Storage and retrieval of microwave fields at the single-photon level in a spin ensemble
C. Grezes, B. Julsgaard, Y. Kubo, W. L. Ma, M. Stern, A. Bienfait, K. Nakamura, J. Isoya, S. Onoda, T. Ohshima, V. Jacques, D. Vion, D. Esteve, R. B. Liu, K. Mølmer, P. Bertet
SStorage and retrieval of microwave fields at the single-photon level in a spin ensemble
C. Grezes , B. Julsgaard , Y. Kubo , W. L. Ma , , M. Stern , A. Bienfait , K. Nakamura , J. Isoya , S.Onoda , T. Ohshima , V. Jacques , D. Vion , D. Esteve , R. B. Liu , K. Mølmer , and P. Bertet Quantronics group, Service de Physique de l’Etat Condens, DSM/IRAMIS/SPEC,CNRS UMR 3680, CEA Saclay, 91191 Gif-sur-Yvette, France Department of Physics and Astronomy, Aarhus University,Ny Munkegade 120, DK-8000 Aarhus C, Denmark. Department of Physics, Centre for Quantum Coherence, and Institute of Theoretical Physics,The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China State Key Laboratory of Superlattices and Microstructures,Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China Energy System Research Institute, Fundamental Technology Department,Tokyo Gas Co., Ltd., Yokohama, 230-0045, Japan Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan Japan Atomic Energy Agency, Takasaki 370-1292, Japan and Laboratoire Aim´e Cotton, CNRS, Universit Paris-Sud and ENS Cachan, 91405 Orsay, France (Dated: March 12, 2018)We report the storage of microwave pulses at the single-photon level in a spin-ensemble memoryconsisting of 10 NV centers in a diamond crystal coupled to a superconducting LC resonator.The energy of the signal, retrieved 100 µ s later by spin-echo techniques, reaches 0 .
3% of the energyabsorbed by the spins, and this storage efficiency is quantitatively accounted for by simulations.This figure of merit is sufficient to envision first implementations of a quantum memory for super-conducting qubits.
Superconducting qubits are attractive candidates forsolid-state implementations of quantum information pro-cessing, but suffer from coherence times shorter than ∼ µ s [1–3]. To circumvent this issue, it has been pro-posed to use ensembles of spins in semiconductors[4–9]as a multimode quantum memory, able to store multi-ple qubit states over longer periods of time, and to re-trieve them on-demand [10]. Inspired by research on op-tical quantum memories [11–13], realistic protocols havebeen proposed recently [14, 15]. The state of a super-conducting qubit is first converted into the state of a mi-crowave photon, propagating or trapped in a resonator.This photon is then resonantly and collectively absorbedby the spin ensemble, resulting in a transverse magneti-zation which, due to the spread of resonance frequencywithin the ensemble, decays in a time T ∗ called the free-induction decay (FID) time. The write step is later fol-lowed by the need to read the stored quantum state. Bothprotocols [14, 15] propose to apply sequences of π pulsesto the spins, combined with dynamical tuning of the res-onator frequency [16, 17] and quality factor [18, 19] inorder to trigger the rephasing of the spins, resulting inthe emission of an echo at a chosen time that faithfullyreproduces the initial quantum state.Whereas the transfer of a qubit state into a spin en-semble has been demonstrated experimentally [20–23],implementing the read step remains the major obstacleto an operational microwave quantum memory. An in-termediate goal consists in storing a classical microwavepulse with an ultra-low power corresponding to an aver-age of 1 photon in the resonator and to retrieve it as anecho after a refocusing pulse, as was achieved at opticalfrequencies [24, 25]. First results in this direction were obtained using ensembles of negatively-charged nitrogen-vacancy (NV) colour centers in diamond [26, 27] and ofrare-earth ions in a Y SiO crystal [28]. The NV’s elec-tronic spin is a spin triplet ( S = 1) well suited for aquantum memory because of its long coherence times inpure crystals [29, 30] and the possibility of repumping itinto its ground state m S = 0 by optical irradiation at532 nm [31] (see Fig. 1). In [27], successive low-powermicrowave pulses were stored in an NV ensemble, andretrieved later as a series of echoes after a refocusingmicrowave pulse was applied. A key aspect in this ex-periment was an active reset of the NVs to increase therepetition rate of successive experimental sequences toobtain sufficient statistics; this was achieved by applyingoptical pumping laser pulses injected through an opticalfiber introduced in the cryostat. The echo efficiency, de-fined as the ratio of the echo energy and the stored pulseenergy, was, however, not sufficient in [27] to observe anecho below 100 photons on average in the resonator.Here, using a sample with a longer coherence time andan improved optical pumping scheme, we increase theecho efficiency and the storage time by one order of mag-nitude. This allows us to observe an echo with an initialpulse power corresponding to on average only one photonin the resonator. The diamond single crystal was synthe-sized by the temperature gradient method at high pres-sure and high temperature (HPHT) using 99 . C-enriched pyrolytic carbon prepared from C-enrichedmethane as a carbon source [32], resulting in a nomi-nal 300 ppm concentration of C nuclei. The original1 . a r X i v : . [ qu a n t - ph ] A p r m I D m s E A
532 nm V N β S =1 B NV // [110] (a)(b) (c) I =1 g ens ω r ω s
532 nm A M W s ou r c e A W G φ θ R
100 mK4 K300 K
FIG. 1. (a) Experimental setup and principle of the exper-iment. An ensemble of ∼ spins is inductively coupledto a planar superconducting LC resonator of frequency ω r (with a collective coupling constant g ens ), cooled at 10 mK.The resonator is measured in reflection through an input cou-pling capacitance. Microwave pulses are produced by mix-ing a continuous microwave source with dc pulses generatedby an arbitrary waveform generator (AWG). They drive thespins via the microwave current induced in the resonator in-ductance. The reflected microwave signal (including the emit-ted echo) is amplified at low-temperature and demodulatedat room-temperature, yielding its amplitude A ( t ) and phase φ ( t ). (b) The spins are Nitrogen-Vacancy color centers in dia-mond, which consist of a nitrogen impurity next to a vacancyof the diamond lattice. A dc magnetic field B NV applied par-allel to the chip along the [110] crystalline axis so that onlyNV centers whose axis are non-orthogonal to the field (shownin blue on the figure) are Zeeman-shifted and contribute tothe signal. Laser pulses can be sent onto the diamond via adirect optical access to the cryostat mixing chamber. (c) NVcenters energy levels in a weak magnetic field. The electronicground state is a spin triplet S = 1, with a zero-field split-ting D/ π = 2 .
88 GHz, coupled by hyperfine interaction tothe N nuclear spin triplet I = 1. This splits each of the | m S = 0 (cid:105) → | m S = +1 (cid:105) transitions into a triplet of lines. perature followed by annealing for 2 hours at 1000 ◦ C,yielding a final [
N V − ] = 0 . P
1] = 0 . S ( ω ), measuredwith a network analyzer, is shown in Fig. 2a, yieldingthe resonance frequency ω r / π = 2 .
915 GHz and quality ω / ( π ) ( G H z ) B NV ( mT ) -20.0-19.5-19.0-18.5-18.0|S | (dB) -19.2-18.8 NV (mT) P L = 280 µ W (b)(c) MWoptical T L µ s -1000100 φ ( ° ) ω /(2 π ) (GHz) (a) p / p m a x L (s) Repump.Sat. Meas.
FIG. 2. (a) Phase φ of the resonator reflection coefficient S ( ω ) measured with a vector network analyzer (blue dots),yielding ω r / π = 2 .
915 GHz and Q = 650 (red line is a fit tothe data). (b) S ( ω ) as a function of B NV around 1 . | S | ( B NV ) at ω/ π = 2 .
915 GHz; blue dots aredata, and red line is a fit to a sum of three Lorentzians withlinewidth 0 .
012 mT. (c) Measured spin polarization for a laserpulse of power P L = 280 µ W as a function of its duration T L ,renormalized to its maximal value. Dashed red and black linesindicate the laser pulse durations T L = 0 . . p/p max = 0 .
72 and 0 . factor Q = 650, fixed by the coupling to the measure-ment line through the input capacitor. NV centers aredetected by their absorption of the microwave whenevertheir transition frequency matches ω r . The energy levelsof the NV centers are schematically shown in Fig. 1c. Theelectronic spin is coupled by hyperfine interaction to thespin-triplet ( I = 1) nuclear spin of the N atom, result-ing in a splitting of the | m S = 0 (cid:105) → | m S = +1 (cid:105) transitioninto three resonances separated by 2 . m I states of the N . A dcmagnetic field B NV is applied parallel to the chip, alongthe [110] crystalline axis of the diamond. Out of the fourpossible orientations of NV centers along [111] crystallineaxes, two are perpendicular to the field and are there-fore not Zeeman-shifted, so that they do not contributeto the signal. The remaining two families are broughtinto resonance with ω r at B NV ∼ . | S ( ω ) | when they cross the resonance. A ∼
200 kHzFull-Width Half Maximum (FWHM) linewidth is mea-sured for each line of the triplet, much narrower than inprevious work [20, 27], due to a lower P1 center concen-tration and to the isotopic enrichment in C .For optical pumping of the NV centers, the laser beamis focused to a 0 . .
28 mW. In this geometry, it is straightfor-ward to optimize the laser beam position on the sam-ple in order to minimize the amount of power neededto reset the spins in their ground state. The efficiencyof the optical pumping is measured as explained in [27].The experimental sequence includes an initial strong mi-crowave pulse that saturates the spins, followed by alaser pulse of varying duration T L . After a 300 µ s delaynecessary for relaxation of the quasiparticles generatedin the superconducting thin film and in the silicon sub-strate, the reflected amplitude of a few-photon microwavepulse reveals the spin polarization. The extracted po-larization level p ( T L ) is shown in Fig. 2c. It changesonly slightly above T L = 1 s, indicating that the maxi-mum NV polarization possible with irradiation at 532 nm( p max = 90% according to [33]) is reached. Comparedto earlier work [27] where the laser position could notbe optimized, the maximum polarization can be reachedwith ∼
20 times lower pulse energy. This makes it possi-ble to perform the experiments at a faster repetition rate(0 . B NV =1 .
74 mT, using microwave pulses at ω = ω r accordingto the sequence shown in Fig. 3a. The sequence startswith a laser pulse of duration T L = 0 . p = 0 . p max = 0 .
65. At t = 0, a firstpulse generates a transverse magnetization in the ensem-ble, followed by a refocusing microwave pulse at t = τ which induces rephasing of the spins at 2 τ and emissionof a spin-echo into the measuring line, as seen in Fig. 3a.Note that due to spatial inhomogeneity of the microwavefield generated by the planar inductance, it is not possibleto apply a well-defined Rabi angle to all the spins, whichresults in a reduced echo visibility. The echo amplitudeis measured as a function of the delay 2 τ between thefirst pulse and the echo, and is found to decay approx-imately exponentially with a time constant T = 84 µ s(see Fig. 3b). Decoherence occurs due to dipolar inter-actions with the bath of paramagnetic species presentin the sample ( C nuclei, P1 centers, and NV centers),whose dynamical evolution causes a randomization of thephase acquired by NV centers during the two halves ofthe spin-echo sequence. The C nuclei bath precesses atthe Larmor frequency γ n B NV = 2 π ·
130 kHz ( γ n beingthe C gyromagnetic ratio), giving rise to a characteris-tic oscillation pattern [34–36] in the spin-echo amplitude, A ( V ) µ s) τ = 50 µ s θ R τ A max. (a)(b) echo2.01.51.00.50.0 A m a x . ( V ) τ ( µ s) reset FIG. 3. (a) Hahn echo sequence. The spins are first resetin their ground state by a laser pulse of power 280 µ W andduration 0 . µ s microwave pulse θ at ω r , of power −
71 dBm, induces a transverse magnetization which decayswithin T ∗ . A 1 µ s-long microwave refocusing pulse ( R ) ofpower −
20 dBm is applied at τ = 50 µ s, which rephases thespins at 2 τ . The microwave amplitude (blue curve) showsboth the reflection of the two microwave pulses driving thespins (with their amplitude trimmed by saturation of our de-tection chain, as indicated in red), as well as the echo emit-ted at 2 τ upon rephasing of the spins. (b) Measured decayof the echo amplitude A as a function of 2 τ (open circles).Calculated decay due to a bath of 213 ppm of C (dashed or-ange curve), 0 . P . T = 84 µ s. visible in the data of Fig. 3b. The dynamics due to flip-flop events within the P1 center bath is responsible for adecoherence process knwon as spectral diffusion [37]. Fi-nally, the bath consisting of NV centers at frequency ω r (only half of the total NV concentration) unavoidably un-dergoes spin flips due to the refocusing pulse itself, whichconstitutes an efficient decoherence process called instan-taneous diffusion [38]. The various contributions of eachbath were calculated using the cluster-correlation expan-sion method [39, 40], with concentrations [ P
1] = 0 . N V − ] = 0 . / . C ] = 213 ppm, com-patible with the sample parameters. Good agreementwith the data is obtained (see Fig. 3b). Overall, dipolar (a) θ R A ( m V ) Time ( µ s) A ( m V ) µ s) (b)0.80.60.40.20.0 A ( V ) A ( m V ) µ s)3525155 echo50 µ s reset FIG. 4. Spin-echo at the few-photon level. The experimentalsequence is the same as in Fig. 3, but with an initial microwavepulse having a power corresponding to (a) 60 and (b) 1 photoninside the resonator. The signal was averaged over 3 × (a)and 5 × (b) sequences, with a repetition rate of 5 Hz (a)and 10 Hz (b), limited by the laser pulse duration. Blue solidlines are experimental data, red dashed-dotted lines are theresults of simulations as explained in the text. interactions between NV centers appear to be the domi-nant source of decoherence in our experiment.Since the echo efficiency was limited by the finite spincoherence time in earlier work [27], a significant improve-ment is expected with this new sample. The echo effi-ciency is first measured by performing a Hahn echo se-quence with a low-power microwave pulse. The experi-mental sequence, shown in Fig. 4, starts with a 0 . µ s by a microwavepulse populating the resonator with on average 60 pho-tons, and, τ = 50 µ s later, by a refocusing pulse. A spin-echo is detected at t = 2 τ . The efficiency, defined as theenergy recovered during the echo divided by the absorbedenergy, reaches E = 0 . g ens / π = 410 kHz (when all spins arepolarized), are compatible with the experimentally deter-mined parameters and yield quantitative agreement withthe shape of both the absorbed microwave pulse and thespin-echo amplitude. The discrepancy noted in [27] isabsent in the present experiment, probably because de-coherence is negligible during the driven evolution. Thefinite T and the imperfect π pulse due to the spread inRabi frequencies are the main factors limiting E , whilethe finite cooperativity C = 0 .
22 [14] limits both the ab-sorption and the echo emission out of the cavity.Owing to the larger value of E , it becomes possible toreach the level where a spin-echo can be observed for aninitial pulse populating the resonator with only a singlemicrowave photon on average. This is shown in Fig. 4b.Note that a shorter repumping time of 0 . × of repetitions of the experiment. Theshorter repumping step yields a lower spin polarization p = 0 .
56 as shown in Fig. 2 and a lower cooperativityof 0 .
19, which results in a correspondingly lower echoefficiency than in Fig. 4a. These results are again quan-titatively reproduced by the simulations with the sameparameters as mentioned earlier, using the experimen-tally determined repumping efficiency.The coherence times demonstrated in this experimentmatch those requested in a realistic quantum memoryprotocol [14], which suggests that a first implementationis within reach. The remaining challenges are the im-provement of the refocusing pulse using adiabatic pas-sage as demonstrated recently [41], and the integrationof dynamical tuning of the resonator frequency and qual-ity factor with more elaborate spin-echo sequences. Thelatter is needed in particular to silence the echo emis-sion [11, 12] in-between the two π pulses in the courseof the read step of the procotol. The microwave currentsneeded to drive the spins during the refocusing pulses aremuch stronger than typical Josephson junctions criticalcurrents. This precludes the use of integrated SQUIDs asin [20, 42], while a combination of coupled linear and tun-able resonators [43] may be employed as tuning elementsin the resonator.In conclusion we report the measurement of a spin-echowith an initial microwave pulse at the single-photon level.The figures of merit reached are sufficient to envision firstimplementations of a spin-ensemble multi-mode quantummemory for superconducting qubits. Acknowledgements