arXiv:0908.2348v2 [quant-ph] 27 Aug 2010 aeatasto rud13n ewe h ground the between which solids, 1530nm doped around erbium state transition on candidate a based only is The have far state. range, so atomic telecom proposed lived the long in a transition involving optical an with medium 24]. 23, [5, efficient architectures certain repeater for quantum required band telecom- are narrow distance at wavelengths long memories munication a quantum to provide Moreover, adapted could source transmission. it photon single source, with in triggered combination pair integrated In photon be network. a easily communication impor- could fiber an memory the provide quantum communication. a quantum would distance Such memory long for quantum resource tant a retrieve and in in store 1550 nm) use (around to wavelengths direct ability telecommunication for at The suited photons not fibers. thus telecom and close optical was range light these visible all stored the For the to [22]. of systems wavelength state the solid experiments atoms and single [21], cavity [13–20], princi- a gases of in proof atomic with in years, demonstrations few ple last has the progress during pho- made Important been implement [6–12]. fibers. to memories optical quantum proposed quantum tonic in been have of losses schemes distance to Several due limited schemes potential implemen- the a communication the overcome are for to which resource solution repeaters[2–5], crucial quantum They of a tation [1]. example, science for information are, essential quantum an in are matter requirement and light between states quantum ota xeieto trg n erea fwa light weak of retrieval and storage re- we of paper, experiment this an using in Yet port preparation memory [30]. be- techniques the pumping challenging, in optical extremely difficulties quantum the is Photonic of materials cause 26] these [27–29]. [25, in storage properties storage light spectroscopic classical for and studied been have ∗ lcrncades [email protected] address: Electronic eeo unu eoyrqie natomic an requires memory quantum telecom A of transfer reversible the allowing memories Quantum 4 eeomncto-aeeghsldsaemmr ttes the at memory solid-state Telecommunication-wavelength I 15 / 2 n h xie state excited the and o60n na rimdpdY singl Erbium-doped the an at in pulses ns Light 600 solid. to a in wavelengths munication ASnmes 03.67.Hk,42.50.Gy,42.50.Md numbers: PACS implemen science. information is wavelength quantum This telecommunication in at demonstrates resource level. photons experiment single This photon for single effect. memory Stark the linear at the time using inhomoge first reversible the controlled with for echoes photon on based edmntaeeprmnal h trg n erea of retrieval and storage the experimentally demonstrate We ru fApidPyis nvriyo eea H11 Gen CH-1211 Geneva, of University Physics, Applied of Group feis ioa agur,CrsohSmn n ioa Gisin Nicolas and Simon, Christoph Sangouard, Nicolas Afzelius, Bj¨orn Lauritzen, 4 I 13 / 2 hs systems These . 2 ∗ SiO Dtd oebr1,2018) 18, November (Dated: ir ıMnar uusd idatn Mikael Jiˇr´ı Riedmatten, Min´aˇr, de Hugues 5 rsa t26Kadrtivdo ead h eoyis memory The demand. on retrieved and K 2.6 at crystal uss,i Eu a The optical in bright , an effect. with demonstrated pulses Stark with first linear done was the scheme be CRIB using can with gradient this solids field doped moment, electric rare-earth dipole In permanent 34]. 33, a 9, [8, reversing (CRIB) is and ing Broaden- scheme Inhomogeneous generating Reversible This Controlled rephas- by as known broadening. the dipoles inhomogeneous A induce artificial atomic to an [32]. the is level of problem unacceptable this ing an overcome to the to storage reduce way the and of emission op- fidelity spontaneous strong amplified the to of [31]. leads application echoes ( the pulse that photon tical is photon pulse issue two traditional main pho- as using The single such possible techniques, (e.g. not echo light however de- quantum is of This tech- tons) echo storage photon The using photon. for niques. the compensated be of can phasing re-emission storage, ef- an collective the be preventing single During ficient place, can to takes dephasing leading [22]. photons inhomogeneous excitations transition, Single optical optical collective this onto line. mapped absorption solid. broadened doped erbium an in level photon single the at fields hs ftesoe ih usswssont ewell 10 and of be order storage to the the shown of experiments, was was these efficiency pulses retrieval For light [35]. stored preserved the of phase mi Pr 606 in at experiments nm recent more in improved dramatically ytein ntebodndln,admpe noa into mapped and line, broadened the in absorbed of is ions photon bandwidth incident the The the by match stored. be to gradient to effect field photon the Stark electric an linear by the spectrum broadened using then The is window. line absorption transparency this narrow of large a a prepare to within has line first one solid, regime. doped quantum the to pho- road single the the opening first at level, the telecommu-ton CRIB report of at also demonstration experiment at we experimental an [37] Moreover, vapor report wavelength. rubidium we nication a Here, in nm. transition 780 spin a on strated aeerhdpdsld aea inhomogeneously an have solids doped Rare-earth nodrt elz RBeprmn narare-earth a in experiment CRIB a realize to order In eu raeig hc sraie here realized is which broadening, neous htnlvlaesoe o ieup time a for stored are level photon e h esblt fasldsaequantum state solid a of feasibility the ,wihwudrpeeta important an represent would which s, ekchrn ih ed ttelecom- at fields light coherent weak 3+ e iha xenlfil gradient field external an with ted π :Y ple oidc h ehsn mechanism rephasing the induce to -pulse) 2 SiO 3+ :Y 5 v ,Switzerland 4, eva 2 3] RBhsas endemon- been also has CRIB [36]. SiO 5 nl htnlevel photon ingle rsa t50n 3] The [33]. nm 580 at crystal − 6 thsbeen has It . 2 single collective atomic excitation. During a time t each Our memory consists of an Y2SiO5 crystal doped with excited ion i will acquire a phase ∆it due to its shift in erbium (10ppm) cooled to 2.6 K in a pulse tube cooler the absorption frequency ωi = ω0 + ∆i from the central (Oxford Instruments). The crystal has three mutually frequency ω0. Switching the polarity of the field after a perpendicular optical-extinction axes labelled D1, D2, time t = τ will reverse the broadening (ωi = ω0 − ∆i) and b. Its dimensions are 3.5 × 4 × 6mm along these and after another time τ the ions will be in phase again axes. The magnetic field of B =1.5 mT used to induce and re-emit the photon. In order to create the initial nar- the Zeeman splitting necessary for the memory prepa- row absorption line, a population transfer between two ration is provided by a permanent magnet outside the ground states (in our case Zeeman states) using optical cryostat and is applied in the D1 − D2 plane at an angle ◦ pumping via the excited state is used [30]. In case of im- of θ = 135 with respect to the D1-axis [38] (Fig.1b). perfect optical pumping there will be population remain- The light is travelling along b. The electrical field gra- ing in the excited state after the preparation sequence. dient for the Stark broadening is applied with four elec- An experimental issue arising when input pulses are at trodes placed on the crystal in quadrupole configuration, the single photon level is the fluorescence from the re- as shown in Fig.1b and described in [39]. The induced maining excited atoms. If the depletion of this level is broadening is proportional to the voltage U applied on slow (as in rare-earth ions, with optical relaxation times the electrodes [39]. T1 usually in the range of 0.1 ms to 10 ms), this can The experiment is divided into two parts: the prepa- lead to a high noise level that may blur the weak echo ration of the memory and the storage of the weak pulses pulse. The problem is especially important for erbium (see Fig.1b). Each preparation sequence takes 120ms of doped solids, where T1 is very long (≈ 11 ms [25] in 3+ optical pumping during which both the pump and the Er :Y2SiO5). In our experiment, the population trans- stimulation lasers are sent into the sample. The fre- fer is enhanced by stimulating ions from the excited state quency of the pump laser is repeatedly swept to create down to the short lived second ground state crystal field a large transparency window into the inhomogeneously level using a second laser at 1545 nm (Fig. 1a) [30]. The broadened absorption line. If the laser is blocked for a application of this laser enhances the rate of depletion of short time at the center of each sweep using an acousto- the excited state and thus reduces the noise from fluores- optical modulator (AOM), a narrow absorption feature cence. Together with a suitable waiting time between the is left at the center of the pit [30]. The time available preparation and the light storage, it allows the realization to perform the memory protocol is given by the Zeeman of the scheme at the single photon level. lifetime of TZ = 130ms [38] of the material. In order to deplete the excited state the laser at 1545nm is left on for 23.5ms after the pump pulses. Then the prepa- +/− ration path is closed and the detection path is opened − / + − / + using an optical switch and mechanical choppers. The storage sequence begins 86ms after the pump pulse, in + − / order to avoid fluorescence from the excited atoms. It is composed of 8000 independent trials separated by 5µs. In each trial, a weak pulse of duration δτ is stored and re- trieved. The initial peak is broadened with an electrical AOM 1545 nm EDFA pulse before the absorption of each pulse. The polarity WDM Chopper of the field is then inverted at a programable time after Switch SSPD AOM the storage, allowing for on demand read-out. The whole WDM 1536 nm EDFA PBS 50/50 Chopper sequence is repeated at a rate of 3Hz. The weak output −XXdB Cryostat mode is detected using a superconducting single photon 3+ FIG. 1: (color online) (a) Level scheme of Er :Y2SiO5. (b) detector (SSPD) [40] with an efficiency of 7% and a low Experimental setup: The pump laser (external cavity diode dark count rate of 10 ± 5Hz. The incident pulses are laser at 1536nm) is split into two paths, one for the prepara- weak coherent states of light |αiL with a mean number tion pulses and one for the weak pulses to be stored. Pulses of photons n = |α|2. We determined n at the input of the are created with acousto-optical modulators (AOMs). In the cryostat by measuring the number of photons arriving at preparation path, the stimulation laser (DFB laser diode at the SSPD (with the laser out of resonance), compensat- 1545nm+fiber amplifier) is added using a wavelength division ing for the transmission(16%) and detection efficiency. multiplexer (WDM). The pulses to be stored are attenuated to the single photon level with a fiber attenuator. An optical We now describe the observation of CRIB photon switch allows us to send either of them into the sample. In echoes of weak pulses. As a first experiment, we sent order to protect the detector (SSPD) and to avoid noise from pulses with n =10 and δτ = 200 ns into the sample. a leakage of the optical switch, two mechanical choppers are The polarity of the electric field (U = ± 50 V) was re- used. The polarization of the light is aligned to maximize the versed directly after each pulse. Fig. 2 shows a time absorption using the polarizing beam splitter (PBS). Inset: histogram of the photon counts detected after the crys- illustration of the crystal with electrodes, magnetic field and tal. The first peak corresponds to the input photons light propagation directions indicated. transmitted through the crystal. The second peak is the 3

CRIB echo. It is clearly visible above the noise floor. time of the stored light. Fig. 3 shows the efficiency of Only a small fraction of the incident light is re-emitted the CRIB echo for different storage times. The signal was in the CRIB echo (about 0.25 %). The reasons for this clearly visible up to a storage time of around 600 ns. The low storage and retrieval efficiency and ways to improve decay of the efficiency is due to the finite width of the it will be discussed in more detail below. As a consis- initial (unbroadened) peak [11] (see below). The solid tency check, we verified that the echo disappears when line is a fit assuming a gaussian shape for the absorption the narrow absorption peak is not present (see blue open line, giving a decay time of 370 ns. Shorter pulses with circles in Fig. 2). By reversing the electric field gra- δτ = 100 ns have also been stored (see the inset of Fig. 3) with a larger broadening (U = ± 70 V), leading to a larger time-bandwidth ratio, with however a reduced storage efficiency. Finally, we gradually lowered n by in- 8 creasing the attenuation, for input pulses with δτ=200 ns . The result is shown in Fig. 4a. Both the number of 6 photons in the CRIB echo and the signal to noise ratio depend linearly on n. This means that the efficiency and the noise are independent of n. Fig. 4b shows the result 4

7 0.04 70 2 60 6 0.03 50 5 0 40 4 0.02 −200 0 200 400 600 800 1000 30 3 2 0.01 20 10 1 FIG. 2: (color online) CRIB measurement with (red triangles, 0 0 0 0 5 10 15 0 400 800 solid line) and without (blue circles, dashed line) absorption peak, with n = 10 and δτ = 200 ns. The pulse on the left is the transmitted part of the incident photons. One can FIG. 4: (color online) (a) Number of photons in the CRIB clearly see that the absorption is enhanced in the presence of echo (open circles) and signal to noise ratio (plain triangles) a peak. The electric field (U=±50 V) was reversed just after as a function of the number of incident photons n, for 200 ns the input pulse. Dark counts have been subtracted from the input pulses. (b) CRIB echo for n = 0.6 (integration time data. Integration time for both curves was 200s. 25000s). Dark counts have been subtracted from the data.

of a measurement with - in quantum key distribution ter- minology - pseudo-single photons (n = 0.6 photons per pulse). In that case, we still obtain a signal to noise ratio of ∼3. The remaining noise floor may be due to residual fluorescence and leakage through the AOM creating the pulses to be stored. In the following we analyze the efficiency and storage time performances of our memory in more detail. Ref. [11] gives a simplified model for the CRIB memory. In this model, the storage and retrieval efficiency if the echo is emitted in the forward direction is given by :

2 2 2 −d −t γ˜ ηCRIB(t)= d e e (1) whereγ ˜ =2πγ is the spectral width (standard deviation) of the initial gaussian absorption peak, and d is the op- FIG. 3: (color online) Efficiency of the CRIB memory as a tical depth of the broadened absorption peak. The main function of storage time, for input pulses with δτ=200 ns , assumption here is that the spectral width of the absorp- n = 10 and U = ±50 V. The error bars correspond to the tion peak is much wider than the spectral bandwidth of statistical uncertainty of the measured photon numbers. The the photon to be stored. By fitting the decay curve of solid line is a gaussian fit (with the first point excluded). The Fig.3 with Eq.1, we find a full width at half maximum inset shows CRIB echoes for three different switching times of linewidth of the central peak of 1MHz. This corresponds the electrical field. For the inset curves, δτ=100 ns, U=±70 well to the results obtained by a measurement of the V and the integration time is 500 s. transmission spectrum. The minimal width is limited by the linewidth of our unstabilized laser diode and power dient at later times, it is possible to choose the retrieval broadening during the preparation of the peak. The op- 4 tical coherence time of the transition under our experi- of the optical and the ground state Zeeman transitions mental conditions has been measured independently by [30]. This could be improved in several ways. First tech- photon echo spectroscopy. It was found to be T2 ≈ 2µs, nical improvements can be implemented, such as using corresponding to a homogeneous linewidth of 160 kHz. lower temperatures, higher stimulation laser intensities 3+ Note that the optical coherence in Er :Y2SiO5could be and spin mixing in the excited state using RF fields, as drastically increased using lower temperatures and higher demonstrated in [30]. Second, the branching ratio and magnetic fields [26]. Zeeman life time strongly depend on the applied mag- In our experiment, imperfect optical pumping results netic field angle and intensity. A full characterization in a large absorbing background with optical depth d0, of the optical pumping efficiency with respect to these which acts as a passive loss, such that the experimen- parameters has not been carried out yet. Finding opti- tal storage and retrieval efficiency is given by: η(t) = mal conditions may lead to significant improvements. It ηCRIB(t)exp(−d0) [22]. The values of d and d0 can would also be interesting to investigate hyperfine states. be measured by recording the absorption spectra. This Finally, other crystals might be explored, e.g., Y2O3, to yields an optical depth of the unbroadened peak d′ = search for longer Zeeman lifetimes. 0.5±0.2 and an absorbing background of d0 =1.6±0.1. A In summary, we have presented a proof-of-principle voltage of 50 V on the electrodes corresponds to a broad- of quantum memory for photons at telecommunication ening of a factor of ∼3 [39], leading to d = 0.17 ± 0.07. wavelengths. Pulses of light at the single photon level In our experiment, the photon bandwidth is of the same have been stored and retrieved in an Erbium doped crys- order as the broadened peak, so that the assumptions of tal, using the CRIB protocol. Continuing efforts to in- the simplified model are not fulfilled. In order to have crease the efficiency and the storage time will be required a more accurate description, we have solved numerically in order to build a useful device for applications in quan- the Maxwell-Bloch equations with the measured d′, using tum information science. Our experiment is nevertheless a gaussian initial peak. This gives storage and retrieval an enabling step towards the demonstration of a fiber efficiencies of order 1.5 · 10−3 (including the passive loss network compatible quantum light matter interface. It d0) for a storage time of 300 ns, in reasonable agreement also confirms the feasibility of the CRIB protocol at the with the measured values (see Fig. 3) single photon level. This study shows that the main reason of the low stor- The authors acknowledge technical assistance by Clau- age and retrieval efficiency in the present experiment is dio Barreiro and Jean-Daniel Gautier as well as stimu- the small absorption in the broadened peak and the large lating discussions with Imam Usmani, Wolfgang Tittel, absorbing background, due to imperfect optical pump- Sara Hastings-Simon, Matthias Staudt and Nino Wa- ing. About 80 % of the retrieved photons are lost in the lenta. This work was supported by the Swiss NCCR absorbing background. The limited optical pumping effi- Quantum Photonics, by the European Commission under ciency is due to the small branching ratio in the Λ system the Integrated Project Qubit Applications (QAP) and and to the small ratio between the relaxation life times the ERC-AG Qore.

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