Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory

2 MB·English

by  Jun Rui

Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum
Memory
Jun Rui,1,2 Yan Jiang,1,2 Sheng-Jun Yang,1,2 Bo Zhao,1,2 Xiao-Hui Bao,1,2 and Jian-Wei Pan1,2
1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics,
University of Science and Technology of China, Hefei, Anhui 230026, China
2CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics,
University of Science and Technology of China, Hefei, Anhui 230026, China
Spin echo is a powerful technique to extend atomic or nuclear coherence time by overcoming the
dephasing due to inhomogeneous broadening. However, applying this technique to an ensemble-
based quantum memory at single-quanta level remains challenging. In our experimental study
we find that noise due to imperfection of the rephasing pulses is highly directional. By properly
arranging the beam directions and optimizing the pulse fidelities, we have successfully managed to
5 operate the spin echo technique in the quantum regime and observed nonclassical photon-photon
1 correlations. In comparison to the case without applying the rephasing pulses, quantum memory
0 lifetimeisextendedby5folds. Ourworkforthefirsttimedemonstratesthefeasibilityofharnessing
2 the spin echo technique to extend lifetime of ensemble-based quantum memories at single-quanta
n level.
a
J PACSnumbers: 32.80.Qk,42.50.Gy,42.50.Md,03.67.-a

6
2
Recent years have witnessed remarkable progresses in the π pulses is highly directional. In our experiment, by

thedevelopmentofquantummemorieswithphotonicin- carefully arranging the Raman-beam directions and op-
]
h terface. Many quantum systems [1], such as single neu- timizingthepulsefidelities,wehavesuccessfullyreduced
p
tral atoms [2, 3], single trapped ions [4, 5], single quan- this noise to much lower than the single-photon signal.
-
t tum dots [6, 7], solid-state ensembles [8] and atomic-gas Quantum nature of the spin echo process is verified by
n
ensembles[9]havebeenemployedtostoresinglephotons observing nonclassical photon-photon correlations. In
a
u or create entanglement with a single photon. Among our demonstration, the distorted spin-wave state gets
q them, the atomic-ensemble approach [10] is particularly rephased by applying two π pulses and the quantum
[ attractive since the light-matter coupling is largely im- memorylifetimeisincreasedby5folds. Ourfindingsand

1 proved by collective enhancement. Plenty of important techniques developed is applicable to all other ensemble-
v experimental progresses have been made in recent years based quantum memories [1].
8 [8, 9, 11]. In an atomic-ensemble quantum memory, a single
7
quantum state is stored as a spin wave spreading over
2 In an atomic-ensemble quantum memory, inhomoge-
thewholeensemble[19,20]. Thespin-wavestateatt=0
6 neous broadening due to ambient magnetic field, atomic
0 random motion and interaction with host spins etc. can be described as
.
1 severely limits the storage time [12, 13]. One universal N
1 (cid:88)
0 solutiontoovercomeinhomogeneousbroadeninginduced |Ψ(cid:105)gs = √ eiks·rj(0)|g...sj...g(cid:105),
5 N
decoherenceistomakeuseofthespinechotechnique[14], j
1
whereaseriesofπ pulsesareappliedtoreversethephase
: where N is the number of atoms, |g(cid:105) and |s(cid:105) are two
v evolution through population inversion. This technique
atomic ground states, k is the wavevector of the spin
i s
X has been widely used in storage of classical light pulses.
wave, r (0) is the position of the j-th atom in the en-
j
For example, with the spin echo technique, the storage
r semble at t=0. This state can be physically interpreted
a lifetime has been extended to second and minute regime
as a phase grating, which enables strong collective inter-
in solid-state ensembles and atomic-gas ensembles, re-
ference in the read-out process [20]. With this collective
spectively [15, 16]. However, whether this technique is
interference, efficient conversion from spin waves to pho-
applicable to the storage of quantum light or photons
tons has been demonstrated [21–23]. As the spin wave
hasnotbeenresolvedyetexperimentally. Themaincon-
is a collective exication over the whole ensemble, inho-
cern [17, 18] is that since the π pulses induce population
mogeneity of frequency or phase difference between the
inversion,tinyimperfectionofthemcouldresultinback-
atomic levels of |g(cid:105) and |s(cid:105) for all atoms will distort the
ground noises which are much stronger than the stored
relative phase between each term in |Ψ(cid:105) , thus results
gs
single-photon signals.
in a distorted phase grating. Atomic motion is one dom-
In this letter we experimentally study the spin echo inantdecoherencemechanismforatomic-ensemblequan-
process of single excitations in a cold-atomic-gas quan- tum memories [12, 24]. Within an atomic ensemble, the
tum memory by employing stimulated Raman transi- velocityv ofeachatomvariesfromatomtoatom,which
j
tions. We find that the noise due to imperfection of will distort the original phase grating in |Ψ(cid:105) . After a
gs
2
(a) (c)
Creation Rephasing Retrieval
EIT: ur ur
e ur k k
probe coupling ∆ k̟ θ̟ 2 pθs kurs
ur ur
g k2 k1 coupling k k
s (read) 1 c
SRS:
write pulses readout / V
Raman 1 / H
(b) read / H
(coupling) MOT
HWP
θ θ
PBS s ̟
write / V
write-out / H probe / V Raman 2 / V
FIG. 1: (color online). Experimental setup. (a) Two methods are used in creating spin-waves in an atomic ensemble. In
the electromagnetically induced transparency (EIT) process, a weak probe pulse at single-photon level is converted to atomic
spin waves by turning off the coupling beam. In the spontaneous Raman scattering (SRS) process, a single-quanta spin-wave
is imprinted in the atomic ensemble heralded by detecting a Raman scattered write-out photon. In the rephasing precess,
rephasing pulses which couple the |g(cid:105) ↔ |s(cid:105) transition through a two-photon Raman transition is applied. Later, spin-wave
statesareretrievedeitherbyturningonthecouplingorthereadbeam. (b)Schematicviewoftheexperimentalconfiguration.
Theatomicensembleispreparedthroughmagneto-opticaltrap(MOT).Thecouplingbeamandthereadbeamhavethesame
frequency, polarization and spatial mode, so do the the probe and read-out photon. H (V) refers to horizontal (vertical)
polarizationrelativetothedrawingplane. HWPandPBSrepresentshalf-waveplate,andpolarizedbeam-splitter,respectively.
(c) Momentum relationships for the control beams, detection modes and the Raman beams.
storagetimeoft=T,themismatchingphaseofj-thterm interval∆t=t −t . If∆φπ isequalto∆φ ,therandom
2 1 j j
in|Ψ(cid:105) is∆φ =k ·r (T)−k ·r (0)=k ·v T wherewe phasescancelwitheachotherandthusthespin-wavecan
gs j s j s j s j
assumetheatomsarefreelymovingwithr (T)=r (0)+ be efficiently read out at t = T. In this way, we obtain
j j
v T. This results in a storage time [12] of τ (cid:39) 1/k v¯ therephasingconditionof2k ∆t=k T,whichsetscrit-
j s s π s
with v¯ the average atomic thermal velocity. icalconstraintsonthedirectionofRamanbeamsandthe
time interval between the two π pulses, and the read out
This phase distortion can be eliminated by applying a
time T.
spin-echo rephasing technique. As shown in Fig. 1, we
applytwolaserbeamstoinducestimulatedRamantran- The layout of our experiment is shown in Fig. 1. An
sitions [25] between |g(cid:105) and |s(cid:105), where one laser couples ensemble of ∼108 87Rb atoms are loaded in a magneto-
the |s(cid:105) ↔ |e(cid:105) transition with a wavevector of k , and optical trap. After polarization-gradient cooling, the
1
the other laser couples the |g(cid:105) ↔ |e(cid:105) transition with a temperatureobtainedis∼10µK,andtheopticaldepthis
wavevector of k . The rephasing scheme is implemented ∼4. The energy levels employed are |g(cid:105)→|F =2,m =
2 F
by applying two Raman π pulses at t = t and t re- 0(cid:105), |s(cid:105)→|F =1,m =0(cid:105) and |e(cid:105)→|F(cid:48) =2,m =±1(cid:105)
1 2 F F
spectively. During the first π pulse, an atom in the state oftheD1line. Notethatbyemployingthe“clockstates”
|g(cid:105) is transferred to |s(cid:105) by absorbing a photon with mo- |F = 2,m = 0(cid:105) and |F = 1,m = 0(cid:105), the decoher-
F F
mentum (cid:126)k and coherently emits a photon with mo- ence due to magnetic field are suppressed and the in-
2
mentum (cid:126)k , thus obtains a phase of k · r(t ) with homogeneous broadening due to atomic random motion
1 π 1
k = k −k . While an atom in the state |s(cid:105) is trans- is isolated for experimental study. Initially we prepare
π 2 1
ferredto|g(cid:105)byabsorbingaphotonwithmomentum(cid:126)k all atoms into the state of |g(cid:105) through optical pumping,
1
andcoherentlyemitsaphotonwithmomentum(cid:126)k ,thus which increases the atom temperature to ∼15 µK. Two
2
obtainsaphaseof−k ·r(t ). Therefore,afterthefirstπ Raman beams with the same power of 2.5 mW origi-
π 1
pulse,thej-thtermin|Ψ(cid:105) ischangedfrom|g...s ...g(cid:105)to nate from two separate diode lasers, which are phase
gs j
|s...g ...s(cid:105) and acquires a net phase −2k ·r (t ), where locked to a frequency synthesizer at 6.8 GHz, i.e., the
j π j 1
we have neglected the overall phase. After the second frequency separation between |g(cid:105) and |s(cid:105). Single-photon
π pulse, the j-th term is transferred back to |g...s ...g(cid:105) detuning ∆ for both Raman beams is +750 MHz rela-
j
and another phase of 2k · r (t ) is obtained. Conse- tive to |e(cid:105). The wave number k of Raman light can
π j 2 π
quently, the overall phase gained by these two π pulses approximated by k ≈ k θ if θ (cid:28) 1 (see Fig. 1c). In
π 1 π π
is ∆φπ = 2k ·(r (t )−r (t )) = 2k ·v ∆t with the order to have high-fidelity Raman pulses, the Rabi fre-
j π j 2 j 1 π j
3
quencies for both Raman beams have to be stable for tor for the probe (coupling) beam. The wave number
long time and identical for all the atoms. Therefore, we k can be expressed as k ≈ k θ . According to the
s s c s
actively stabilize the intensity for both Raman beams rephasing condition, k has to be in the same direction
π
with two independent digital proportional-integral con- ask ,whichissatisfiedapproximatelysinceθ andθ are
s s π
trollers. We also increase the diameter of the Raman rather small. The time interval between the two Raman
beams to 3.8 mm to improve the intensity homogeneity pulses has to satisfy ∆t/T =k /2k ≈θ /2θ where we
s π s π
ofthecentralregion. Rabifloppingbetween|g(cid:105)and|s(cid:105)is have used k ≈ k . Under the condition of T = 600 µs
c 1
measured as shown in Fig. 2b. By fitting the curve with and θ = 2.1◦, we measure the photon detection proba-
π
I(τ) = Acos(2πΩ τ)e−γτ +B, we obtain a two-photon bility in the read-out mode as a function of time interval
r
Rabi frequency of Ω = 87.1 kHz and a decay rate of ∆t. The result is shown in Fig. 2c, which gives a Gaus-
r
γ = 13.4 kHz. The fidelity of a single π pulse is esti- sian 1/e width of 46(1) µs, and an optimal interval of
mated to be 96%. Slight imperfection is mainly limited 154.9(5) µs. With this method the optimal intervals ∆t
by slight intensity variations in the central region of the fordifferentT aredetermined,theaveragevalueof∆t/T
Raman beams, which originate from the imperfection of is calculated to be 25.8(1)%, which agrees very well with
the optics used. the theoretical estimate of θ /2θ ≈ 26.2(8)%. We also
s π
change the Raman angle θ for several different values,
π
(a) (b) 16 and redo the optimization process for each angle. We
T
findthattherephasingconditionissatisfiedverywell,as
Coupling 12
shown in Fig. 2d.
%) 8
Probe P (r m)
t1 t2 4 0.8 (m
RPuelpsheassing 00 15 30 45 y unit)0.6 4
(c)12 (d) 35 Pulse Du ration (µs) y (arbitrar0.4 32
sit
n0.2
P (%)r 48 ∆tT/ (%)2350 Inte 00.8 0.8 010
0
0
50 100 150 200 250 1.5 1.8 2.1 2.4
∆t ( µs) θ̟ 0 1 2 3 4(mm)
FIG. 3: (color online). Angular distribution of the read-out
FIG. 2: (color online). Verification of the rephasing condi-
noise due to imperfection of the π pulses. Data is measured
tion via EIT storage. (a) Time sequences for the coupling,
with a CCD camera of 53 cm away from the atomic ensem-
probeandrephasingpulses. (b)Two-photonRamanRabios-
ble. Image center corresponds to θ =θ . Slight interference
π s
cillationsbetweentwogroundstates|g(cid:105)and|s(cid:105). Thevertical
fringeisduetoimperfectionofopticsusedalongtheimaging
axisisthephotondetectionprobabilityintheread-outmode,
path.
whichisproportionaltotheatompopulationin|s(cid:105)state. (c)
Optimization of time interval ∆t = t −t between two π
2 1 Note that when θ is approaching θ = 1.1◦, namely
pulses for a storage time of T = 600 µs. (d) Measured rela- π s
k approaching k , extremely strong noise due to the π
tionshipbetween∆t/T andtheintersectionangleθπ between π s
thetwoRamanbeams. Thesolidlinereferstothetheoretical pulse imperfections is observed in the probe direction.
estimate of θ /2θ determined by the rephasing condition. We use a CCD camera to measure the angular distribu-
s π
tionofthisnoise,withtheresultshowninFig. 3. Itsug-
Wefirstverifytherephasingconditionviaelectromag- geststhattheread-outnoiseduetoimperfectionoftheπ
netically induced transparency (EIT) [26]. A weak co- pulsesishighlydirectional,whichisinconflictwithboth
herent laser pulse with an average photon number of ∼1 of our intuition and a previous theoretical study [18].
couples the |g(cid:105) ↔ |e(cid:105) transition, and a control beam The angle width of this noise is calculated to be 0.28◦,
resonant with the transition of |s(cid:105) ↔ |e(cid:105) controls the which corresponds to a Gaussian mode with a waist of
storage and read-out process. The waist of the probe 102 µm at the position of the atomic ensemble, which
beam is 90 µm, and that of the coupling beam is 200 is slightly smaller than the read beam [27]. This highly
µm. There is an angle of θ =1.1◦ between the coupling directional noise implies that the imperfection of the π
s
light and probe light. According to the time sequences pulsescreatesanothercollectiveexcitationstatewiththe
shown in Fig. 2a, by turning off the coupling beam, an wavevector k . When the angle separation between θ
π π
input probe light pulse is converted to an atomic spin andθ ismuchlargerthantheanglewidthinFig. 3, the
s
wave with k = k −k , where k (k ) is the wavevec- noise can be treated incoherently, which gives the result
s p c p c
4
of 2εN∆Ω/4π in the unit of photon numbers, where N Afteroptimizationofthebeamqualities,thefidelityofa
is number of atoms in the mode of the coupling beam, single π pulse is about 97%. The π-pulse-induced noise
ε is the imperfection for a single π pulse and ∆Ω is the in the read-out mode is measured to be p = 0.8%. We
r
solid angle. When θ = θ , this read-out noise is collec- measure the cross-correlation for a series of time points
π s
tivelyenhancedbyafactorofN. Thusinordertoreduce with the result shown in Fig. 4b. In comparison to the
the π-pulse-induced read-out noise, the angle separation case without applying the rephasing pulses, lifetime is
between θ and θ has to be large. increased by 5 folds. With the rephasing pulses on, the
π s
cross-correlationg(2) dropsfromaninitialvalueof5.2(1)
(a)30 (b) andstayswellabove2forabout1msstoragetime. This
6 result does prove that quantum nature of storage is well
preserved. Higher nonclassical photon-photon correla-
20
4 tion can be achieved by improving the accuracy of the π
(2)g (2)g pulses. We estimate that a π-pulse fidelity of 99% would
10
2 improve the cross-correlation to well above 10.
In summary, we have successfully managed to operate
0
0 100 200 300 0 500 1000 1500 2000 thespinechotechniqueinthesingle-quantaregimeforan
T (μs ) T ( μs) atomic-ensemble quantum memory. In our experiment,
we find that the noise induced by slight imperfection of
FIG. 4: (color online). Cross-correlation measurement as a
the π pulses is highly directional and can be avoided by
functionofstoragetimeT. (a)Withoutapplyingtherephas-
arranging the rephasing beam directions properly. With
ingpulses,thelifetimeismeasuredtobe228(6)µs. (b)With
the rephasing pulses applied, the lifetime is measured to be π pulses of moderate fidelities, the quantum nature of
1.20(7) ms. The reduction in g(2) is due to imperfection of the spin echo process is verified by observing nonclas-
the rephasing pulses. At T = 1 ms, nonclassical correlation sical photon-photon correlations. We emphasize that
(g(2) >2) is well preserved. The detection probability of the although in our experimental demonstration we merely
write-outphotonforbothmeasurementsissettop =0.35%.
w studythemotion-induceddecoherenceforacold-atomic-
gas ensemble, our findings and techniques developed do
In order to directly test the feasibility of applying apply to other decoherence mechanisms and other phys-
theserephasingpulseswithoutdestroyingthesinglespin ical systems, like the solid-state photon-echo quantum
waves stored in the atomic ensemble, we implement the memories [8].
Duan-Lukin-Cirac-Zoller(DLCZ)[20]protocol,forwhich
This work was supported by the National Natu-
nonclassical photon-photon correlation can be used as
ral Science Foundation of China, National Fundamen-
a criteria to verify the quantum nature of storage [28].
tal Research Program of China (under Grant No.
We apply a weak write pulse coupling the transition of
2011CB921300), and the Chinese Academy of Sciences.
|g(cid:105) ↔ |e(cid:105) with a small detuning to induce spontaneous
X.-H. B. and B. Z. acknowledge support from the Youth
Ramanscattering. Heraldedonthedetectionofasingle-
Qianren Program.
photon in the write-out mode, a single-quanta spin-wave
Note added.−After completing this work we became
is created with the wavevector k = k − k , where
s w wo aware of a related experiment by Jobez et al. [30].
k (k ) is the wavevector of the write beam (write-
w wo
out mode). Configuration for the beam directions are
shown in Fig. 1. After a storage time of T, a strong read
pulse coupling the |s(cid:105) ↔ |e(cid:105) transition converts the spin
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