# Switching, Amplifying, and Chirping Diode Lasers with Current Pulses for
High Bandwidth Quantum Technologies

Gianni Buser<EMAIL_ADDRESS>University of Basel, Department of
Physics, Klingelbergstrasse 82, 4056 Basel, Switzerland

###### Abstract

A series of simple and low-cost devices for switching, amplifying, and
chirping diode lasers based on current modulation are presented. Direct
modulation of diode laser currents is rarely sufficient to establish precise
amplitude and phase control over light, as its effects on these parameters are
not independent. These devices overcome this limitation by exploiting
amplifier saturation and dramatically outperform commonly used external
modulators in key figures of merit for quantum technological applications.
Semiconductor optical amplifiers operated on either rubidium D line are recast
as intensity switches and shown to achieve ON:OFF ratios $>${10}^{6}$$ in as
little as $50\text{\,}\mathrm{ns}$. Current is switched to a
$795\text{\,}\mathrm{nm}$ wavelength (Rb D1) tapered amplifier to produce
optical pulses of few nanosecond duration and peak powers of
$3\text{\,}\mathrm{W}$ at a similar extinction ratio. Fast rf pulses are
applied directly to a laser diode to shift its emission frequency by up to
$300\text{\,}\mathrm{MHz}$ in either direction and at a maximum chirp rate of
$150\text{\,}\mathrm{MHz}\text{\,}{\mathrm{ns}}^{-1}$. Finally, the latter
components are combined, yielding a system that produces watt-level optical
pulses with arbitrary frequency chirps in the given range and
$<$2\text{\,}\mathrm{\char 37\relax}$$ residual intensity variation, all
within $65\text{\,}\mathrm{ns}$ upon asynchronous demand. Such systems have
broad application in atomic, molecular, and optical physics, and are of
particular interest to fast experiments simultaneously requiring high power
and low noise, for example quantum memory experiments with atomic vapors.

##  I Introduction

Rapid control of the amplitude and frequency of laser light fields is critical
to many of their key applications, including optical communication [1],
optical computing [2], and control over atomic or molecular matter [3]. In the
domain of quantum optical technologies, the signals of interest are single
photons or weak coherent pulses with intensities on the single photon level
[4, 5, 6, 7]. Here the nanosecond-timing, gigahertz-bandwidth regime is
intrinsically attractive to applications because high rates are
technologically useful. Simultaneously, it is home to high quality single-
emitter photon sources [8, 9], including ones suited for hybrid atomic
interfaces such as Rb-like quantum dots [10].

A serious challenge in fast quantum optics experiments is the discrimination
of these weak photonic signals from intense laser fields. Diverse and useful
non-linear optical processes, including quantum frequency conversion by sum-
or difference frequency generation [11] in the context of transduction[12],
(entangled) photon pair production by parametric down conversion[13], and an
abundance of schemes facilitating quantum light-matter interactions[14] all
place high power “pumping” or “control” beams into spatial modes shared by
single photon signals. This puts high demands both on the speed and dynamic
range of laser control, and when the latter is insufficient, this must be
compensated by filtering leading to photon loss. Simply put, commonly used
optical switches for external laser modulation, including ubiquitous acousto-
and electro-optic modulators (AOMs and EOMs), do not reach intensity
extinction ratios (IER) concordant with the notion of a laser being OFF in
nanoseconds when the signal of interest is on the single photon level.
Comparing energies, the emissions of a $\mathrm{mW}$–$\mathrm{W}$ laser in
$1\text{\,}\mathrm{ns}$ contain $E=$\mathrm{pJ}$$–$\mathrm{nJ}$, whereas a
photon at $795\text{\,}\mathrm{nm}$ contains only
$E_{\text{ph}}\approx$2.5\text{\times}{10}^{-19}\text{\,}\mathrm{J}$$.
Desirable IER may thus exceed even $100\text{\,}\mathrm{dB}$.

Switch |  $\tau_{d}$ [s] |  $\tau_{s}$ [s] | IER |  $P_{\text{max}}$ [W]
---|---|---|---|---
Shutter | ${10}^{-4}$ | ${10}^{-4}$ | $\infty$ | >${10}^{2}$
AOM | ${10}^{-6}$ | ${10}^{-5}$ | >$80\text{\,}\mathrm{dB}$ | ${10}^{1}$
Waveguide EOM | ${10}^{-9}$ | ${10}^{-10}$ | $30\text{\,}\mathrm{dB}$ | ${10}^{-3}$
Bulk EOM | ${10}^{-7}$ | ${10}^{-9}$ | $30\text{\,}\mathrm{dB}$ | $undef$
SOA | ${10}^{-8}$ | ${10}^{-8}$ | >$60\text{\,}\mathrm{dB}$ | ${10}^{-2}$
TA | ${10}^{-8}$ | ${10}^{-8}$ | $60\text{\,}\mathrm{dB}$ | $undef$
Table 1: Comparison of speed and intensity performance of commonly used
optical switches, by typical order of magnitude only. $\tau_{d}$ latency, i.e.
the time between triggering a device and the beginning of an effect on the
optical output, $\tau_{s}$ fall time, after the latency, to reach the
specified extinction ratio, IER ratio of optical powers in ON and OFF states,
$P_{\text{max}}$ maximum feasible continuous optical output in vis/NIR

Mechanical shutters physically blocking a beam generally extinguish it
completely. If the aperture is closed with a mirror redirecting the laser to
an actively cooled beam trap, even kilowatt powers can be handled.
Unfortunately, accelerating an object into a beam path is far slower than
electronic means of switching. Almost as good in steady-state IER are AOMs,
given sufficient electronic isolation and care in spatially separating the
diffracted order from the direct transmission. Although these devices are
often specified with nanosecond scale switching times, however, the measure at
hand for such claims is a $90:10$ response. AOMs cannot achieve their steady-
state IER until 10s of microseconds after being triggered. This delay is an
inherent property of their principle of operation [1] – there are limits on
how fast sound waves can travel and dissipate – not merely a technical
limitation. In the visible and NIR, EOMs can switch intensities over about 3
orders of magnitude. Waveguide-based devices outperform their bulk
counterparts in speed, but they tend to accumulate photorefractive damage [15]
when operated even just at milliwatt powers. Higher IER can be achieved by
cascading devices, but this compounds insertion loss reducing the available
optical output. For a generic overview of typical performance across common
devices see Table 1. Generally, modern, performant systems externally
modulating both a laser’s amplitude and phase sport considerable device
overhead, and achieve what they set out to do in synchronous operation [16].
Typically, component latency is such that control within short times in
response to asynchronous demand is simply not possible.

Direct current modulation of laser diodes and optical amplifiers is a well
known alternative approach. The method is simple, cheap, and enables tens of
$\mathrm{Gbit}\text{\,}{\mathrm{s}}^{-1}$ data rates when used to encode
information in a telecommunications context [17]. In quantum optical control
applications, however, it is quite rare due to perceived downsides. The most
prominent troubles are twofold. Primarily, modulation of a laser diode’s
current has a linked and modulation frequency dependent effect on both the
amplitude and phase of the light[18], which is at odds with independently
varying these parameters. Secondarily, the response of the system must be
characterized optically, as variations in the semiconductors preclude precise
prior predictions of the output[19]. Nevertheless, in this paper I make a case
for the direct modulation approach, demonstrating detection limited IER beyond
$60\text{\,}\mathrm{dB}$ achieved in 10s of nanoseconds by current switching
continuously seeded semiconductor optical amplifiers (SOA) and tapered
amplifiers (TA), as well as controlled pulse chirps at rates up to
$150\text{\,}\mathrm{MHz}\text{\,}{\mathrm{ns}}^{-1}$ by applying rf pulses
directly to laser diodes. For the latter, I minimize intensity fluctuations by
passing the frequency modulated light through an optical amplifier in
saturation, imprinting the frequency shifts on stable $3\text{\,}\mathrm{W}$
peak-power pulsed output. Further, I find that given an initial
characterization, diode response follows simple phenomenology enabling
straightforward precision control.

##  II Optical Amplifiers as Switches

Semiconductor optical amplifiers are a staple of optical switching in
telecommunication network architectures [20]. In this field, they are famous
for exceptional dynamic range and high extinction ratios [21]. This attribute
lies close at hand. When current is passed through the device input seed light
is amplified, with typical small signal gains on the order of
$30\text{\,}\mathrm{dB}$. Simultaneously, in the absence of current, the
semiconductor acts as a saturable absorber, yielding significant insertion
loss rather than gain. In recent years devices with gain regions in the NIR
compatible with alkali transitions have become commercially available, and the
favorable properties that lead to their use in telecom translate seamlessly
into the field of atom optics. Measured in the steady-state, a commercial,
fiber-pigtailed SOA (Superlum SOA-332-DBUT-PM) configured to output
$20\text{\,}\mathrm{mW}$ of light on a rubidium D line (D1 at
$795\text{\,}\mathrm{nm}$, D2 at $780\text{\,}\mathrm{nm}$) and utilizing its
full gain range transmits no more than $500\text{\,}\mathrm{pW}$ (measurement
limit) of the incident seed light when no current is passed through it,
implying a steady state IER $\geq$75\text{\,}\mathrm{dB}$$.

Experiments utilizing laser light even for simple quantum control applications
like state preparation can quickly become limited by the quality of optical
switching in the high bandwidth regime [22, 23, 24]. Particularly relevant in
characterizing a switch for such uses is the IER as a function of time, as
this is the critical metric for their use in realistic asynchronous
applications. This characterization is demanding as it simultaneously requires
a high time resolution to resolve the dynamics (beyond the typical performance
of spectrum analyzers) and excellent dynamic range (beyond the typical
performance of photo diodes and oscilloscopes) to cover many orders of
magnitude in intensity.

Figure 1: (a) Setup to characterize SOA switching performance. DDG digital
delay generator, TTL transistor-transistor logic, FSCS (home built) fast
switching current source, SOA semiconductor optical amplifier, ND neutral
density, SNSPD superconducting nanowire single photon detector. (b) Time
resolved optical switching behavior of a SOA under $1\text{\,}\mathrm{MHz}$
pulsing of a forward current of $168\text{\,}\mathrm{mA}$ for
$75\text{\,}\mathrm{ns}$. The data are collected in
$12\times$81\text{\,}\mathrm{ps}$$ time bins, and the time axis is corrected
for propagation and detection delay to correspond to the intensity at the
SOA’s pig-tailed fiber output. The device’s maximal output power at
$795\text{\,}\mathrm{nm}$ is $20\text{\,}\mathrm{mW}$, which is used to
calibrate the y-axis. Simultaneously, this light can be turned off over seven
orders of magnitude within $200\text{\,}\mathrm{ns}$, limited by the dark
count set dynamic range of the detector.

A sketch of the characterization setup to determine the SOAs performance as an
optical switch is shown in Fig. 1(a). To satisfy both timing and dynamic range
demands, optical signals are measured using superconducting nanowire single
photon detectors (SNSPD). An operating current of $168\text{\,}\mathrm{mA}$ is
switched periodically to the SOA for $75\text{\,}\mathrm{ns}$ at a rate of
$1\text{\,}\mathrm{MHz}$. Here and everywhere, logical signals are generated
internally by a digital delay generator (Highland Technology T564). Response
to an external trigger adds only $20\text{\,}\mathrm{ns}$ insertion delay and
$30\text{\,}\mathrm{ps}$ jitter, which immediately readies all setups for
asynchronous operation. The SOA is seeded with
$60(6)\text{\,}\mathrm{\SIUnitSymbolMicro W}$ of cw laser light, chosen to
obtain the rated maximum of $20\text{\,}\mathrm{mW}$ output power
($g=$25.2(4)\text{\,}\mathrm{dB}$$). This power is sufficient, for instance,
to optically pump an ensemble of alkali atoms at saturation in a volume of
radius $1\text{\,}\mathrm{cm}$. The light is attenuated to a level where, on
average, one million photons are detected each second by the SNSPD (Single
Quantum EOS, $85\text{\,}\mathrm{\char 37\relax}$ system detection efficiency,
$20\text{\,}\mathrm{ps}$ FWHM jitter, dark count rate
<$10\text{\,}{\mathrm{s}}^{-1}$). Detection events are recorded with a time-
tagger (quTools quTau, $81\text{\,}\mathrm{ps}$ time resolution). The
switching behavior of this current controlled SOA is shown in Fig. 1(b), in a
measurement integrated for $12.7\text{\,}\mathrm{min}$ to resolve the y-axis
as well as possible. The known maximum optical output is used to calibrate the
y-axis into units of power. The output falls on a steep flank, reaching a
suppression level of $-56\text{\,}\mathrm{dB}$ in $17\text{\,}\mathrm{ns}$
from the start of switching, and over $-60\text{\,}\mathrm{dB}$ within
$50\text{\,}\mathrm{ns}$. A direct comparison reveals that after this point
the measured suppression is limited by dark counts, recorded separately
without any light incident over the same integration time for comparison. The
observed average dark count rate is only
$1.2\text{\,}\mathrm{counts}\text{\,}{\mathrm{s}}^{-1}$, considerably better
than bare instrument specification. This is achieved by turning down the bias
current to the nanowire well below its critical point. Dark count rates in
SNSPDs can be illumination dependent due to thermal radiation from the fibers,
or in more complicated ways too[25], and some care must be taken to ensure
that only their intrinsic rate limits a measurement.

In a separate characterization with careful compensation of cables, the
latency (i.e. the time between an electronic trigger input and the start of an
optical response) of the device is measured to be $23\text{\,}\mathrm{ns}$,
and full output is reached within $45\text{\,}\mathrm{ns}$ from the beginning
of its response. The electronic driver powering the switch is home built and
its current output follows a transistor-transistor logic (TTL) signal with no
restrictions on cycle time, but it does limit the switching flank steepness.
This is verified experimentally using a faster pulsed current source (Highland
Technology T160) suitable for low duty cycle operation. The ultimate limit,
which I do not resolve, is expected to be a function of the photon lifetime in
the semiconductor[1]. In the past couple of years, turnkey SOA/driver devices
for switching applications at alkali wavelengths have been commercialized,
simplifying their use even further. This choice of home built driver is made
to suit the application of optical pumping, which can require large duty
cycles. The switching performance is replicated over four tested devices with
light on both rubidium D lines. Operation near the current threshold of the
SOA ($g=1$) limits the maximum IER to about $-45\text{\,}\mathrm{dB}$, but
this level is reached equally quickly. It is thus plausible, albeit just
barely beyond the measurement limit of available devices, that the full steady
state IER is reached within only $60\text{\,}\mathrm{ns}$ when the SOAs are
operated at full gain. The output power obtained is a strict limitation, as
higher powers induce catastrophic optical damage on the chip end facet where
it is fiber pig-tailed.

To overcome the limitation on output power, the same switching principle is
applied to a tapered amplifier (Eagleyard EYP-TPA-0795-02000-4006-BTU02-0000)
rated to output $2\text{\,}\mathrm{W}$ of $795\text{\,}\mathrm{nm}$ light into
free space. The current to this device, maximally $4\text{\,}\mathrm{A}$, is
switched by a commercial driver (Aerodiode CCS-HPP, $4\text{\,}\mathrm{A}$
maximum current, $10\text{\,}\mathrm{ps}$ ($2\text{\,}\mathrm{ns}$) resolution
for pulse output up to (longer than) $10\text{\,}\mathrm{ns}$). It is used to
generate intense laser pulses of a few nanoseconds width. The thermal load of
the peak current to the driver MOS limits the output duty cycle to
$10\text{\,}\mathrm{\char 37\relax}$ on timescales longer than a few seconds.
To protect the amplifier from spurious back-scattering its output is first
passed through a two-stage Faraday isolator (Qioptiq FI-780-5TVC,
$75\text{\,}\mathrm{dB}$ isolation, $85\text{\,}\mathrm{\char 37\relax}$
transmission) and as an abundance of caution two interference filters
(Laseroptic L-12490, $0.4\text{\,}\mathrm{nm}$ FWHM pass-bandwidth at
$795\text{\,}\mathrm{nm}$) are used to filter out any broad amplified
spontaneous emission. This setup is sketched in Fig. 2(a).

Figure 2: (a) Setup to characterize TA switching performance. DDG digital
delay generator, TTL transistor-transistor logic, IPG current pulse generator,
TA tapered amplifier, FI Faraday isolator, IF interference filters, ND neutral
density, SNSPD superconducting nanowire single photon detector. (b) Time
averaged optical power output of the TA under $4\text{\,}\mathrm{A}$ current
pulsing at $1\text{\,}\mathrm{MHz}$, divided by the programmed pulse duty
cycle, in $1\text{\,}\mathrm{ns}$ ($2\text{\,}\mathrm{ns}$) steps for pulses
up to (longer than) $10\text{\,}\mathrm{ns}$. The rated cw output is
$2\text{\,}\mathrm{W}$. All power measurements are accurate to
$5\text{\,}\mathrm{\char 37\relax}$. (c) Instantaneous output power as a
function of time and pulse length (see legend) in
$2\times$81\text{\,}\mathrm{ps}$$ time bins. (d) as (c) but on a logarithmic
scale. Slight ringing after the pulses, four orders of magnitude below the
peak amplitudes, is visible on timescales similar to the pulse length,
whereupon the steady state IER is reached. (e) Behavior for longer pulse
duration, revealing short term overshooting on mildly sloped rectangular pulse
shapes.

The instantaneous power available within a pulse is generally the primary
factor in determining achievable Rabi frequencies with which to drive an
optical transition. As suitable lenses are simple objects, appropriate
intensities are almost always obtainable and the power therefore sets the
maximum mode volume addressable by optical control. This figure of merit is
obtained in two steps. Short pulses of programmed length $\tau$ are generated
every $T=$1\text{\,}\mathrm{\SIUnitSymbolMicro s}$$. A slow-integrating
thermal power sensor (Thorlabs S401C, $5\text{\,}\mathrm{\char 37\relax}$
measurement uncertainty) is used to determine the average output power. The
time averaged powers follow the naively expected relation of
$2\text{\,}\mathrm{W}$ specified continuous output at $4\text{\,}\mathrm{A}$
current times the programmed pulse duty cycle $D=\tau/T$ quite closely, data
are shown in Fig. 2(b). Notable is the overshoot on specification for short
pulses.

Time resolved photon rate data from the SNSPD yield the pulse shapes with
$162\text{\,}\mathrm{ps}$ time resolution and relative amplitude information
over six orders of magnitude. To avoid errors stemming from detector dead
time, average detection rates are lowered to
$<$1\text{\times}{10}^{5}\text{\,}{\mathrm{s}}^{-1}$$. This ensures accurate
amplitude resolution on short term ringing at the cost of dynamic range, a
worthy trade-off as the steady state IER of the TA is only
$58\text{\,}\mathrm{dB}$ and thus relatively easily resolvable. Short time
switching behavior is shown in Figs. 2(c) and 2(d). These data are normalized
to agree with the average power, yielding the absolute amplitudes after
isolation and filtration to $5\text{\,}\mathrm{\char 37\relax}$ accuracy.

A comparison of the few nanosecond scale pulses to longer ones,
$20\text{\,}\mathrm{ns}100\text{\,}\mathrm{ns}$ range shown in Fig. 2(e),
reveals fortuitous abnormal behavior of the amplifier on short time scales. As
inversion builds, the amplifier output rises to a maximum value in about
$3\text{\,}\mathrm{ns}$ ($10:90$), but as foreshadowed by the average powers
and confirmed by longer pulses, this initial peak is a considerable overshoot
of its specified output and is maximally maintained for about
$5\text{\,}\mathrm{ns}$. The driver is designed to limit the peak current
supplied to the TA and indeed should not be capable of passing more than the
$4\text{\,}\mathrm{A}$ rated maximum through the TA by design. Limited control
over the driver’s behavior is possible via the compliance voltage, but
adjusting this value has had no effect on unexpected extra optical output, and
it thus could be inherent to the response of the amplifier. As the output is
into free space optical damage is of no additional concern, but naturally some
general caution, e.g. with fiber end facets, is advisable at these powers.
Note that the overshoot can be eliminated by a more conservative choice of set
current at the price of lower peak and average output powers, however, as high
peak powers are desirable, I have chosen to operate this TA as is over
multiple months without finding performance degradation. One notable side
effect is that the falling flank of the optical pulses follows two time
scales, one set by the return from overshoot to the expected output power, and
one corresponding to the current switching off. On short pulses these overlap
and produce a roughly piecewise-linear falling flank. On long pulses, however,
they are temporally well separated and can thus be cleanly specified to about
$3\text{\,}\mathrm{ns}$ ($90:10$) and $1.5\text{\,}\mathrm{ns}$ ($90:10$)
respectively. The latency of the device, defined and measured as above, is
$41\text{\,}\mathrm{ns}$ for short pulses, increasing by a further
$17\text{\,}\mathrm{ns}$ for $\tau\geq$10\text{\,}\mathrm{ns}$$.

##  III RF Pulsing Laser Diodes for Chirping

We now turn to the question whether this current modulation approach can be
profitably applied to establish laser phase control as well. For a single mode
diode laser to emit light at a specific, stable frequency, the current passing
though it should be constant. Therefore, to ensure reliable operation for all
applications requiring spectroscopic accuracy, cw diode lasers are typically
driven by current sources. These drivers rapidly vary the diode voltage, often
within certain limits for over voltage protection, to maintain a stable set
current running through it. On long time scales, such as those at play when
adjusting the set current by hand via a potentiometer, frequency shifts of
$100\text{\,}\mathrm{MHz}$ can correspond to current changes as small as
$1\text{\,}\mathrm{mA}$. Devices capable of adding a nanosecond scale current
pulse of such an amplitude onto a constant current two orders of magnitude
larger fall well outside of typical design specifications. Pulsed laser
drivers usually strive to reach peak currents within
$0.1\text{\,}\mathrm{A}1\text{\,}\mathrm{A}$, resulting in poor resolution at
such low amplitudes. Moreover, with some exceptions once again born from
telecom applications, they typically cannot drive the
$50\text{\,}\mathrm{\SIUnitSymbolOhm}$ loads of standard bias-tees,
complicating the addition of the pulse onto a constant current.

In comparison to the regulatory timescale of a constant current source, a
frequency chirp of a few nanoseconds effectively requires a fast transient
effect on the instantaneous diode current. Intuitively, it is equivalent to
achieve this by modifying the voltage across the diode much faster than the
driver responds to stabilize the current. I pursue this approach by
connectorizing a $9\text{\,}\mathrm{mm}$ TO-can laser diode (Toptica
LD-0790-0120-AR-3) in a home built interference filter based external cavity
laser housing to a bias-tee (Minicircuits ZFBT-4R2GW-FT+). I run the output of
a standard analog laser current driver (Toptica DCC 110) through the bias-
tee’s DC port while applying fast voltage signals from a pulse generator
(Picoquant PPG512, $200\text{\,}\mathrm{ps}$ horizontal,
$8\text{\,}\mathrm{bit}$ vertical resolution, $12\text{\,}\mathrm{V}$ maximum
amplitude into $50\text{\,}\mathrm{\SIUnitSymbolOhm}$) to the rf port. As
diodes respond very differently to fast transients than in cw[18], the
resultant effect is ill-suited to quantitative _a priori_ predictions. I
proceed with an optical characterization of this “chirp laser”.

Figure 3: (a) Frequency chirps closely follow the $5\text{\,}\mathrm{ns}$ FWHM
Gaussian shapes programmed onto the applied rf pulses. The amplitudes must be
calibrated by this kind of optical characterization initially, but thereupon
quite arbitrary chirps can be generated with minimal effort. (b) The chirp
amplitude scales linearly with the amplitude of the applied rf pulse. The
orange line is a fit to the slope alone yielding a scaling of
$123(2)\text{\,}\mathrm{MHz}\text{\,}{\mathrm{V}}^{-1}$.

The chirp laser is offset locked at a frequency of
$\omega_{c}=2\pi\times$1.261\text{\,}\mathrm{GHz}$$ to an auxiliary laser,
which is itself locked to a rubidium line. The lasers are interfered on a
$50:50$ beam splitter and one output is detected by a biased photo diode
(Hamamatsu PD G4176-03, $30\text{\,}\mathrm{ps}$ rise and fall times). The
resulting beat note is registered by a frequency counter (aim-TTi TF930) and
is used to digitally generate feedback to a piezo modifying the laser cavity
length using a computer run PI-control LabVIEW routine and integrated analog
I/O card (NI PCIe-6363). Its long term frequency is thus stabilized to
$\omega_{\text{CL,set}}=2\pi\times$377.110\,526(1)\text{\,}\mathrm{THz}$$. For
characterization purposes this is an arbitrary choice, important is only that
$\omega_{c}$ is sufficiently larger than the frequency chirps to be measured.
Simultaneously, the beat note between the lasers is monitored from the second
beam splitter output with a fiber coupled photo detector (Thorlabs DXM25CF,
$25\text{\,}\mathrm{GHz}$ bandwidth) and oscilloscope (Tektronix DSO6,
$2.5\text{\,}\mathrm{GHz}$ bandwidth), and the diode’s intensity response is
recorded separately using a more economical detector (Thorlabs DET025AFC/M).
The setup for this measurement is included in Fig. 4.

The challenge at hand is simultaneously achieving high time and frequency
resolution near the Fourier limit. Even without applying rf pulses, the
standard deviation on the beat signal, stabilized to $\omega_{c}$ but recorded
in the time domain in a $200\text{\,}\mathrm{ns}$ trace, is about
$15\text{\,}\mathrm{MHz}$. This is true even when a pure tone from a signal
generator is measured in this manner and is merely a limitation of sampling,
without corresponding to any real fluctuation. To reveal induced shifts on
nanosecond timescales I proceed as advocated for by White et al.[26],
recording such short time traces of the beat note, then fitting sine waves to
the data in $1\text{\,}\mathrm{ns}$ windows. As the phase of the beat note
with respect to the timing of chirping rf pulses is random, averaging in
hardware merely erases the signal. Thus, to overcome statistical error, these
frequency fits are averaged in post-processing over 12500 traces enabling sub-
megahertz precision.

Both the amplitude and frequency response of the diode functionally follows
the applied rf pulses near perfectly. As a test case, I use Gaussian voltage
pulses of $5\text{\,}\mathrm{ns}$ FWHM and vary their amplitude. Pulse width
and flank form are imprinted onto the diode output. I forego an attempt to
directly measure instantaneous electrical signals across the diode, orienting
us by its optical response instead. I thus limit the amplitude of the rf
pulses such that the maximum rating of the diode’s optical output is not
exceeded at their peaks, using weak attenuation in the rf line to make full
use of the pulse generator’s vertical resolution. The resulting chirps are
shown in Fig. 3(a), with
$\Delta\omega_{\text{CL}}=\omega_{\text{CL}}-\omega_{\text{CL,set}}$. Each
trace in Fig. 3(a) corresponds to a single point in Fig. 3(b), where they are
identified by their amplitudes. The ringing visible after higher amplitude
pulses corresponds exactly to what is present in the electronic signal when
directly measured, i.e. it is not a result of how the rf pulses are applied to
the diode. A trace without a programmed pulse is included as well – here the
frequency determined by fitting and averaging varies (peak-to-peak) less than
$500\text{\,}\mathrm{kHz}$ from $\omega_{\text{CL,set}}$ over its duration.
The rf pulse amplitudes as measured into
$50\text{\,}\mathrm{\SIUnitSymbolOhm}$ that produce these chirps are shown in
Fig. 3(b). The data reveal an effectively Ohmic response of the diode to the
applied transient.

The positive and negative amplitude pulses are generated by different
generations of the same nominative model of pulse generator. The slight
difference in the temporal shape of positive and negative chirps can be traced
back to differences in the electronic pulse shapes of these two devices. This
is a choice of convenience as while both are unidirectional in amplitude one
happens to have been designed with inverted output. One such device plus a
sufficiently fast voltage inverter should yield an identical effect. In
addition to some ringing after the chirp, an amplitude dependent shift to the
baseline laser frequency is induced by positive voltage pulses despite
frequency stabilization. The scale of this shift is roughly
$8\text{\,}\mathrm{\char 37\relax}$ of the amplitude. As only one pulse
generator produces this effect, it is most probably an electronics problem.
Fortunately, it can be compensated for trivially by modifying the offset lock
frequency. For the steepest flanks producible by these pulse generators
(programmed rectangle) the effect on the optical output ($10:90$) is achieved
in $1.8\text{\,}\mathrm{ns}$, corresponding to a maximum chirp rate of about
$150\text{\,}\mathrm{MHz}\text{\,}{\mathrm{ns}}^{-1}$ at the greatest tested
rf amplitude. For this and any similar system this limit is ultimately a
function of risk tolerance, as eventually the rf power enters a regime where
diode damage becomes likelier. It is worth noting that, although analyzing
chirps by measuring changes in a beat note is laborious, once the
proportionality of the induced intensity and frequency shifts on the timescale
of interest is established, it is theoretically sound to extrapolate the
effect of similar duration voltage pulses on laser phase by simply measuring
amplitude variations. This drastically mitigates the effort required for
adjustments after an initial setup.

##  IV Chirped and Amplified Laser Pulses

Combination of the techniques presented so far to produce pulses with
instantaneous power amplitudes of $3\text{\,}\mathrm{W}$ and arbitrarily
shaped chirps within a few hundred megahertz is as simple as using the chirp
laser to optically seed the TA, then electronically aligning the rf pulse for
chirping to the current pulse for amplifying in time, accounting for insertion
and propagation delays. A complete setup of the combined system is sketched in
Fig. 4. As both amplitude and frequency vary dramatically over the short
duration of an amplified and chirped pulse, and as there is no measurable
reference beat note outside of the amplification time, frequency analysis as
performed above suffers from technical artifacts and is accurate when
performed with automated routines befitting the data volume only over the very
short durations for which the pulses are fully on. Therein the data agree with
the characterization shown in Fig. 3(a), and short chirp pulses on top of
longer stretches of amplification also reproduce the data of the previous
section. Including all device and propagation induced delays, the output can
be produced in less than $65\text{\,}\mathrm{ns}$ upon receiving an
asynchronous external trigger.

Figure 4: Experimental setup to produce and characterize chirped and amplified
laser pulses, on-demand and entirely with direct current modulation. DDG
digital delay generator, VPG voltage pulse generator, DCC constant current
source, I in laser current input, X:Y beam splitter with ratio R:T, DL diode
laser, PD photo detector, FC frequency counter, PC computer running PI control
software, I/O analog input/output card, PZT in laser piezo input, IPG current
pulse generator, TA tapered amplifier, FI Faraday isolator, IF interference
filter.

Amplification of chirped pulses has a significant advantage beyond just
reaching higher peak powers. The TA saturates from $20\text{\,}\mathrm{mW}$
input, and it tolerates up to $50\text{\,}\mathrm{mW}$ of injected seed light.
Thus, there exists an operating regime where it is saturated for all
instantaneous input powers present during a chirp. This tempers undesired
intensity modulation on the output pulse. The maximum input power variation
resulting from chirping produces less than $2\text{\,}\mathrm{\char 37\relax}$
output power variation from the TA, tending towards zero with increasing pulse
length. Implemented with an amplifier suited for cw operation, this approach
would decouple phase and amplitude control despite relying on direct current
modulation. Moreover, in the typical use case of optical pulses where
desirable chirp coincides with intensity variation, ringing in the chirp
signal is made irrelevant as the amplitude modulation effectively gates it
away.

##  V Applications, Limitations, and Outlook

High power laser pulses are an important tool of quantum control. Generally
speaking, they are used to drive transitions, e.g. Raman transitions in atom
optics. Optimal control often simultaneously demands that these pulses exhibit
some chirp, for instance to maintain adiabaticity conditions [27] or tailor
forces on atoms [28]. As a particularly illustrative example as well as the
initial motivation for this investigation, consider the application of a
quantum memory for spectrally broad single photons[29, 30]. An ensemble of
three-level lambda systems has 2 metastable ground states which we label
$\ket{s}$ and $\ket{g}$. The systems are prepared in $\ket{g}$. An incoming
signal is near resonant to the transition from the prepared ground to the
third, excited state $\ket{g}$–$\ket{e}$. Ideally, a strong control pulse on
the $\ket{e}$–$\ket{s}$ transition and in two-photon resonance with the signal
can now be used to map the photon into a spinwave excitation between the two
ground states. In the appropriate limit for fast processes, the bandwidth of
this memory scheme is roughly equal to the Rabi frequency of the control,
which in turn is linear in its amplitude. The problem with a fixed frequency
control pulse is apparent – as its peak amplitude is necessarily high for a
broadband signal, the pulsed control induces a time varying light shift on
$\ket{s}$, precluding the optimal storage conditions of continuous two-photon
resonance. This effect is known to limit memory efficiencies in high
bandwidth, off-resonant storage schemes [31, 32, 33]. Critically, to interface
such memories with probabilistic photon sources or to make use of them in
realistic networking applications requires that all of their components
rapidly respond to an asynchronous external trigger. This is typical of
technological applications.

For this class of experiments the current-based approach to chirping and
amplifying shines particularly brightly. It is conceptually and
technologically simple and exceptionally performant for its price point. It
offers less flexibility in amplitude shaping and cannot reach the same
chirping range as state-of-the-art external modulation systems[16], not even
by ignoring absolute maximum ratings. Moreover, it demands some
straightforward optical characterization of the performance for every diode
the technique is implemented with, which scales only tediously. Nevertheless,
all characterizations here have yielded neat and predictive phenomenology for
reasonable effort. In exchange, switching, pulsing and chirping are all
achieved rapidly upon demand and with vastly superior intensity extinction
than any external modulation system matching the speed and power handling.
These attributes make this approach the prime candidate for experiments that
have been treading the most common path of quantum technological
investigations where optimal control requires chirping, which is just to forgo
optimal control. Similarly, many experiments with photons limited by control-
induced noise or hampered in their rates by required filters can benefit from
the high intensity extinction ratios demonstrated here, likely even by using
already commercialized devices.

###### Acknowledgements.

I cordially thank Philipp Treutlein for feedback on the manuscript and probing
questions pushing the quality of my device characterizations, Michael
Steinacher for his design of the SOA driver and helpful conversations
regarding the rf pulsing of the laser diode, Roberto Mottola for obtaining the
butterfly packaged TA and high current driver, including a custom solution to
an atypical diode pin layout, and Janik Wolters, who has always claimed that
atomic physics should borrow ideas from the telecom realm with more
enthusiasm. Further, I gratefully acknowledge financial support from the Swiss
National Science Foundation and the Swiss State Secretariat for Education,
Research, and Innovation (SERI) through the project Scalable High Bandwidth
Quantum Network (sQnet).

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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