Controlled rephasing of single collective spin excitations in a cold atomic quantum memory

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by  Boris Albrecht

Controlled rephasing of single collective spin excitations in a cold atomic quantum
memory
Boris Albrecht,1 Pau Farrera,1 Georg Heinze,1 Matteo Cristiani,1 and Hugues de Riedmatten1,2
1ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
2ICREA-Instituci´o Catalana de Recerca i Estudis Avanc¸ats, 08015 Barcelona, Spain
(Dated: January 30, 2015)
We demonstrate active control of inhomogeneous dephasing and rephasing for single collective
atomicspinexcitations(spin-waves)createdbyspontaneousRamanscatteringinaquantummem-
ory based on cold 87Rb atoms. The control is provided by a reversible external magnetic field
gradient inducing an inhomogeneous broadening of the atomic hyperfine levels. We demonstrate
5 experimentally that active rephasing preserves the single photon nature of the retrieved photons.
1 Finally, we show that the control of the inhomogeneous dephasing enables the creation of time-
0 separated spin-waves in a single ensemble, followed by a selective readout in time. This is an im-
2 portant step towards theimplementation of afunctional temporally multiplexed quantumrepeater
n node.
a
J PACSnumbers: 03.67.Hk,32.80.Qk

9
2
Photonic quantum memories (QMs) [1–3] are devices the implementationofcontrolleddephasingsandrephas-

] which can faithfully store and retrieve quantum infor- ings ofsingle spin-waveswouldallow the creationofsev-
h mation encoded in photons. They are essential build- eral time-separated single spin-waves in a single ensem-
p
ing blocks for scalable quantum technologies involving blewhichcouldbeselectivelyreadoutatdifferenttimes.
-
t photons, such as linear optics quantum computing and Rephasing protocolshavealso been proposedandimple-
n
longdistancequantumcommunicationusingquantumre- mented for optical collective atomic excitations, leading
a
u peaters [4–6]. QMs have been implemented with single to the storage and retrieval of 64 weak optical modes
q atoms and ions [7–11], atomic vapors [12–21], and solid in a rare-earth doped crystal [35], with pre-determined
[ state systems [22–27]. storage times. The capability to control the dephasing

1 Atomic ensembles provide an efficient way of reaching ofspin-waveshasalsobeenusedrecentlyto implementa
v coherent optical pulse sequencer [36], efficient light stor-
the stronginteractionbetweenmatter andlightrequired
9 ageforbright[37]andweakcoherentpulses[17]usingthe
for the implementation of quantum memories, without
5
gradientechomemoryprotocol[38], as wellasstorageof
5 the need for high finesse cavities. In addition, they give
several temporal modes of bright pulses [37].
7 the possibility to multiplex quantum information, which
0 isdesirableinseveralapplications. Inparticular,inquan-
. Inthispaperwedemonstrateactivecontroloftheinho-
1 tum repeater architectures, this alleviates the limitation
mogeneousdephasing and rephasingof single spin-waves
0 due to the communication time between the nodes [28].
storedinanatomicensemble. Acold87Rbatomicensem-
5 In atomic ensembles, quantum information is stored as
1 ble QM is used to create heralded single spin excitations
collectiveatomicspinexcitations,calledspin-waves. Sin-
: usingthe DLCZscheme. Weimplementacontrolledand
v gle spin-waves offer the important advantage that they
reversible spin inhomogeneous broadening using a mag-
Xi can be efficiently transferred to single photons in a well
netic field gradient [38], leading to spin-wave dephasing
defined spatio-temporal mode thanks to constructive in-
r andrephasingatacontrolledtime. Weinfer the dephas-
a terference between the involved atoms. In 2001, Duan,
ing and rephasing of the spin-waves by converting them
Cirac, Lukin and Zoller (DLCZ) proposed a protocol to
into single photons. We show that with this ability, sev-
implement a quantum repeater using the heralded cre-
eral temporally separated spin-waves can be stored and
ation of spin-waves in an atomic ensemble [5]. Several
read out selectively. This is the first enabling step to-
demonstrationsofthebuildingblockoftheprotocolhave
wards the implementation of a temporally multiplexed
beenreported[12,16,29]includingfunctionalelementary
DLCZ quantum repeater, following the proposal of [34].
segments of a quantum repeater [30, 31]. Most of these
demonstrationshowever,usedonlyasinglespin-waveper
To implement a DLCZ QM, we start by an optically
ensemble, although several ensembles have been already
thick ensemble of N identical atoms exhibiting a Λ-type
implemented in the same atom trap [32, 33].
level scheme with two metastable ground states g and
| i
A recent theoretical proposalhas shown that the abil- s andanexcitedstate e (seeFig.1(b)). Alltheatoms
| i | i
ity to precisely control the quantum state of single spin- are initially prepared in g . A weak, off-resonant write
| i
waveswouldopennewavenuesfortherealizationofmore pulse onthe g e transitionprobabilisticallycreates
| i→| i
efficient, temporally multiplexed quantum repeater ar- a spin-wave heralded by a Raman scattered write pho-
chitectures [34]. In particular, it has been proposedthat ton. The write photons and the associated spin-waves
2
are described by a two-mode squeezed state as magnetic gradient of 20G/cm along the probing axis.
We address the D line, which is resonant with light
2
φ =p1 p(0w 0s +√p 1w 1s +p 2w 2s +o(p3/2)), at 780nm. The cooling laser, red detuned from the
| i − | i| i | i| i | i| i
(1) ′
F =2 F =3 transition, and the repumper laser,
where p is the probability to create a spin-waveper trial | i → | i ′
resonant with the F =1 F =2 transition, will
in the detection mode, and w and s stand for write pho- | i → | i
be referred to as the trapping beams. All the atoms
tonandspin-waverespectively. Upondetectionofawrite
areinitiallyopticallypumpedinthe g,m =2 Zeeman
F
photon, the state of the associated spin-wave to first or- | i
sublevel,permitting us tocreateamagneticallysensitive
der is given by
spin-wave, which is necessary for this experiment. The
write pulse is red detuned by 40MHz from the g e
1 N | i→| i
1s = ψ(0) = Xeixj·(kW−kw) g1...sj...gN , transitionandhasadurationof16ns. Withtheseparam-
| i | i √N | i eters, a peak power of 590 µW leads to a write photon
j=1
(2) detection probability pw of 1%. The read pulse, coun-
where x is the position of atom j, and k and k are terpropagatingwiththe writepulse,is resonantwiththe
j W w
the wavevectors of the write pulse and write photonic s e transition and has a duration of 20ns. A peak
| i→| i
mode respectively. The spin-wave can be read out at a power of 570µW maximizes the retrieval efficiency. The
latertimewithacounterpropagatingreadpulseresonant polarization of the write and read pulses in the frame
with the s e transition. This converts the atomic of the atoms is σ− and σ+ respectively, while the de-
excitation|iint→oa|siinglereadphoton. Thankstocollective tected write and read photons are σ+ and σ− polarized.
◦
interferenceofallcontributingatoms,the readphotonis We set an angle of 0.95 between the write/read pulses
emittedinawelldefinedspatialmodegivenbythephase axisandthephotonsdetectionaxis,tospatiallyseparate
matchingconditionk =k +k k ,wherek andk theclassicalpulsesfromthewriteandreadphotons. The
r R W w R r
−
are the wavevectors of the read pulse and read photonic writeandreadphotonsarespectrallyfilteredbyidentical
mode respectively. The retrieval efficiency is defined as monolithicFabry-Perotcavitieswith20%totaltransmis-
η = p /p , where p is the probability per trial sion(includingcavitytransmission,subsequentfibercou-
ret w,r w w,r
to detect a coincidence between write and read photons, plingandspectrummismatchbetweenthesinglephotons
and p is the probability to detect a write photon. and the cavity mode), before detection by single photon
w
For the active rephasing experiment, we apply a mag- detectors (SPDs) with 43% efficiency.
netic field gradientto the ensembleduring the storageof
thespin-waves. Thiscreatesaninhomogeneousbroaden-
ingofthehyperfinelevels,duetothespatiallydependent
Zeeman shift and leads to a rapid dephasing of the spin-
wave, with no further spontaneous rephasing. In this
case, the state of the spin-wave evolves as
N
ψ(t) = 1 XeiR0t∆ωj(t′)dt′+i(xj+vjt)·(kW−kw)
| i √N
j=1
g ...s ...g , (3)
1 j N
| i
where ∆ω (t) is the relative detuning of the state asso-
j
ciated with atom j in s , which is proportional to the
magnetic gradient amp|litiude, and v is the velocity of
j
atom j.
If we reverse the magnetic gradient at a time T ,
rev
a rephasing will be induced when Trev ∆ω (t′)dt′ +
R0 j
t ′ ′
∆ω (t)dt = 0, which happens at a time 2T for
RTrev j rev FIG. 1: (color online) (a) Schematic of the experimental
a symmetric reversal, e.g. if ∆ω (t T )= ∆ω (t
j ≤ rev − j ≥ setup. HWP: half-wave plate, QWP: quarter-wave plate,
T ). The retrieval efficiency at a time t is proportional
rev PBS: polarizing beam splitter, SPD: single photon detector.
to the overlap of the state at that time with the initial (b)Energylevelsstructure. (c)Experimentalsequencetime-
state: ηret(t) ψ(0)ψ(t) 2 [39]. Therefore, we use line for the active rephasing experiment. W: write pulse, C:
∝ |h | i|
ηret to monitor the spin-waves dephasing and rephasing cleaningstage, R:readpulse,Ts: storagetime,Ti: interroga-
in the following. tion time
The experimental setup is shown in Fig. 1(a) [40].
We use an ensemble of laser cooled 87Rb atoms loaded Theexperimentalsequencefortheactiverephasingex-
in a magneto optical trap (MOT), with a longitudinal periment is shown in Fig. 1(c). After a MOT loading
3
phaseof15ms,weswitchofftheMOTgradientwhilethe 35
trapping beams are kept on during a molasses (1.6ms)
phase. Afterwards,weperformopticalpumpingfor10µs. 30
The measured optical depth at this stage is 6 1. The
magnetic gradient is then switched on again b±efore the 25
beginning of aninterrogationperiodofup to 660µsdur-
ing which a train of up to 200 write pulses is sent. For %] 20
eachtrial,ifnowritephotonisdetected,acleaningstage [et 25 25
ηr15 20 20
sets the memory back into its initial state. It consists of
15 15
anopticalpumpingpulse,whichisσ+ polarizedandres-
10 10 10
′
onant with the F =2 F =3 transition, and read 5 5
| i → | i
light. If instead a write photon is detected, we reverse 0 0
5 0 0.05 0.1 0.15 20.6 20.8 21
the magnetic gradientand send a readpulse after a pro-
grammabledelay. This leadsto the end ofthe interroga- 0
0 5 10 15 20 25 30 35
tion of the current ensemble and to the loading of a new
Time [µs]
one with a repetition rate of 59Hz.
We now present the experimental results. We start
FIG. 2: (color online) Retrieval efficiency vs. readout time
by measuring the retrieval efficiency ηret as a function for pw = 1%. (grey open circles) Standard DLCZ experi-
of storage time, for a standard DLCZ experiment, i.e. ment. Theoscillations areduetoimperfect opticalpumping.
whenno magneticgradientis appliedduring the interro- (grey line) Fit of the experimental data. (blue dots) Active
gationperiod. The results areshown in Fig.2 (open cir- rephasing experiment. (green line) Fit of the experimental
data.
cles). We observe an oscillation which can be attributed
to a beating between two different classes of spin-waves
due to imperfect optical pumping into the g,m =2
| F i on equation (3), corrected for the memory lifetime and
state [41, 42]. The overall decay in retrieval efficiency
the temperaturedriftofthe readphotonsfilteringcavity
has a time constant of 57 1µs, limited by atomic mo-
± during the measurement time (see [42]). The signal to
tion [21, 39] and spurious magnetic field gradients [43].
noise ratio (SNR), calculated as the maximum value of
We then switch on the gradient during the interrogation
the fit at the rephasing time divided by the mean of the
period. Inthatcase,weobservearapiddephasingofthe
background,is 13.3 0.9.
spin-waveat shortstoragetimes (see left inset), followed ±
Next, we investigate the single photon nature of the
by background noise for a period of about 20µs. If the
rephased read photons. For this measurement, we mod-
gradient is reversed after the detection of a write pho-
ified the setup by sending the read photons through a
ton, we observe a rephasing, witnessed by a pronounced
balanced fiber beamsplitter connected to two SPDs. We
increase in retrieval efficiency. The measured efficiencies
measuredtheantibunchingparameterαofthereadpho-
after the rephasing are again at the noise level. The re-
tons [44] defined as
versal instruction is sent 3µs after the write pulse, but
due to the temporal response of the coils driving cir- p p
α= w,r1,r2 · w, (4)
cuit, the rephasing occurs at 20.84µs (see right inset). p p
w,r1 · w,r2
The fullwidth athalfmaximumofthe rephasingpeak is
150 3ns, and its position can be precisely modified by wherep is the probabilitytomeasureatriple coin-
± w,r1,r2
changing the magnetic gradient reversaltime [42]. cidence between a write photon and both read photons
The retrieval efficiency at the rephasing peak is about detections, and pw,r1,pw,r2 are the probabilities to mea-
60% of the retrieval efficiency in the standard DLCZ ex- sureacoincidencebetweenawritephotonandeitherone
periment for the same storage time [42]. Several effects of the read photon detections. The measured values of
mayexplainthisreduction. First,slowfluctuationsofthe α as a function of pw in the case of the active rephas-
currentinthecoilsgeneratingthemagneticfieldgradient ing experiment are shown in Fig. 3. An antibunching
canchangethe positionoftherephasingpeakduringthe parameter lower than 1 is a proof of non-classicality, 1
measurement time, which will decrease the efficiency for corresponding to coherent states and 0 to perfect single
a given read-out time. Moreover, time varying magnetic photons. We expect to be in the single photon regime
field gradients over the interrogation time lead to fluc- for low excitation probabilities. We observe values be-
tuations of the rephasing time depending on the write low 1 within the error for pw up to 0.5%, with values
photons detection time. Finally, the quality of the opti- as low as 0.20 0.14 for pw = 0.17%. The data are fit-
±
cal pumping may be degraded during the interrogation ted using the formula α=2p(2c(1+p) p)/(c(1+p))2,
−
period because of the presence of the magnetic field gra- wherecistheproportionalityfactorbetweentherealand
dient. This decreases the optical depth and therefore ideal g(2), the cross-correlation function between write
w,r
the efficiency. The experimental data are fitted based and read photons (see [42]).
4
2
0.2 (a)
‰]
1.5 [w,r0.1
p
0
α 1 19.8 20 20.2 20.4 20.6 20.8 21 21.2
Time [µs]
0.5 0.3 200 0.760.24 200 0.460.54 200 0.250.75 (b)
‰] 100 100 100
0.2
[w,r 0 2nd 1st 0 2nd 1st 0 2nd 1st
0 p 0.1
0 0.5 1 1.5
p [%] 0
w 19.8 20 20.2 20.4 20.6 20.8 21 21.2
Time [µs]
100
FIG.3: Antibunchingparameterasafunctionofwritephoton (c)
detection probability. Open circles: experimental data. The %] 1st write
dashed line representsthe limit for classical states (α≥1). S [ 75 2nd write
50
1 10
p [%]
w
It has been predicted that the controlled dephasing
and rephasing of single collective excitations as demon- FIG. 4: (Color online) Temporally separated spin-waves. (a)
strated in this paper should enable the creation of mul- Single rephasing case for pw =1%: first write pulse in green,
tiple time-separated spin-waves that can be selectively second write pulse in blue. (b) Both pulses sent in black.
The histograms display the relative weight of each peak, at
read-out in time [34]. To confirm this prediction, we
thecircled points. (c)Selectivityasafunctionofpw foreach
send two write pulses separated by 600ns, first indepen-
rephasing.
dentlyandthenconjointlybeforeperformingthereadout
around the rephasing time. Fig. 4 (a) shows the coinci-
dence probabilities per trial p when each write pulse
w,r rephasing SNR which varies with p (see Fig. 4 (c) and
w
issendindependently. Thereadouttimeisdefinedasthe
[42]). For the results shown in Fig. 4 (b) we find S =
timebetweenthefirstwritepulseandthereadpulse. As
(S(1)+S(2))/2 = 76 6%. For lower p = 0.28%, we
w
expected, the spin-wave created by the first write pulse ±
obtain a selectivity of 92 4%.
rephases later and vice versa. Fig. 4 (b) shows the coin- ±
TheresultsofFig.4showthatwhenseveralspin-waves
cidence probability when both write pulses are sent con-
are created, the rephasing efficiency of each one remains
jointly. The values at the maximum of the rephasing
the same, but the background noise increases. With the
peaks are similar, when background-subtracted. How-
current status of the experiment, this limits the benefit
ever, the background probability outside the rephasing
of multiple temporal mode storage, since the excitation
peaks is higher in this case. This can be explained by
probabilityneedstobereducedforeachpulseinorderto
expressingthecoincidenceprobabilityinthebackground
keep the same SNR. However, this issue is addressed in
outside the rephasings as p = p p . Noting that
B w · r theschemeproposedin[34]. Apossiblesolutionwouldbe
p p [45], one gets p p2. In the case where
r ∝ w B ∝ w tobuildalowfinessecavityresonantwiththe writepho-
we send two write pulses, the write detection probabil-
tons but invisible to the read photons around the QM.
ity p is twice the one of the single write pulse case
2w This would decrease the proportion of unwanted spin-
p . Therefore, the background probability for two write
w waves created per write pulse by increasing the propor-
pulses becomes p(B2) ∝ p22w = 4∗p2w. This is compatible tionofwritephotonsemittedinthecavitymode. There-
with the measured value of 4.1 0.3. fore, the noise would decrease by a factor corresponding
±
To investigate the cross-talk between the two spin- to the cavity finesse.
waves, we construct the histograms shown in the insets In conclusion, we demonstrated active rephasing of a
by performing start-stop measurements. The starts are single spin-wave at a controllable time by inverting the
write photon detections, and the stops are read photon polarity of an external inhomogeneous broadening cre-
detections. The two contributions are equally weighted ated by a magnetic gradient. We showed that in this
in the noise region, but on each rephasing peak, we de- case, the retrieved photons still exhibit antibunching,
tectasignificantimbalance. Thisshowsthatmostlyonly which proves that active rephasing preserves single pho-
one spin-wave rephases at a time. To quantify the pro- tons statistics. Finally, we demonstrated experimentally
cess,wecalculatethe relativeweightofeachpeak,which thatthistechniqueenablesthecreationofmultipletime-
we call selectivity: S(i) = p / p , with p the separated spin-waves that can be read-out with high se-
C,i Pk C,k C,i
probability to detect a coincidence in the binning corre- lectivity in time. These results pave the way towards
spondingtothepeaknumberi. Itsvaluedependsonthe the realization of a temporally multiplexed DLCZ-type
5
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