission (MUST), MU–MIMO and CoMP,
broadcast/multicast and unicast, and network-assisted interference
cancellation and suppression (NAICS), underpin the development of RSMA.

Specifically, MU–MIMO has been considered in 3GPP Release 8 [205] and CoMP has
been considered in 3GPP Release 11 [206]. Both of them are essential
technologies in LTE. In 3GPP Release 12 [207], NAICS is introduced and it uses
SIC receivers to manage interference. SC at the transmitter and SIC at the
users have been considered in LTE 3GPP Release 13 under the name of MUST
[208]. In 3GPP Release 17 [209], a study item on NR mixed mode
broadcast/multicast is included for enabling broadcast/multicast over NR.
Besides the aforementioned four approved study items in 3GPP, non-orthogonal
multiplexing of multicast and unicast are being discussed for 3GPP Release 18.

Though RSMA could leverage the machinery discussed/approved by 3GPP, there are
some other unique implementation issues in RSMA that need to be resolved,
which are summarized in the following:

  * •

Downlink and uplink signaling: As discussed in Section VI.E, RSMA requires the
knowledge of how to split/combine the messages to be perfectly synchronized
and available at both the transmitters and receivers. Additional downlink and
uplink signaling is needed to guarantee the synchronization of the knowledge
of how RS is performed (i.e., all transmitters and receivers have the
information on how the user messages are split and combined).

  * •

CSI feedback mechanisms: In [71], RSMA is shown to be capable of reducing the
CSI feedback overhead based on the conventional quantized feedback approach.
However, CSI feedback mechanisms have not been specifically designed for RSMA
yet.

  * •

System-level performance: The PHY layer design and LLS performance of RSMA has
been investigated in [79] and the performance gain of RSMA over the 5G NR
design has been brought to light in [88]. However, system-level performance
evaluations, which take into account the impact of the design of the higher
layers (such as Hybrid-ARQ, user scheduling, QoS provisioning in the
application layer), are still not available.

Last but not least, it is also necessary to design prototypes and testbeds for
RSMA so as to further validate and evaluate the various developed solutions.

##  VIII Conclusion

In this paper, we have provided the first holistic tutorial on, and survey of,
RSMA including

  * •

an exhaustive survey of the RSMA literature from both the information-
theoretic and communication-theoretic perspectives,

  * •

a thorough elaboration of the principles and transmission frameworks of
downlink uplink and multi-cell RSMA,

  * •

a comprehensive summary of two strategies for precoder design, namely precoder
optimization and low-complexity precoder design,

  * •

a detailed performance comparison between RSMA and existing MA schemes
(including SDMA, NOMA, OMA, multicasting) in terms of their DoF, complexity,
and performance,

  * •

a summary of the major advantages and disadvantages of RSMA,

  * •

an illustration of the PHY layer design and link-level simulation of RSMA,

  * •

an extensive discussion of emerging applications of RSMA as well as
corresponding research challenges and future directions including many
uninvestigated areas,

  * •

a synopsis of the standardization and implementation of RSMA.

The existing literature on RSMA has shown that non-orthogonal transmission in
multi-antenna networks should be designed such that interference is partially
decoded and partially treated as noise in order to fully exploit the benefits
of multiple antennas at the transceivers and SIC at the receivers. Thus, RSMA
is a promising PHY layer transmission paradigm for interference management,
non-orthogonal transmission, and multiple access in 6G, which will
fundamentally reform the PHY layer and lower MAC layer design of wireless
communication networks. Many previous studies of communication design merit
revisiting under the RSMA framework. RSMA indeed opens up many interesting
research problems for both industry and academia, and offers the prospect of
boosting data rate, enhancing transmission reliability, increasing energy
efficiency, saving transmit power, reducing transmission latency, improving
interference management, and providing robustness to CSIT inaccuracies.

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