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Light-shift modulated photon-echo Thierry Chanelière1 and Gabriel Hétet1,2 1Laboratoire Aimé Cotton, CNRS, Université Paris-Sud and ENS Cachan, CNRS-UPR 3321, 91405 Orsay, France 2Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France 5 compiled: February25,2015 1 0 2 We show that the AC-Stark shift (light-shift) is a powerful and versatile tool to control the emission of a b photon-echo in the context of optical storage. As a proof-of-principle, we demonstrate that the photon-echo e efficiency canbefullymodulated byapplyinglight-shiftcontrol pulsesinanerbiumdoped solid. Thecontrol F oftheechoemissionisattributedtothespatialgradientinducedbythelight-shiftbeam. 4 OCIS codes: (020.1670); (160.5690); (160.2900); (210.4680); (270.5565); (270.5585) 2 http://dx.doi.org/10.1364/XX.99.099999 ] h p - The photon-echo technique has been reconsidered re- Within this generalframework,we investigateexperi- t n cently with important applications in the context of mentally the use of light-shift pulses in a standard two- a quantum information storage and processing [1]. The pulse photon-echosequence. We showthatthe emission u two-pulse or three-pulse schemes have inspired a vari- can be fully modulated by applying light-shift pulses. q ety of storage protocols [2]. The echo techniques have Our demonstration is in that sense equivalent to the [ been implemented in different systems from atomic va- DC-Stark shift modulated spectroscopy pioneered by 2 pors to doped solids with remarkable performances in Meixner et al. [24]. In our case, we attribute the mod- v terms of efficiency [3, 4], bandwidth [5], multiplexing ulation to the phase spatial pattern imprinted on the 1 capacity [6, 7]. The two-pulse echo is indeed a stim- coherences by the light-shift beam. This phase gradi- 1 ulating source of inspiration to propose new protocols. ent is a starting point to realize an all-optical version 4 In the echo sequence, the classical π-pulses must be as- of the gradient-echo memory [19, 25]. We first show 5 0 sociated with an extra control parameter to make the that the emission of a two-pulse photon-echo (2PE) in 1. protocol suitable for quantum storage. This can be a Er3+:Y2SiO5 canbecontrolledbyapplyingastrongoff- rapidly switched electric field [8–11], a magnetic field resonant pulse. The latter produces a light-shift during 0 5 [12–14], a modified phase-matching condition [15] or a the free evolution of the coherences partially inhibiting 1 frequency tunable active cavity [16, 17].These propos- the echo emission later on. We compensate this extra : als cover different realities, atomic vapors and doped dephasing by a second light-shift pulse thus validating v solids,bothintheopticalortheradio-frequencydomain. the method for controlling the emission of an optical i X TheAC-Starkshiftorlight-shiftcannaturallycomplete memory. ar tithyistpoatnhoeplDyCfo-rStmarakteoriralZsewemithanaewffeeacktsoarszeprooinsteendsitoiuvt- We choose Er3+:Y2SiO5 as a test-bed for the light- shiftmodulatedphoton-echoexperimentbecauseitisre- early by Kraus et al. [9]. As a counterpart of the DC- calcitranttotheefficientimplementationofthegradient- Stark shift which has alreadyprovento be veryefficient echo scheme with DC-Stark shifts [26]. Our experimen- for quantum memories based on the so-called gradient tal setup has been extensively described previously in echo protocol [4], the light-shift is considered because refs.[27, 28] (see Fig.1). We implement a 2PE sequence of its versatility for the gradient design [18] and its fast in Fig.2 with a probe beam polarized along D whose switching time [19]. The imprinted phase pattern can 1 waistis 50 µm. Its Rabi frequency is 2π 150kHz mea- also apply for optical memories based on “electromag- × sured by an optical nutation experiment [29]. There netically induced transparency” [20]. This latter result is no preparation of the medium by optical pumping. demonstratesthedeflectionoftheretrievedsignalwhich The sequence is repeated every 20ms so the atoms are is clearly a possibility offered by the light-shift gradi- all initially in the ground state. The 2PE is composed ent design. The shift induced by strong laser pulses on of two gaussian 1µs pulses (rms-duration) separated by spin transitions (electronic and/or nuclear) is also used t =35µs. Theechoisobservedat2t =70µs(Fig.2). in spin-echo sequences showing the omnipresence of the 12 12 A second beam is used to produce off-resonant excita- phenomenon in different fields [21–23]. tion (light-shift pulse) within the echo sequence. The 2 latter has a waist of 110 µm and is polarized along D . pulses haveadurationof1µsso their bandwidth is typ- 2 Its Rabifrequencyis Ωmax 2π 330kHz. Itis counter- ically 150kHz very comparable to the Rabi frequency of LS ≃ × propagating and overlapped with the probe beam. 2π 150kHz. This is significantly lower than the light- × shift beam detuning 1.5MHz. We now investigate the light-shift dependency as a function of the experimental parameters. If the light- shift pulse is described by its time-varying Rabi frequency Ω(t), one expects the transition of the atoms under the probe to be shifted by Ω2(t). The accumu- ∆ lated phase Φ is then LS Ω2(t) Ω2 Φ = dt=√2π LSτ (1) LS Z ∆ ∆ t given by the gaussian pulse parameters, Ω its ampli- LS tudeandτ itsduration. Weinvestigatethisdependency (Eq.1)byfirstvarying∆. Thetimesequenceisthesame Fig. 1. Y2SiO5 sample doped with 50 ppm of Er3+. At 1.8 asbefore(seeFig.2)expectthatτ =2µsand∆isvaried K and under a 2T magnetic field in the plane (D1-D2), the from 2π×1MHz to 2π×3MHz. coherencetimeis∼130µs(4I -4I transitionfor“site 15/2 13/2 1” ) [28, 30]. 1 0.8 arb.u.)2.235 Light−sh1ift. 5pMulHsez Echo intensity0000....12468 Echo intensity00..46 y (1.5 0 0.2 ntensit 1 0 ILS0/.5ILmSax 1 0 I 1 1.5 2 2.5 3 Detuning∆/(2π)(MHz) 0.5 0 Fig. 3. Echo intensitywhen thelight-shift pulsedetuning∆ 0 10 20 30 40 50 60 70 80 Time (µs) is varied (square symbols). The experiment is repeated by varying∆butbykeepingτ/∆=2µs/MHzconstantsoτ goes Fig.2. Two-pulsephotonechosequence(dashedblackline). from2µsto6µs(circles). Thedashedlinesareusedtoguide Weapplytwostrongpulsesatt=0andt12 =35µs(clipped theeye. Measurement errors are again a few percents. bytheoscilloscopescale). Weobserveanechoat2t12 =70µs. The intensity is normalized so that the echo amplitude is 1. When ∆ is increased (Fig.3), the effect of the light- When a light-shift pulse detuned by 1.5MHz (in solid red) shift pulse is reduced, thus qualitatively following the is applied at t12/2=17.5µs, the echo intensity (solid black) is reduced from 100% to 30%. Inset: Reduction of the echo 1/∆dependency. A quantitative analysisis notdirectly intensity as a function of the light-shift intensity ILS (the possiblebecauseaperturbativetreatmentisinappropri- dashed line is used to guide the eye). Measurement errors ate when strong pulses are used [29]. Alternatively, we are a few percents given by shot-to-shot fluctuations due to propose to vary ∆ but by keeping τ/∆ constant to val- thelaserjitter(theyroughlycorrespondtothemarkerssize). idate Eq.(1). In this latter case, we observe that the effect of the light-shift is quasi-constant. A weak sig- In Fig.2, we show that when a light-shift pulse whose nificant variation from 30% to 38% is still observable. rms-durationτ =3µsanddetunedby∆=2π 1.5MHz It cannot be explained by Eq.(1). Additional modeling is applied at 1t = 17.5µs, the echo is redu×ced from would be requiredbut the agreementwith the expected 2 12 100%to30%. InFig.2(inset),wealsoincreasegradually τ/∆ dependency is satisfying. thelight-shiftpulseintensityI from0toitsmaximum Tofurtherexplorethiseffect,wenowproposetoapply LS value Imax corresponding to Ωmax. a first phase shift within the sequence and to compen- LS LS Thedestructionoftheechobyanextrapulseinserted sateitbyasecondpulse. LookingatEq.(1),anintuitive in the time sequence is not obviously attributed to the compensation solution is to apply two successive pulses light-shift induced on the coherence rephasing. Never- with opposite detunings during the free evolution be- theless it should be noted that the light-shift beam is tween t = 0 and t . A less obvious solution offered by 12 sufficiently detuned to produce only an off-resonant ex- the 2PE sequence is to apply one light-shift pulse be- citation on the atoms driven by the probe. The probe tween t = 0 and t (called region I) and a second one 12 3 between t12 and 2t12 (called region II) with the same (a) +1.5 MHz detuning. To justify this compensation scheme, we can 2 −1.5 MHz simply track down the accumulated phase φ(ω,t) due 0.98 to the inhomogeneous dephasing [29]: (i) In region I, 1 after the first excitation,the coherence atthe frequency 0 ω freely evolves, accumulating φ(ω,t)=ωt. Just before (b) +1.5 MHz the second pulse at t , the phase is φ(ω,t−) = ωt . 2 +1.5 MHz 12 12 12 (ii) If a light-shift pulse is applied in region I, an extra termΦI isadded: φ(ω,t−)=ωt +Φ . (iii)Thesec- 1 LS 12 12 LS 0.06 ond pulse conjugates the coherence so the phase is now 0 φ(ω,t+) = ωt ΦI right after the second pulse. (c) (iv) D12uring−the f1r2ee−evoLlSutionfromt to t in regionII, 2 +1.5 MHz +1.5 MHz 12 0.98 the accumulatedphase is ω(t t ) sothe totalphase is 12 1 φ(ω,t)= ωt ΦI +ω(t −t )=ω(t 2t ) ΦI . As expect−ed, 1t2he−retLrSieval tim−e122t12 corre−spon12ds−to tLhSe u.)0 (d) icnohreergeionnceIIr,epahnaesxintrga. t(evr)mIfΦaILISligishta-dshdiefdt.pTulhsuesisthaepptoliteadl y (arb.2 +1.5 MHz −1.5 MHz inhomogeneous phase at the instant of retrieval is sit1 n Region I Region II e 0.03 φ(ω,t)=ω(t−2t12)−ΦILS+ΦILIS. (2) Int00 20 40 60 80 Time (µs) As a conclusion, similar pulses (same detuning) applied in region I and II compensate each other. Pulses with Fig. 4. Light-shift pulses compensation scheme. (a) If two opposite detunings cancels each other only if they are pulses with opposite detunings are applied in region I, the both in region I or II exclusively. As we see in Fig.4, echo intensity is 98% of its initial value. (b) With the same by properly choosing the sign of the detuning and the detuning, the effect of the light-shift is cumulative and the region of application, we can retrieve an echo with 98% echoisonly6%. WhenappliedinregionIandIIrespectively, (Fig.(4.a) and (4.c)) of its initial reference intensity. the pulses compensate each other with the same detuning As a summary, the dependency as τ/∆ illustrated in (98% echo intensity in (c)) or add up with opposite detun- Fig.3 and the compensation scheme presented in Fig.4 ing (3% echo intensity in (d)). The light-shift pulses have a based on Eq.(2) is a strong evidence that the echo is ±1.5MHz detuningand a τ =3µs duration (as in Fig.2). indeed controlled by the light-shift induced by the off- resonant pulses. This analysis justifies the main claim of our paper. Even if we have shown that the induced A spectral dependency induced by the light-shift has light-shift can be used to fully modulate the echo from anegligibleinfluenceinourcasebecausethedetuningis 100%to3%(Fig.4.d),aquantitativelinkbetweenEq.(1) significantlylargerthantheexcitedbandwidthasprevi- and the echo amplitude including gaussian propagation ously mentioned. It should be noted that the first order effects is not obvious. In a first approach, the echo am- effect of a spectral dependency described by plitude isthe totalcontributionoftheexcitedatoms(at Ω2 Ω2 Ω2 frequencyω)atagivenpositionRleadingtoanemission Φ (ω)=√2π LS τ √2π LSτ √2π LSτω (4) in the k direction proportional to [29]: LS ∆+ω ≃ ∆ − ∆2 is to modify the retrieval time from 2t to 2t exp(k.R k .R+φ(ω,t)) (3) 12 12 Xω,R~ − in √2πτΩ2LS/∆2 (see Eq.2 depending if the pulse is in re±- gion I or II). The pulse should be delayed to the first wherek istheprobewave-vector. Theinhomogeneous order. This is not what we observe so the spectral de- in phase φ(ω,t) may also include a spatial dependency pendency is certainly negligible. if the light-shifts depend on R. Without light-shift, The spatial dependency of the induced light-shift the echo peaks in the k direction (phase-matching) Φ (z,r) can now be discussed. It may be both lon- in LS at t = 2t (eq.2). It is important to note that a net gitudinal(alongz)andtransverse(along r, in the (x,y) 12 global added phase to all the atoms excited by the 2PE plane). We choose to overlap the probe and light-shift does not change the echo amplitude but only its phase. beams,asaconsequencethelongitudinalandtransverse The echois reducedonlyif the phasevariesthroughthe gradients are decoupled (rotational symmetry). It sim- inhomogeneous profile (depends on ω, spectral depen- plifies our analysis at this level. Nevertheless, we have dency)orisnotconstantthroughthesample(R,spatial alsoverifiedexperimentallythatangledbeamsproduces dependency). A spectral dependency may prevent the a significant reduction of the photon-echo. It should be coherence rephasing at t = 2t . A spatial dependency kept in mind when more practical conditions are con- 12 modifies the phase-matching condition when the echo is sidered. In our case, the z-gradient may be due to the emitted. We discuss these two possible effects before absorptionofthelight-shiftbeamΩ (z)alongtheprop- LS concluding. agationdirectionz. The r-gradientappearsbecausethe 4 light-shift beam as a finite size (110 µm) with respect [3] M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, tothe probe(50µm). The longitudinaldependency can and B. C. Buchler, Nat.Commun. 2, 174 (2011). be evaluated. At z = 0, we have Ω (0) 2π 330kHz [4] M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, LS andthenΦ (0) 1.1π. Thegaussiandiv≃ergen×ceofthe Nature 465, 1052 (2010). LS ≃ [5] E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, light-shiftbeamisnegligiblebecauseitsRayleighlength D. Oblak, F. Bussieres, M. George, R. Ricken, is ten times longer than the crystal. On the contrary, W. Sohler, and W. Tittel, Nature469, 512 (2011). its complete absorptionwouldproduce a phase gradient [6] M. Bonarota, J.-L. L. Gouët, and T. Chanelière, from 1.1π at z = 0 to 0π at the output of the sample. New J. 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Phys. 13, 3% absorption for a 7π area pulse. The transverse ∼ 093031 (2011). spatial dependency is a very likely explanation. A first [16] B. Julsgaard, C. Grezes, P. Bertet, and K. Mølmer, order estimation of the transverse shift induced by the Phys. Rev.Lett. 110, 250503 (2013). probe (50 µm) and light shift beam (110 µm) spatial [17] M.Afzelius,N.Sangouard,G.Johansson,M.U.Staudt, mode mismatch only predicts a 10% echo modulation. and C. M. Wilson, New J. Phys. 15, 065008 (2013). 3D-Bloch-Maxwell numerical simulations would be nec- [18] G. Hétet and D. Guéry-Odelin, essaryto accountfor the three-dimensionalpropagation arXiv:quant-ph/1501.01194. of the echo. [19] B. M. Sparkes, M. Hosseini, G. Hétet, P. K. Lam, and To conclude, we show that the photon echo emission B. C. Buchler, Phys. Rev.A 82, 043847 (2010). [20] U. Schnorrberger, J. D. Thompson, S. Trotzky, can be fully modulated by applying off-resonant pulses R. Pugatch, N. Davidson, S. Kuhr, and I. 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