Observation of prolonged coherence time of the collective spin wave of atomic ensemble in a paraffin coated Rb vapor cell

0.22 MB·English

by  Shuo Jiang

APS/123-QED
Observation of prolonged coherence time of the collective spin wave of atomic
ensemble in a paraffin coated 87Rb vapor cell
Shuo Jiang1, Xiao-Ming Luo1, Li-Qing Chen1, Po Ning1, Shuai
Chen3, Jing-Yang Wang2, Zhi-Ping Zhong2 and Jian-Wei Pan1,3
1Physics Department, Tsinghua University, Beijing 100084, P.R.China
2College of Physical Sciences, Graduate University of the Chinese Academy of Sciences, PO Box 4588, Beijing 100049
3Physikalisches Institute, Universit¨at Heidelberg, 69120 Heidelberg, Germany
We report a prolonged coherence time of the collective spin wave of a thermal 87Rb atomic
ensembleinaparaffincoatedcell. ThespinwaveispreparedthroughastimulatedRamanProcess.
Thelongcoherencetimetimeisachievedbyprolongingthelifetimeofthespinswithparaffincoating
and minimize dephasing with optimal experimental configuration. The observation of the long
9
time delayed-stimulated Stokes signal in the writing process suggests the prolonged lifetime of the
0
0 preparedspins;adirectmeasurementofthedecayofanti-Stokessignalinthereadingprocessshows
2 thecoherencetimeisupto300µsafterminimizingdephasing. Thisisonehundredtimeslongerthan
the reported coherence time in the similar experiments in thermal atomic ensembles based on the
n
Duan-Lukin-Cirac-Zoller (DLCZ) and its improved protocols. This prolonged coherence time sets
a
theupperlimit of thememorytimein quantumrepeatersbased on suchprotocols, whichiscrucial
J
for the realization of long-distance quantum communication. The previous reported fluorescence
3
backgroundinthewritingprocessduetocollision inasamplecellwithbuffergasisalsoreducedin
2
a cell without buffergas.

]
PACSnumbers:
h
p
-
t Quantum communication is the absolute secure time based on cold atoms is in the time scale of 10 mi-
n
methodfortheinformationtransfer. Atpresentthecom- croseconds[10,13,16],whichwasattributedmainlylim-
a
u municationdistanceislimitedtohundred-kilometerscale ited by the residual magnetic field. For thermal atoms,
q mainlyduetotheinevitablelossofthephotonduringthe the bottleneck of the coherence time was reported to be
[ transfer. Totacklethisproblem,amodelofquantumre- the atomic diffusion out of the read laser region and the

peater[1]isintroduced,combiningthequantummemory, inelastic collisions between the atoms and glasswall, the
1
v entanglement purification and entanglement swapping. reported cohererence time was only about 3µs [8].
7 In the protocols to realize it, such as the DLCZ proto- During the preparation of this paper, a study on cold
2 col[2]andthefollowingimprovedschemes[3,4,5],quan- atomic ensemble which is simultaneously carried out by
6 tum memory is essential to increase the success proba- another group also led by Jian-Wei Pan at Heidelberg
3
bility of such protocols because the generation of entan- recently reported ms coherence time in cold Rb ensem-
.
1 glement states are probabilistic. ble [18]. This is achieved by reducing the effect of mag-
0
The quantum memory is achieved by coherent manip- netic field using ’clock state’ and the dephasing caused
9
ulation of the atomic states, such as preparing a total by random atomic motion with correct detection config-
0
: symmetric collective state (spin wave) by Raman scat- uration.
v tering process [2]. The qubit can then be stored and re- Thethermalatomicvaporcellsenjoysimpletechnique
i
X trieved by manipulating such state. The coherence time and better magnetic shielding, but in regular glass cells,
r of this collective state will determine the memory time the coherence time of the prepared spin wave is limited
a of the quantum repeater. Long memory time is desir- bythecollisionsbetweenwallsandatomsthemselves. In
able for the long-distance quantum communication. For the regular glass cell collisions with wall will cause the
instance, to establish entanglement of two qubits over spin flip, reducing its lifetime. The time scale is on the
hundred-kilometer scale, the memory time needs to be orderoftensusforarealisticpencilshapedcell(cmindi-
on the order of hundred-microsecond. mension),whichismuchfasterthanthecollisionbetween
Severalgroupsarepresentlyworkingontheimplemen- atoms ( under our temperature T = 78 oC, the atomic
tation of the quantum repeater based on the DLCZ and densityis1012/cm3,andthemeancollisiontimeisonthe
its improved protocols and have achieved many signifi- orderofms). Acellwithparaffincoatedwalls[19]would
cant experimental advances [6, 7, 8, 9, 10, 11, 12, 13, exceedthislimit, sinceparaffincoatinghadbeendemon-
14, 15, 16, 17]. This includes the coherent manipula- strated in reducing such destructive collisions, allowing
tion of the atomic states through Raman process in an atoms to undergo many elastic wall-collisions and pro-
atomic ensemble [6, 7, 8, 9, 10, 11]; entanglement of the long the spin lifetime up to 1 second [20]. The paraffin-
atomic states [12, 13, 14, 15] and the realization of the coated alkali-vapor cells had been successfully used in
building block of the quantum repeater [16, 17]. Both entanglement between atomic ensembles with continu-
the thermal vapor and cold atomic ensembles are em- ous variables [21], and slow light experiment [22]. To
ployed in those experiments. Most reported coherence our knowledge, the study on the coherence time of spin
2
waves in a paraffin coated cell based on the DLCZ pro- Write Photon Detector
Pump
tocol and the effect of dephasing as reported by Zhao
et al. [18] in a thermal ensemble has not been reported
Fiber Coupler
yet. In order to prolong the coherence time, buffer gas Anti-Stok-esnti PBS Stokes
is often filled in the sample cell, it would slow the diffu-
PBS Rb Cell Fiber Coupler
sion speed of atoms to some extent, but also brought a Filter Set (Shielded by Magnetic Shielding) Filter Set
new problem [23]: an additional and considerable fluo-
rescence noise signal, caused by collisional perturbation Read
Photon Detector
of the excited state due to buffer gas during the write
(read) process, severely limited the fidelity of quantum ∆ r 5 P1/2
communication. ∆ w 5 P1/2 δ(cid:83) ∆Τ
Pump
Inthis letter, we investigatethe capability ofapplying Write Stokes Anti-Stokes Read
the thermal atomic ensembles as candidate for quantum Write
repeater,bystudyingthecoherencetimeofthespinwave 5 S1/2 F = 2 5 S1/2 F = 2 Read δ(cid:90)
using 87Rb vapor in a buffer-gas-free paraffin coated cell 5 S1/2 F = 1 5 S1/2 F = 1 Delayδ(cid:85)
(P-cell). Experiments were carried out to test whether
FIG. 1: Schematic of experiment for generation of atomic
theprolongedlifetime ofthespinsunderparaffincoating
collective state. Off-axis, counter-propagating geometry of
and minimizing the dephasing process could enable long
Braje et al.[22] is adopted in our experiment, in which write
coherence time in a thermal sample as well. This coher-
and read pulses collinearly propagate into a Rb cell in se-
encetimewillprovidetheupperlimitofthememorytime quence and we collect the generated output fields (Stokes,
inthequantumrepeater. Wealsoinvestigatewhetherthe Anti-Stokes),thedirection of thiscollection forms a 20 angle
buffer-gas-free environment would reduce the collision- with the direction of the write-read input light. PBS stands
induced fluorescence background. Though in the DLCZ forpolarizingbeamsplitters;theFilterSetiscomposedofse-
protocol, the coherent manipulation of atomic state is lectiveabsorptionbyatomiccellsandnarrow-bandfilter. The
implementedbyspontaneousRamanscatteringwithsin- insetillustratestherelevantatomiclevelscheme. ∆w =1GHz,
gleexcitation,stimulatedRamanscatteringcouldalsobe ∆r =400MHz
used to realize such goal, as Raymer group [24] pointed
out. The coherence time would be same for both cases, e) 5 e) 0.05
and we measure it in a P-cell in the stimulated Raman n/puls 4 (a) fluorescence write n/puls 0.04 (b) stokes
region for the ease of signal detection and background oto 3 stokes oto 0.03 write
distinction. ph 2 ph 0.02
Figure 1 provides an overview of our experimen- kes( 1 kes( 0.01 fluorescence
o o
tal setup. The 87Rb atoms are in a P-cell which is St (cid:19) St (cid:19)
50mm(length)by5mm(diameter)andisheatedto78oC. 0 Sc1annin2g tim3e of 4F-P(G5Hz)6 0 Sc1annin2g tim3e of 4F-P(G5Hz)6
The sample cell is put in a 3-layer magnetic shielding
with residual field inside 10nT. A pump laser in reso-
FIG.2: StimulatedStokessignalafteraF-P.(a)istheresult
nant with 5S1/2,F =2 to 5P1/2 is first turned on for ina glass cell with7 torrNeonbuffergas; (b)is theresult in
| i | i
50µs to pump atoms to 5S1/2,F = 1 ; then the write a P-cell with no buffergas. The pulse width of write is 2 µs.
| i
laser whose frequency is blue shifted 1GHz with respect Onlypolarization andnarrow-bandfilterisapplied toletthe
′
to the 5S1/2,F = 1 to 5P1/2,F = 2 is turned on signal of the write laser appear as wavelength marker. With
| i | i
whose durationdepends on the laser intensity, lasted till furtherfrequencyfilterbyatomiccells, thewritelightcanbe
the stimulated Stokes signal is observed; after a contro- completely suppressed.
lable delay the read laser pulse of 2us whose frequency
is red shifted 400MHz with respect to the 5S1/2,F =2
to 5P1/2,F′ = 1 is turned on. The writ|e-read beamsi locked at the respective fine structures of the 87Rb ab-
| i
are counterpropagatingandthe collectionof Stokes and sorption peaks, and the frequency detuning and pulse
Anti-Stokessignalsbyopticalfibersisalsocollinear. Ini- generation are achieved by AOMs. The detection of the
tiallywechoseaskewedconfigurationasBrajeet al.[23] Stokes signal signifies the preparation of the spin wave,
where the two directions forms an angle θ = 2o to min- andthedecayoftheanti-Stokessignalatspecifieddirec-
imized the background laser signal. The signals, after tioninthereadingprocessatdifferenttime delayisused
the polarization filter and frequency filter, were passed to measure the coherence time of the spin wave. This is
througha scanning Fabry-Perot(F-P) spectrometer (Fi- essentiallya Time-resolvedCoherentAnti-stokesRaman
nesse 200, 7.5GHz FSR, transmission 10%) and the out- Scattering (T-CARS) method.
put was fed to the single photon detector. Thus allow First we report the frequency analyze of the signals
us to analyze the intensity of the frequency components during the writing process in the buffer-gas-free P-Cell.
and single out the Stokes and anti-Stokes signals. The Fig 2(a) is from the regular cell with 7 torr neon buffer
writelaserhasamaximumpowerof7mWandreadlaser gas where a considerable fluorescence signal is observed
of 80mW at the input face of the cell. The lasers are besides the Stokes; Fig 2(b) is from a buffer-gas-free P-
3
icmiflnseuulgtolc.rhrheeeasIpbtctluueyinrffserceerercdligbeunaaacsrcaekdctsge.helrlanToitsushenutshdtusheptaaphsStretertopsehksrpeeoeodsbflrltubseeioymdgrnueboassyficlneciMgnonclbaleitunshffbizoiaesnerc-t-kPignga-acrdls.oeu-luf[cl2rnee3iddes] Stokes (Arb. Unit) 23456789 (a) wwwwrrrriiiitttteeee 5221m.m.56mmWWWW Stokes (Arb. Unit)0001111.......46824681 (b) wwwwrrrriiiitttteeee 3410m...7775mmWmWWW(s(isginganla×l×103)0)
sample cells. 1 0.2
0 0
Next we measure the temporal pulse shape of the 0 50 100 150 200 250 0 10 20 30 40 50 60
Time (microsecond) Time (microsecond)
Stokes signal in the writing process. This is achieved
by using a long write pulse and monitoring the Stokes
FIG.3: (a)Thelong-delayedstimulated RamanStokessignal
signalaftertheF-P,setthegate(1µslong)ofsinglepho-
in the paraffin-coated Rb cell. The write laser has a waist
ton detector at various temporal positions of the write
of 3mm inside the cell and its power is varied. Time zero is
pulse, the results are shown in Fig 3. An interesting the turn-on of the write pulse which lasts for 200µs. (b) In
phenomenon is observed for the first time, we discover a thenon-coated Rb cell, as theintensity of thewrite light de-
long-delayedstimulatedStokesatvariouswritingpowers. creases,thestimulatedexcitationtransformedtospontaneous
AStokessignalisgeneratedbyspontaneousRamanscat- excitationwithoutanylong-delayedstimulatedexcitationob-
teringduringthefirstmicrosecondsafterthewritelightis served. The long delayed rise of stimulated Stokes in P-cell
turned on, correspondingto the flat region at early time suggests the paraffin coating helps in protecting the Rb spin
from being destroyed by thecollision with thewall.
in Fig 3(a), and increased exponentially at later time to
reach the stimulated Raman scattering. Fig 3(a) shows
the variations of this rise time at different write powers.
with respect to 0 delay between read and write) in a P-
Depending on the power, the rise time of the simulated
cell, which displays two exponential decays. Below 20µs
Stokes can be as long as 150 µs.
is a fast decay with characterized time 10µs. The later
Phenomenon of this long-delayed stimulated Raman
partisaslowdecay,characterizedtimeabout80µs. This
in P- cell is in great contrast to what we observed in a
longdecaytimeisinagreementwiththeresultsfromthe
non-coated glass cell in Fig 3(b). Here the rise of the
long-delayed stimulated Raman and suggested this long
stimulated Stokes is only on the order of a few µs. The
decayisresultingfromthelonglifetimesofthespinsdue
rise time is delayed at lower laser power but only about
toreducedinelasticcollisionwiththeparaffincoatedsur-
10µs, further reduce the power would make the stimu-
face. Westillneedtoaddressthemechanismcausingthe
lated signal disappear. This phenomenon is the result
initial fast decay in Fig 4(a).
of longer lifetime of the spins in a P-cell and can be
qualitatively explained as follows: The stimulated emis-
sion happens only when the number of excited spins or Unit) 1 (a) Unit) 1.21 (b)
toPtthhhl-deeac.nesalpTlmitichnspoelugwiltelodaunnvdeogere,natltioiy.imfeo.nhethatdbpehyepelsaetpdnyhieenecidfawwystrthaiiovetmfeereutpehliaxusetclesaesedepn.disnaScccauwectcruathtemvareaiiunncilscgatutshiimnloroneuwtslhheaoer--f Anti-Stokes (Arb. 0000....02468 Anti-Stokes (Arb. 0000....24680
0 20 40 60 80 100 0 100 200 300 400
tion takes longer time at lower write intensity as long as Delay between read and write (microsecond) Delay between write and read (microsecond)
aboveconditionissatisfied. Thislongtimedelayedstim-
FIG. 4: Decay of Anti-Stokes V.S. delay between read and
ulatedStokesinP-cellsuggeststhat the decayingrateof
write. (a) The decay of anti-Stokes signal at θ = 2o. The
the amplitude of the spin wave is much slowerthan that
diameter of the write laser is 3mm and the read is 10mm.
in a regular cell, because the paraffin coating helps in
Decay time in paraffin-coated cell is composed of fast part,
protecting the prepared spin wave from being destroyed
which is 10µs, and slow part, which is 80µs. (b)Thedecay of
bythe collisionwiththe walls,thus makingthelonglife- anti-Stokesatθ=0o. Thediameterofthewritelaseris6mm
time possible. This long lifetime is a necessarycondition and the read is 10mm. It only shows a slow decay with time
to achieve long coherence time of the spin wave. of 320µs.
Furthermore the coherence time of the spin wave gen-
erated in the writing process can be directly measured Onereasonforthefastdecayiscausedbythediffusion
by the reading process, this is the T-CARS method as of the spin wave out of the effective retrieval region cov-
described before. The write pulse is shut off at the peak eredby the readinglaser,assuggestedby M.D.Eisaman
of the stimulated Stokes, which is 40µs for 5mW write et al. [8], but this is not the major one because further
power. Theintensity ofthe anti-Stokessignalduringthe studiesatdifferentwritebeamwidthsandatflatterread
retrievalprocessisrecordedandplottedagainstthetime powerdistribution coveringthe entire cell showsthe fast
delay between the read and write pulses. The decay of decay is always there under θ = 2o detection configura-
the anti-Stokes signal is caused by decoherence of the tion. AspointedoutintheDuanetal’s originalpaper[2]
spinwave. Fig4(a)(writepower5mW,writebeamdia.3 and investigated in detail recently by Zhao et al [18] in
mm,readpower80mW,readbeamdia.10mm)showsthe coldatomensemble,thereisadephasingofspinwavein-
entire decay of the anti-Stroke signal (relative intensity duced by random motion of the atoms and can be easily
4
understood in the case of single excitation. decay is shown in Fig 4(b), the initial fast decay due to
Upon detection of the forward Stokes signal, a singly thedephasingbythermalmotiondisappears,onlyalong
excited spin wave is created in the atomic ensemble in decay remains and the fitted (e−t2/τ2) exponential de-
the form of cay time is τ 320 µs. This demonstrated the robust of
∼
thelongwavelengthofthespinwaveagainstthedephas-
1
ψspin = Xei△k·rj 1...2j...1 ing and the dominant decoherence effect here becomes
| i √N | i
the spin lifetime. This result in the thermal vapor cell
agrees with the recent study by Zhao et al in cold atom
with k = k k the wave vector of the spin wave,
w s
△ − system [18].
where k ,k are those of the write laser and the Stokes.
w s
The atoms position changes to r (t)=r + rt at later Inconclusion,wedemonstratetheprolongedcoherence
j j
time and will introduce a random phase △shift. This time τ 320 µs of the collective spin wave in a paraffin
will cause a drop in the overlap between the spin waves coated ∼87Rb cell. The coherence time is one hundred
ψ (t)ψ (0) , and thus the decay in retrieval effi- times longer than the previous reported in the thermal
spin spin
chiency in|the readiing process. vapor system. In such system, the two major factors
Under condition k l << π, with l the dimension of dominating the decoherence process are the lifetime of
the atomic ensembl△e, s·uch dephasing is negligible, but the spin and the dephasing of the spin wave due to ther-
this is not the case in our skewed detection configura- mal motion. The paraffin coating helps prolong the life-
tion. With θ =2o, and k = k k k sinθ, then time of the spin by reducing the inelastic collision with
w s w
λ λ /sinθ=23µm|△. T|his|ism−uch|s≈mallerthanthe the walls which is manifested by the long delayedstimu-
spin w
size(a≈ndthe maximumvalueof r )ofourcell,andthe lated Stokes signal under weak write laser, and the long
dephasing caused by the random△motion will be severe decay of anti-Stokes signal with T-CARS method. The
and the dominating factor in this case. In order to min- dephasing can be overcome by choosing the correct de-
imize the effect of dephasing, the created spin wave has tection configuration and preparing the long wavelength
to have a longer wavelength. The longest wavelength of spin wave, this is manifested in the disappearing of the
the spin wave is achieved under collinear detection con- fast decay in the anti-Stokes measurement. This coher-
figuration with θ = 0o, where λ 4.4cm. In fact to ence time though measured in the stimulated region, of-
spin
have the wavelengthof the spin wave≈on the order of cm fers at least anupper limit for memory time in quantum
comparabletothedimensionofthesamplecell,theangle repeater. In our study we also demonstrated that the
θ between the write and Stokes signal has to be smaller buffer-gas-free cell also greatly suppresses the collision-
than 10−4 arc. So the only meaningful configuration to induced fluorescence background.
minimizethedephasinginourexperimentisthecollinear We gratefully thank Prof. J¨oerg. Schmiedmayer for
one. discussions. Dr. ChengZhi Peng, Dr. Dong Yang and
Thoughtheaboveargumentisappliedtothesingleex- ChengXi Yang offered great help in the designing and
citation, it can be extended to the multi-excitation case programming of the data collecting system. This work
andprovidesthebasisforthe improvementinthe stimu- was supported by the National Natural Science Founda-
lated Raman region. A T-CARS experiment was carried tionofChinaunderGrantNo.10474053andNo.10574162
outunder thecollinearconfigurationandthe anti-Stokes and Tsinghua University 985 Grant/051110001.
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