Frequency filtered storage of parametric fluorescence with electromagnetically induced transparency

0.52 MB·English

by  K. Akiba

APS/123-QED
Frequency filtered storage of parametric fluorescence
with electromagnetically induced transparency
K. Akiba1, K. Kashiwagi1, T. Yonehara1, and M. Kozuma1,2
1Department of Physics, Tokyo Institute of Technology,
2-12-1 O-okayama, Meguro-ku, Tokyo 152-8550, Japan
2PRESTO, CREST, Japan Science and Technology Agency, 1-9-9 Yaesu, Chuo-ku, Tokyo 103-0028, Japan
(Dated: February 1, 2008)
The broadband parametric fluorescence pulse (probe light) with center frequency resonant on
87Rb D line was injected into a cold atomic ensemble with coherent light (control light). Due to
1
the low gain in the parametric down conversion process, the probe light was in a highly bunched
photon-pairstate. Byswitching offthecontrollight,theprobelightwithin theelectromagnetically
induced transparency window was mapped on theatoms. When the control light was switched on,
8 theprobe light was retrieved and frequency filtered storage was confirmed from the superbunching
0 effect and an increase of thecoherence time of the retrieved light.
0
2 PACSnumbers: 42.50.Gy, 42.50.-p,32.80.Qk

n
a
J Dark state polariton theory [1, 2] of electromagneti-
7 cally induced transparency (EIT) [3] presents the pos-
2 sibility of coherently transferring a quantum state of
light to an atomic collective excitation by manipulating

4 control light, where the control light turns an opaque
v medium for a weak probe light into a transparent one.
3
Such a quantum state transfer has been successfully
7
demonstrated for nonclassical light generated from an
0
1 atomic ensemble [4, 5, 6]. The advantage of generating
0 nonclassical light from the atoms is that the bandwidth
7 of the light is matched by the narrow atomic resonant
0 width. Compared to the process of generating nonclas-
/
h sical lights with atoms, the parametric down conversion
p (PDC) process has been widely used in fundamental ex- FIG. 1: (Color online) Schematic diagram of experimen-
- perimentsinquantumoptics[7,8,9]andfordemonstrat- tal setup. AOM: acousto-optic modulator; LN: quasi-phase-
t matched MgO:LiNbO waveguide; PBP: Pellin Broca prism;
n ing various quantum information protocols [10, 11]. The 3
DM: dichroic mirror; DP: dispersing prism; HG: holographic
a process also enables the generation of rich nonclassical
u grating;PMF:polarizationmaintainedsinglemodefiber;λ/4:
photonic states such as the antibunched state [12, 13],
q quarterwaveplate; ET: etalon; BS: beam splitter; SMF:sin-
hyperentangled state [14] GHZ state [15], W state [16],
: gle mode fiber; D1, D2: avalanche photodetectors.
v and cluster state [17]. Storing such nonclassical light
i inatomicensemblesgeneratescorrespondingnonclassical
X
atomic states. Furthermore,the state of the nonclassical diabatic part. The control light was turned off when
r
a light can be manipulated by applying an additional field the pulse was propagating in the medium, thus storing
to the atoms storing the photonic state or by changing the adiabatic part. After the nonadiabatic part passed
the properties of the control light [18, 19, 20]. throughthe medium, the controllightwasturnedon,al-
In this paper, we report frequency filtered storage lowing the retrieved adiabatic part to be separated from
of parametric fluorescence (highly bunched photon-pair the nonadiabatic part in time. We call this technique as
state) with EIT. The frequency bandwidth of paramet- time-frequency filtering with storageoflight. The disad-
ric fluorescence is typically of the order of 1013 Hz, vantageofthistechniqueisthatthefrequencybandwidth
which is much broader than an atomic resonance inter- of the retrieved light is limited to that of the EIT trans-
action width (∼ 106 Hz). The discrepancy between the parencywindowandthecountrateafterthe storageand
frequency bandwidth and the resonance width presents retrievalisdecreasedbyafactorequaltothe ratioofthe
a problem for photon counting in experiments, since EIT width to the incident light bandwidth.
photons interacting with atoms cannot be selectively Fig. 1 shows a schematic diagram of the experimen-
counted. We avoided this problem in our experiments tal setup. The states {|ai, |bi} and |ci of a Λ type
by utilizing the properties of the optical pulse propaga- three level system correspond to 52S1/2, F ={1,2} and
tion inside the EIT medium [1, 2, 21]. When the pulse 52P , F′ =2ofthe87RbD line,respectively. Wegen-
1/2 1
spectrumwasbroaderthanthetransparencywindow,the eratedparametricfluorescencebyusingtwoindependent
pulse was split into an adiabatic part having a spectrum quasi-phase-matchedMgO:LiNbO waveguides(LN1,2in
3
withinthetransparencywindowandanoscillatingnona- Fig.1)[22,23]. Opticalpulses(pulsewidth: 190ns;peak
2
the shape of the parametric fluorescence pulse. The ob-
tainednormalizedautointensitycorrelationfunctionwas
g(2)(0)=4.4±0.2>3[23],whichiscalled“superbunch-
ing”. We remeasured the sharp coincidence peak at 0.1
nsresolution(Fig.2(b))tocloselyevaluatethecoherence
time of the probe light. The temporalwidth of the coin-
cidence(fullwidthathalfmaximum: FWHM)was1.2ns
withtotaltimeresolution0.8ns,whichmeansthecoher-
ence time of the probe light is about or less than 0.2 ns.
The auto intensity correlation function is theoretically
given by g(2)(0) = 37 with a squeeze parameter of 0.17
obtainedfromthe classicalparametricgain[24],whichis
much larger than the experimental value. This disagree-
mentcanbe explainedby the longertime resolution(2.3
ns) than the coherence time (≤ 0.2 ns) and fluctuation
ofthe secondharmoniclightintensity[23]. We notethat
FIG.2: Experimentalresultsofintensitycorrelationwith1.6-
the superbunching effect is not direct proof of the non-
ns resolution of the MCS: (a) broadband parametric fluores- classicality of the light. However, when g(2)(0) is much
cence, (c) retrieved component of coherent light, and (d) re-
greater than 3, the state of the parametric fluorescence
trieved component of parametric fluorescence. The insets of
can be approximated as a highly bunched photon-pair
(a)and(d)showmagnifications ofthecoincidencesat0time
state i.e. |φi ≈ |0i+ǫ|2i (|ǫ|2 ≪ 1). In our experiment,
delay. (b) Sharp coincidence peak in (a) measured with 0.1
ns resolution of theMCS. we prepared the parametric fluorescence such that the
fluorescence was in the highly bunched state.
Before performing an experiment with broadband
intensity: ∼110mW)weregeneratedbyanacousto-optic parametric fluorescence, we performed an EIT exper-
modulator (AOM1) from the linearly polarized continu- iment using narrowband coherent light (spectrum line
ous output of a Ti:sapphire laser. The pulses were cou- width < 100 kHz) as probe light. Magneto-optically
pled to LN1 with 50% efficiency and generated second trapped 87Rb atoms were used as an optically thick
harmonic pulses (pulse width: 130 ns; peak intensity: medium, placed in a vacuum cell magnetically shielded
∼16 mW). The second harmonic light was injected into by a single permalloy. One cycle of the experiment com-
LN2 (coupling efficiency 40%) and the parametric fluo- prised an atomic medium preparation period (6.3 ms)
rescencewasgenerated. Thefrequencyofthe degenerate and a measurement period (3.7 ms). After laser cooling,
component in the parametric fluorescence was resonant themagneticfieldsandthecoolingandrepumpinglights
with the |ai → |ci transition. The frequency bandwidth were turned off, and depumping lights illuminated the
ofthefluorescencewasabout10THz,whichwasreduced atomic ensemble for 45 µs, so that all atoms were pre-
to23GHzusingaholographicgrating(HG)andapolar- paredinstate|ai,wheretheopticaldepthofthe|ai→|ci
izationmaintainedsinglemodefiber(PMF).Theoutput transition was ∼6. In the measurement period, a weak
ofthe PMFwasusedasbroadbandprobelight. Inorder (about1pW)probelight(beamdiameter330µm)anda
to obtain a high extinction ratio between the probe and 400 µW control light (beam diameter 770 µm) with the
controllights,thetwobeamswereoverlappedatthecold same circular polarizations were injected into the unpo-
atoms with a crossing angle of 2.5◦ and an etalon (ET) larizedatomicensemble. Thecontrollightwasgenerated
was inserted into the probe optical axis. The frequency fromasecondTi:sapphirelaseranditsintensitywasvar-
widthoftheparametricfluorescencewasthusreducedto ied using an acousto-optic module (AOM2).
about 600 MHz before detection. The overall transmis- Fig. 3 shows probe intensity transmissions as a func-
sionefficiencyforthedegeneratecomponentoftheprobe tion of the detuning ∆/2π, where signals were obtained
light without the atoms was about 3%. bysweepingtheprobefrequencyduringthemeasurement
We firstevaluatedthe intensity correlationfunctionof period. In the absence of the control light (dotted line),
the obtained broadband probe light. The light was de- the probe light was absorbed by the atomic medium.
tected by photon counting using silicon avalanche pho- With the addition of the control light (solid line), the
todiodes (D1, D2; PerkinElmer model SPCM-AQR; de- medium was rendered transparent around ∆/2π = 0
tection efficiency: 62%; time resolution: 350 ps). The (peak transmission: 77%; FWHM of the transparency
outputs of D1 and D2 were fed to the start and stop in- window: 8.3MHz). We classifiedthisEITspectruminto
puts, respectively, of a multi-channel scaler (MCS). Fig. three regions: (A) transparent, (B) absorption, and (C)
2(a)shows the normalizedcoincidence rate as a function off resonant regions. The broadband parametric fluores-
of time delay with 1.6 ns resolution. A sharp coinci- cence was spread over all regions
dence peak superposed on a moderate profile of width We observed the propagation of the coherent probe
0.2 µs appears at 0 µs, shown magnified in the inset. pulse in the three regions by injecting probe pulses into
The moderate profile of the coincidence peak is due to the coldatoms 3390times overthe measurementperiod.
3
(B) region), −10 ns of “superluminal” propagation was
observed(dottedcurvein(b)), dueto anomalousdisper-
sion corresponding to the absorption. Under the storage
condition,theprobeintensityincreasedwhenthecontrol
light was tuned off and a slight retrieval was observed
whenthecontrollightwasturnedon(solidcurvein(b)).
The increase of the probe intensity can be explained as
beingduetoachangeintheprobetransmissionfromthe
solid to the dotted curve at ∆/2π = 10 MHz in Fig. 3.
The slight retrieval will be due to the frequency compo-
nent of the probe corresponding to the transparent (A)
region,sincethe frequency widthofalightpulseis given
FIG. 3: (Color online) Measured transmission spectra of a
bytheinverseofitstemporalwidth. Whentheprobewas
weak coherent probe as a function of detuning with (solid
detuned by ∆/2π= 100MHz, the probe signals were al-
line) and without (dotted line) thecontrol light.
most identical under each of the conditions (Fig. 4(c)).
Fig. 2(c)showsthe intensitycorrelationoftheretrieved
componentinFig.4(a), wherethe outputs ofD1 andD2
were gated from 675 ns to 745 ns. The obtained inten-
sitycorrelationfunctiong(2)(0)=1.05±0.01agreeswith
that of coherent light (g(2)(0)=1) [25].
Finally, we observed the propagation of broadband
parametricfluorescenceunder EIT,wherethe centerfre-
quency of the fluorescence was set to the resonant fre-
quencycorrespondingto|ai→|citransition. Figs. 4(d)
shows photon count rates as a function of time under
reference,slowpropagation,andstorageconditions. The
insetshowsmagnificationsofthecountratesfrom600ns
to 850 ns. The experimental conditions were the same
as for the case of the probe light in the coherent state.
Since the frequency width of the probe light was broad,
corresponding phenomena from each of the regions oc-
curred simultaneously. There was almost no difference
FIG.4: (Coloronline)Obtainedprobepulsesunderreference between the reference and the slow propagation condi-
(brokenline),slowpropagation(dottedline),andstoragecon- tions, since the dominant frequency components of the
ditions(solid line). Seetextfor details.. Theprobelight was
probe were far from resonance. However, storage con-
coherent light with frequency detuning of (a) 0 MHz, (b) 10
dition was slightly different from the other conditions.
MHz, and (c) 100 MHz. (d) The probe light was broadband
There was a small retrieved component from 650 ns to
parametricfluorescence. Theinsetof(d)showsmagnification
750 ns. The broken and dotted lines in the inset of (d)
of the count rate from 600 ns to 850 ns.
showresidualcontrollightunderreferenceandslowprop-
agation conditions, respectively. Almost all components
of the residual control light were caused by the diffuse
Figs. 4(a)–(c)showtypicalprobesignalsinthe(A)–(C)
reflection from the vacuum cell. The solid line in the in-
regions. The broken curves correspond to transmitted
set of (d) (storage condition) shows the clear retrieved
probe intensity signals without cold atoms, where the
component. (We checked that the retrieved component
intensity of the control light was dynamically changed
disappearedintheabsenceoftheprobelight.) Thegross
(reference condition). The dotted curves correspond to
count of the retrieved component (the offset due to the
probe signals with cold atoms and constant control light
residual control light was subtracted) was 0.12% of that
(slow propagationcondition). The solidcurves showsig-
oftheincidentbroadbandprobelight(in(d)brokenline),
nals with cold atoms and control light with dynamically
whichagreeswiththeproductofthefrequencywidthre-
varied intensity (storage condition). The control light
duction (8.3 MHz/600 MHz) and the retrieval efficiency
(intensity: 400µW)wasturnedofffrom300nsto350ns
(8%) of the coherent light in (a).
and turned on from 650 ns to 700 ns. For probe detun-
ingof∆/2π =0((A)tranparentregion),apulsedelayof Fig. 2(d) shows the intensity correlation of the re-
25nswasobservedundertheslowpropagationcondition trieved component. The obtained normalized auto in-
(dotted curve in (a)), which corresponds to more than tensity correlation function was g(2)(0) = 9.0±0.2 > 3,
three orders of magnitude reduction in group velocity. i.e. superbunching was obtained, where the coincidence
Under the storage condition, the probe pulse was par- count rate was 0.4 s−1 and the experimental time was 2
tiallystoredandretrieved(solidcurve). Whentheprobe hours. Thecoincidenceat0time delayinFig.2(a)hasa
frequency was detuned by ∆/2π = 10 MHz (absorption sharppeak superposed on a moderate profile,while that
4
coherent light and photon count rates of the retrieved
parametric fluorescence (the offset due to the residual
control light was subtracted) as a function of storage
time. The obtained 1/e decay times were 2.3 µs and 1.6
µsforcoherentlightandparametricfluorescence,respec-
tively. Signal decay was the result of the destruction of
atomiccoherence,whichwasinourexperimentcausedby
residualmagnetic fields due to eddy currents. The small
difference in the atomic coherence times may be caused
by a disturbance of the collective atomic state due to
absorptions of the broadband parametric fluorescence in
FIG. 5: (Color online) Integral intensities of retrieved co-
the absorption (B) region .
herent lights and photon count rates of retrieved parametric
fluorescence as a function of storage time. Inconclusion,wehavedemonstratedfrequencyfiltered
storage of broadband parametric fluorescence (highly
bunched photon-pair state). The frequency component
in (d) does not have such a double structure, where the
ofthefluorescencewithinanelectromagneticallyinduced
signals were obtained under the same time resolution.
transparency window was stored in an atomic ensemble
The observed coherence time of the retrieved light was
and then retrieved after other components had passed
∼35 ns, which is much longer than that of the incident
through the atoms, confirmed by the observation of su-
probe pulse. The increase of the coherence time shows
perbunching and from evaluating the coherence time for
that frequency filtered storage and retrieval occurred,
the retrieved light. This experiment also demonstrated
that is, we have demonstrated the time-frequency filter-
the time-frequency filtering with storage of light tech-
ing with storage of light technique. The experimentally
nique. Whiletheobservationofthesuperbunchingeffect
obtained g(2)(0) should be equal to the theoretical value
is not direct proof of the nonclassicality of the light, the
of 37, since the coherence time was larger than the time
results obtained here are the first steps toward the gen-
resolution for detection. The disagreement can be ex-
erationofvariousnonclassicalstatesofatomicensembles
palainedasfollows. Theratiooftheretrievedlighttothe
with the widely used parametric down conversion pro-
residualcontrollightwasalmostunityinthegatedtime.
cess.
Mixingoftheparametricfluorescence(g(2)(0)=37)with
the coherent light(g(2)(0) = 1) by 1 to 1 ratio gives the WegratefullyacknowledgeR.Inoue,D.Akamatsuand
theoretical value of g(2)(0)=11, which well explains the Y. Yokoi. One of the authors (K. A.) was partially
experimentallyobtainedvalue (9.0±0.2). Theslightdif- supported by the JSPS. This work was supported by
ferencecanbe explainedbythe fluctuationofthe second a Grant-in-Aid for Scientific Research (B) and the 21st
harmonic light intensity (squeeze parameter: r). CenturyCOEProgramatTokyoTech“Nanometer-Scale
Fig. 5 shows the integral intensities of the retrieved Quantum Physics” by MEXT.
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