Cavity-enhanced single-shot readout of a quantum dot spin within 3 nanoseconds Nadia O. Antoniadis1Mark R. Hogg1Willy F. Stehl1Alisa Javadi1Natasha Tomm1R udiger Schott2Sascha R. Valentin2Andreas D. Wieck2Arne Ludwig2and Richard J. Warburton1y

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Cavity-enhanced single-shot readout of a quantum dot spin within 3 nanoseconds

Nadia O. Antoniadis,1, ∗Mark R. Hogg,1, ∗Willy F. Stehl,1Alisa Javadi,1Natasha Tomm,1R¨udiger

Schott,2Sascha R. Valentin,2Andreas D. Wieck,2Arne Ludwig,2and Richard J. Warburton1, †

1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

2Lehrstuhl f¨ur Angewandte Festk¨orperphysik, Ruhr-Universit¨at Bochum, D-44780 Bochum, Germany

(Dated: October 26, 2022)

Rapid, high-ﬁdelity single-shot readout of quantum states is a ubiquitous requirement in quantum

information technologies, playing a crucial role in quantum computation, quantum error correction,

and fundamental tests of non-locality. Readout of the spin state of an optically active emitter can

be achieved by driving a spin-preserving optical transition and detecting the emitted photons. The

speed and ﬁdelity of this approach is typically limited by a combination of low photon collection

rates and measurement back-action. Here, we demonstrate single-shot optical readout of a semi-

conductor quantum dot spin state, achieving a readout time of only a few nanoseconds. In our

approach, gated semiconductor quantum dots are embedded in an open microcavity. The Purcell

enhancement generated by the microcavity increases the photon creation rate from one spin state

but not from the other, as well as eﬃciently channelling the photons into a well-deﬁned detection

mode. We achieve single-shot readout of an electron spin state in 3 nanoseconds with a ﬁdelity of

(95.2±0.7)%, and observe quantum jumps using repeated single-shot measurements. Owing to the

speed of our readout, errors resulting from measurement-induced back-action have minimal impact.

Our work reduces the spin readout-time to values well below both the achievable spin relaxation

and dephasing times in semiconductor quantum dots, opening up new possibilities for their use in

quantum technologies.

I. INTRODUCTION

The ability to perform a projective measurement of

a quantum state in a single measurement (single-shot

readout) is an enabling technique in quantum technolo-

gies [1, 2]. Single-shot readout is necessary in quantum

computation in order to extract information at the end

of the protocol, as well as in error detection and cor-

rection as the quantum processor runs [3]. Additionally,

single-shot readout is necessary to close the fair-sampling

loophole in tests of quantum non-locality, and was a key

ingredient in recent demonstrations of loophole-free Bell

inequality violations [4]. The ideal single-shot readout

protocol achieves high-ﬁdelity qubit readout in the short-

est time possible; readout within the qubit dephasing

time is essential for quantum error correction, and en-

ables measurement-based quantum feedback [5, 6] and

quantum trajectory tracking [7].

The spin states of semiconductor quantum dots (QDs)

show exceptional promise in quantum technology [8–10].

Optically-active QDs, established bright and fast sources

of coherent single photons [11–14], can be occupied with

a single electron and the electron spin can be initialised

[15, 16] and rotated on the Bloch sphere [17, 18] on

nanosecond timescales using all-optical techniques. The-

oretical proposals [19, 20] and recent experiments [21–

23] have established the spin-photon interface provided

by the InGaAs platform as a leading contender for cre-

ating photonic cluster states, an important resource for

∗These two authors contributed equally

†To whom correspondence should be addressed:

mark.hogg@unibas.ch, richard.warburton@unibas.ch

quantum repeaters [24] and measurement-based quantum

computation [25]. The dephasing time of the electron

spin in optically-active QDs is limited by magnetic noise

arising from the nuclear spins. However, there are pow-

erful mitigating strategies. A double-QD can be used to

create a clock-transition [26]; a switch to a hole spin sup-

presses the eﬀect of the magnetic noise particularly in

an in-plane magnetic ﬁeld [27, 28]; and the noise can be

almost eliminated by laser-cooling the nuclei [29, 30]. In

the context of cluster states, spin readout is necessary in

order to disentangle the spin from the photons, thereby

releasing an entirely photonic entangled state. To date,

single-shot spin readout on a timescale comparable to

the rapid spin initialisation and manipulation times has

remained elusive.

Spin readout with an optical technique typically pro-

ceeds by applying a magnetic ﬁeld to a QD contain-

ing a single electron, resonantly driving one of the

Zeeman-split trion transitions, then collecting the spin-

dependent resonance ﬂuorescence [31]. However, during

readout, the applied laser can induce an unwanted spin

ﬂip [32, 33], a process known as ‘back-action’. The key

challenge for spin readout is to collect enough photons to

determine reliably the spin state before the back-action

ﬂips the spin. Of the small number of previous experi-

ments to achieve single-shot readout of InGaAs QD spin

states [34–36], the most rapid to date achieved a ﬁdelity

of 82% in a readout time of 800 ns [35]. This 800 ns read-

out time was similar to the back-action timescale, and is

signiﬁcantly longer than the dephasing time for an elec-

tron spin bound to an InGaAs QD (T∗

2= 125 ns following

nuclear bath cooling [29, 30]).

In this work, we report nanosecond-timescale, all-

optical, single-shot spin readout. We use an open mi-

arXiv:2210.13870v1 [quant-ph] 25 Oct 2022

-50 0 50

Laser Detuning (GHz)

Intensity

100

Repetitions

024

Time (ns)

0.5

Count fraction

Readout

pulse

laser

AWG

SNSPD

EOM

PBS

98 %

1.8 ns

Start

read

laser

AWG

SNSPD

EOM

PBS

Trion

splitting

cavity

modes

(a)

(c)

(b)

H V

FIG. 1. Experimental setup and system eﬃciency. (a)

Resonant laser pulses with variable intensity and duration

are sent to the QD using an electro-optic modulator (EOM)

driven by a fast arbitrary waveform generator (AWG). The

photons emitted by the QD are collected in the output arm

of the cross-polarised microscope and measured on a SNSPD

(superconducting nanowire single photon detector). (b) Fre-

quency conﬁguration of the QD and mode-split cavity with

respect to the laser. With a 2.0 T magnetic ﬁeld, only one

trion transition is resonant with the H-polarised cavity mode,

resulting in spin-selective Purcell enhancement. (c) Read-

out characterisation at zero magnetic ﬁeld: here, the readout

pulses are set to a duration of 2 ns (top panel) with a repeti-

tion time of 100 ns. Photons emitted by the QD are detected

and the arrival times registered for 100,000 repetitions of the

pulse sequence; 100 example traces are depicted in the middle

panel where the blue dots represent a photon detection event.

In 98% of the repetitions a photon is detected within 1.8 ns.

crocavity to boost the photon collection eﬃciency in or-

der to reduce the spin readout time. We achieve single-

shot readout in only 3 nanoseconds with a ﬁdelity of

(95.5±0.7)%, an improvement in readout speed of more

than two orders of magnitude with respect to previ-

ous experiments. To the best of our knowledge, this is

the fastest single-shot readout of a quantum state ever

achieved across any material platform. Our approach

brings the readout time well below the dephasing time

for an electron spin in this system. Our open microcav-

ity approach can be used to enhance optical spin readout

in other systems, such as nitrogen vacancy centres in di-

amond [37].

II. RESULTS

A. High eﬃciency photon collection

A schematic of the setup used in our experiments is

shown in Fig. 1 (a). Our sample is a gated, charge-

tunable InGaAs/GaAs device, with a highly reﬂective

Bragg mirror integrated into the semiconductor het-

erostructure [14, 38]. The gate structure allows the

charge occupancy of the QD to be set, as well as ﬁne tun-

ing of the emission frequency via the quantum-conﬁned

Stark eﬀect. We operate with a single electron occupying

the QD, which is our spin readout target. A miniaturised

Fabry-P´erot cavity is created between the semiconductor

bottom mirror and a free-standing concave top mirror.

The QD sample is attached to an XYZ nano-positioning

stage. This ﬂexibility of the open microcavity design al-

lows the cavity to be re-positioned to address a chosen

QD. Once a QD is positioned at the anti-node of the cav-

ity ﬁeld (XY positioning), its frequency can be matched

to one of the QD transitions (Z positioning).

Figure 1 (c) demonstrates the high photon collection ef-

ﬁciency of our microcavity system and its potential for

rapid spin readout. A photon emitted by the QD exits

the output facet of the collection single-mode ﬁbre with

57% probability [14]. The overall system eﬃciency, η, the

probability that an exciton in the QD results in a click

on the detector, is 37%. Initially, we set the magnetic

ﬁeld to zero, such that the optical transitions for both

electron spin states are degenerate. In this scenario, a

resonant laser pulse excites the QD optical transition re-

gardless of the electron spin state. The readout pulse

drives the optical transition, and the QD emits photons

at a rate set by the (Purcell-enhanced) optical decay rate.

The time required for a photon emitted from the QD to

be registered by the detector depends on the overall sys-

tem eﬃciency; for high eﬃciencies a photon is rapidly de-

tected. We apply a train of 2 ns readout pulses (temporal

shape close-to-square, separated by 100 ns, with an op-

tical power equal to six times the QD saturation power)

to the QD, and monitor the collected photons on the

single photon detector (an SNSPD). The SNSPD has a

dead time of ∼12 ns, meaning that after one photon has

been detected another detection event stemming from the

same pulse is extremely unlikely. Thus, although the QD

emits at a constant rate during the 2 ns readout pulse,

a maximum of one photon detection event occurs. We

repeat the pulse sequence 100,000 times, and analyse the

fraction of pulses in which a photon was detected as a

function of the readout duration. We note that although

the readout pulse length is ﬁxed to be 2 ns in the exper-

iment, we can determine the fraction of pulses contain-

ing a detection event as a function of a software-deﬁned

read duration that is less than 2 ns by analysing the pho-

ton time-of-arrival data. We ﬁnd that for 98% of the

traces, a photon is detected within 1.8 ns (see bottom

panel Fig 1(c)). When the same pulse sequence is re-

peated with the QD detuned out of resonance with the

readout laser, we detect a photon (due to laser leakage

within the cross-polarised setup) for <0.1% of the pulses,

demonstrating that the photons we detect are almost ex-

clusively created by the QD.

0.2

0.4

Count fraction

012345

Time (ns)

0.6

0.8

Fidelity

0.2

0.4

Count fraction

012345

Time (ns)

Errors

0.5

Photon counts

Time (ns)

(a) (b) (c) (d)

|〉

Fidelity = 95.2 %

Bright state: Bright state:

ebright = 6.9 %

edark = 2.6 %

0.1

0.2

0.3

FIG. 2. Single-shot readout of the QD spin at 2.0 T. (a) Example single-shot readout traces. If a photon is detected

during the readout pulse, the state of the QD is assigned to the bright state (here, spin up |↑i). Repetitions with no detected

photon are assigned to the dark state (here, spin down |↓i). (b) Schematic of the QD energy levels in a magnetic ﬁeld, indicating

the readout transition (here, bright state |↑i, blue arrow) and the cavity frequency. (c)/(d) Experimental count fraction (top)

and corresponding readout ﬁdelity/errors (bottom) as a function of readout time for the bright state being up/down. Here,

readout pulses with a duration of 5 ns are used. The pulse sequence is repeated 100,000 times. We achieve a readout ﬁdelity

of 95.2% for a readout time of 3 ns.

B. Single-shot spin readout

To perform single-shot spin readout, we apply a mag-

netic ﬁeld of 2.0 T along the growth direction of the sam-

ple (Faraday conﬁguration), which creates a four-level

system in which the two strongly allowed trion transitions

are split by 55 GHz (the sum of the electron and hole Zee-

man splittings, 6.8 GHz/T and 20.7 GHz/T respectively).

Spin readout is achieved by tuning the cavity into reso-

nance with one of the strongly allowed transitions, as

shown in Fig. 2(b). The readout pulse sequence is then

similar to that shown in Fig. 1(c), but photon emission

is now only enhanced for the trion transition resonant

with the cavity. Figure 2 (a) shows example single-shot

readout traces: here, we apply a train of readout pulses

(5 ns duration with a repetition time of 100 ns) resonant

with the cavity-enhanced |↑i ↔ |⇑,↑↓i trion transition.

We note that for this experiment, the frequency align-

ment of cavity modes and trion transitions is identical to

that shown in Fig. 1 (b). If the electron is projected into

the |↑i spin state, Purcell-enhanced ﬂuorescence from the

|↑i ↔ |⇑,↑↓i trion will be rapidly registered by the de-

tector. The spin is thus projected into the “bright” state,

and detecting a single photon emitted by the QD during

the readout pulse constitutes a measurement of the spin

state. Conversely, if the electron is projected into the

|↓i (“dark”) spin state no ﬂuorescence is detected, as the

|↓i ↔ |⇓,↑↓i trion is out of resonance with the readout

laser. In this case, the absence of a detector event during

the readout pulse indicates that the spin was projected

into the dark state. We stress again that the readout time

is less than the dead time of the detector: a maximum of

one photon can be measured during the readout process.

Furthermore, the overall system eﬃciency is high enough

that the absence of a detected photon contains signiﬁcant

information: it denotes that the spin was projected into

the dark state. The detection is thus binary: detection

of one photon corresponds to the |↑i state, and zero pho-

tons to the |↓i state. Equivalently, our photon number

threshold for discriminating the spin states is one single

photon.

We repeated the spin-readout measurements with the

cavity and readout laser tuned such that either |↑i or

|↓i is the bright transition. In Fig. 2 (c) we show the

results of 100,000 repetitions of the spin readout pulse

sequence with |↑i set as the bright state (the conﬁgura-

tion shown in Fig. 2 (b)). We plot the fraction of readout

traces containing one photon, i.e. the fraction of traces

we assign the electron spin state to be |↑i. We observe

a rapid increase in the count fraction (on a timescale of

a few nanoseconds) as a function of the readout time.

Compared to the 0 T results in Fig. 1 (c), the maxima

of the count fractions now saturate close to 50%: each

spin state is almost equally likely. The reason is that the

spin is not initialised in these experiments. Instead, be-

fore readout, the spin is in a mixed state as co-tunnelling

between the QD and the Fermi sea of the back contact

regularly randomises the spin state (on a timescale of

∼300 ns) during the 100,000 readout pulse repetitions,

such that both |↑i and |↓i spin states have approximately

equal probabilities. Figure 2 (d) shows data for 100,000

repetitions of the readout pulse sequence, now with the

readout laser resonant with the low frequency trion tran-

sition, |↓i ↔ |⇓ ↑↓i (thus making the |↓i state the bright

state and |↑i the dark state).

Compared to the 0 T readout in Fig. 1(c), the readout

speed is slightly slower (high-ﬁdelity readout is achieved

in 3 ns rather than 1.8 ns). The reason for this slower

readout is that at 2.0 T we operate with the laser on

resonance with the QD but detuned by 7.5 GHz from

the actual cavity resonance, where we observe optimal

laser suppression at the cost of a reduced Purcell fac-

tor (FP= 6.1 compared to FP= 8.5 exactly at reso-

nance). Consequently, the readout speed is slightly re-

duced compared to 0 T. However, we still achieve high-

ﬁdelity single-shot spin readout within 3 ns.

In order to estimate the spin-readout ﬁdelity, we per-

form Monte Carlo simulations of the single-shot traces

with parameters matching our experiment. The simu-

lations include only a few parameters: the overall sys-

tem eﬃciency η, the Purcell factor FP, and the spin-ﬂip

time, i.e. the relaxation time, T1. At B= 0, η= 37%.

At B=2.0 T, technical issues result in a slightly reduced

eﬃciency, η= 25% (Supplementary Sec. VI). The spin

T1= 158 ns was measured via the quantum jump ex-

periments discussed in the next section. We deﬁne the

readout-time-dependent ﬁdelity as [34]

F(t)=1−pbright ·ebright(t)−pdark ·edark(t),(1)

where pbright (pdark) is the occupation probability of the

bright (dark) state, and ebright (edark) the respective

time-dependent probability of assigning the spin state

incorrectly. The spin occupation probability distribution

depends on the spin-ﬂip rates, as well as the readout

pulse duration and repetition rate; for our experiments

it is approximately 50:50 (|↑i:|↓i). The error ebright is

determined on these timescales by imperfect overall sys-

tem eﬃciency (which can lead to a spin projected into

the bright state being incorrectly assigned as the dark

state should no photon be detected). The error edark is

determined by laser leakage (which can lead to a spin

projected into the dark state being incorrectly assigned

as the bright state). Errors due to spin-ﬂips during the

readout time (either due to laser back-action or spin re-

laxation) play a minor role in our experiment. Our Monte

Carlo simulations capture all of these error sources quan-

titatively (edark = 2.6%, ebright = 6.9% at 3 ns; full details

of the ﬁdelity calculation and the inﬂuence of readout

errors can be found in Supplementary Sec. VI). The sim-

ulated count fractions show very good agreement with

our experimental results and allow us to extract a max-

imum readout ﬁdelity of (95.2±0.7)% in 3 ns. The cal-

culated readout ﬁdelity as a function of readout-time for

the conﬁgurations with |↑i and with |↓i as the bright

state is plotted in Figs. 2(c) and (d), respectively.

C. Repeated readout and quantum jumps

The fast spin readout enables us to probe the electron

spin dynamics. By repeated single-shot measurements of

the spin state, we can determine the spin-ﬂip time from

the correlation between sequential measurements. Addi-

tionally, we can track the electron spin state in real time,

observing quantum jumps as the spin ﬂips. In Fig. 3 (a)

we perform a pulse sequence consisting of two readout

pulses separated by a time τ. Here we ﬁx the length of

both readout pulses to be 3 ns, and the pulse repetition

time to be 400 ns. The ﬁrst readout pulse is a projec-

tive measurement of the spin state: in eﬀect, the spin is

initialised at τ= 0 with a ﬁdelity given by either ebright

or edark. The second readout pulse can then be used to

determine the spin state at τ > 0 allowing us to measure

the correlation between the two measurement outcomes

as a function of τ. Figure 3 (a) shows the conditional

probability of measuring spin |↑i in the second pulse (as

a function of τ), given that the ﬁrst read result returned

|↑i. We note that the minimum spacing between the two

pulses is limited to τ&12 ns by the dead time of the

detector. Increasing τdecreases the probability of read-

ing out the same spin state for both pulses due to spin

ﬂips, and for large τthe second read is completely un-

correlated with the ﬁrst. By ﬁtting an exponential decay

to the data in Fig. 3 (a), we extract a spin-ﬂip time of

150 ±30 ns. Furthermore, the limit as τ→0 of this

conditional probability is approximately 1 −ebright, con-

ﬁrming the value of ebright determined from the Monte

Carlo simulations. Similarly, a measurement of the dark-

dark conditional probability conﬁrms the value of edark.

Given that our readout sequence is much shorter than

the spin lifetime, we can use repeated single-shot mea-

surements to detect real-time quantum jumps of the elec-

tron spin state. For that purpose, we send in a train of

3 ns readout pulses spaced by the minimum 12 ns allowed

by the detector’s dead time. We observe quantum jumps

in the spin state, as shown in Fig. 3(b). (In the original

quantum jump experiment, the quantum jumps between

the bright and dark states were driven with weak co-

herent excitation [39]. Here, the jumps are driven by

a dissipative process, energy exchange with the Fermi

sea via co-tunneling.) The time between spin-ﬂip events

during a 2.4 ms total acquisition period is extracted and

summarised in the histogram in Fig. 3(c). From the ex-

ponential decay in the number of events per ﬂip time,

we can extract the spin-ﬂip time to be approximately

165 ns, consistent with the results from the double-pulse

experiment in Fig. 3(a).

III. DISCUSSION AND OUTLOOK

We have demonstrated that the frequency-selective

Purcell enhancement provided by our optical microcav-

ity enables us to perform single-shot readout of a QD

spin state within a few nanoseconds, with a ﬁdelity as

high as 95%. Our results bring the spin readout time

for semiconductor QDs close to the short optical spin

manipulation times [17, 18], and well below previously

demonstrated relaxation (T1) [40] and dephasing (T∗

times [18, 29, 30]. For recent loophole-free Bell tests, en-

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Cavity-enhancedsingle-shotreadoutofaquantumdotspinwithin3nanosecondsNadiaO.Antoniadis,1,MarkR.Hogg,1,WillyF.Stehl,1AlisaJavadi,1NatashaTomm,1RudigerSchott,2SaschaR.Valentin,2AndreasD.Wieck,2ArneLudwig,2andRichardJ.Warburton1,y1DepartmentofPhysics,UniversityofBasel,Klingelbergstrasse82,CH-4056Base...

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Cavity-enhanced single-shot readout of a quantum dot spin within 3 nanoseconds Nadia O. Antoniadis1Mark R. Hogg1Willy F. Stehl1Alisa Javadi1Natasha Tomm1R udiger Schott2Sascha R. Valentin2Andreas D. Wieck2Arne Ludwig2and Richard J. Warburton1y.pdf

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Cavity-enhanced single-shot readout of a quantum dot spin within 3 nanoseconds Nadia O. Antoniadis1Mark R. Hogg1Willy F. Stehl1Alisa Javadi1Natasha Tomm1R udiger Schott2Sascha R. Valentin2Andreas D. Wieck2Arne Ludwig2and Richard J. Warburton1y

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