PHYSICAL REVIEW X 4, 021049 (2014)

Multimode Storage and Retrieval of Microwave Fields in a Spin Ensemble
C. Grezes,1 B. Julsgaard,2 Y. Kubo,1,7 M. Stern,1 T. Umeda,3 J. Isoya,4 H. Sumiya,5 H. Abe,6 S. Onoda,6T. Ohshima,6 V. Jacques,7,8 J. Esteve,9 D. Vion,1 D. Esteve,1 K. Mølmer,2 and P. Bertet1
1

Quantronics group, SPEC (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
2
Department of Physics and Astronomy, Aarhus University,
Ny Munkegade 120, DK-8000 Aarhus C, Denmark3
Institute of Applied Physics, University of Tsukuba, Tsukuba 305-8573, Japan
4
Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan
5
Sumitomo Electric Industries Ltd., Itami 664-001, Japan
6
Japan Atomic Energy Agency, Takasaki 370-1292, Japan
7
Laboratoire de Photonique Quantique et Moléculaire, ENS Cachan and CNRS UMR 8537,
94235 Cachan, France
8
Laboratoire Aimé Cotton, CNRS, Université Paris‐Sud and ENS Cachan, 91405 Orsay, France
9
Laboratoire Kastler Brossel, ENS, UPMC-Paris 6, CNRS, 24 rue Lhomond, 75005 Paris, France(Received 28 January 2014; revised manuscript received 14 April 2014; published 16 June 2014)

A quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits
for long times, is a key element for quantum information processing. Electronic and nuclear spins arenatural candidates for the storage medium as their coherence time can be well above 1 s. Benefiting fromthese long coherence times requires one to apply the refocusing techniques used in magnetic resonance, amajor challenge in the context of hybrid quantum circuits. Here, we report the first implementation of sucha scheme, using ensembles of nitrogen-vacancy centers in diamond coupled to a superconducting
resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of
the nitrogen-vacancy spins into their ground state by optical pumping and their refocusing by Hahn-echo
sequences. This enables the storage of multiple microwave pulses at the picowatt level and their retrieval
after up to 35 μs, a 3 orders of magnitude improvement compared to previous experiments.
DOI: 10.1103/PhysRevX.4.021049

Subject Areas: Condensed Matter Physics,
Quantum Information

I. INTRODUCTION
The ability to store a quantum state over long times is a
desirable feature in many quantum information protocols.
In the optical domain, quantum memories are necessary to
implement the quantum repeaters needed for future longdistance quantum networks and are the object of active
research [1–5]. Quantum memories at microwave frequencies have also become of great interest in recent years
because of the development of superconducting qubits,
which have their resonance frequency in the GHz range, inthe perspective of implementing holographic quantum
computing [6–8]. For such schemes, the memory should
act as an ideal multiqubit register, able to store the state oflarge numbers of qubits over long times and to retrieve
them on demand.
Spin ensembles have emerged as promising candidates
for such a microwave quantum memory because of their

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2160-3308=14=4(2)=021049(9)long coherence time [9–12] and because a spin ensemble
withstands many orthogonal collective modes that are well
suited to store multiple qubit states. Existing proposals[13,14] (inspired by optical quantum memory protocols[4,5]) proceed in two distinct steps. In the write step, themicrowave field prepared in a well-defined quantum statejψi (for instance, by a superconducting qubit) is absorbedby the spin ensemble. This generates a transverse magnetization that decays rapidly in a time T 2 due to the spreadof resonance frequencies in the ensemble. Given the
weakness of the coupling constant of a single spin to themicrowave field, efficient absorption requires embedding
the ensemble in a high-quality factor microwave resonatorin order to reach the so-called high-cooperativity regime[15–19]. The second step (read) of the memory operationconsists of retrieving the initial state. It relies on theprinciple of Hahn echoes [20]: dephasing due to inhomogeneous broadening can be counteracted by applying a πpulse to the spins at time τ, which acts as a time reversal
and, thus, causes all the magnetic dipoles to return in phase(refocus) at time 2τ. Quantum memory proposals [13,14]
combine two consecutive refocusing π pulses applied to thespins with dynamical tuning of the resonator frequency and021049-1

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C. GREZES et al.

PHYS. REV. X 4, 021049 (2014)

quality factor, thereby retrieving the amplitude of the input
microwave field while preventing the addition of noise, as
required for a high-fidelity memory performance [21]. The
maximum storage time of the memory is approximately the
Hahn-echo decay time T 2 , so that the maximal number ofstored quantum states is of order T 2 =T 2, a figure which canbe very large in many spin systems.
The write step of this protocol (quantum state transfer)
has been demonstrated at the single-photon level in recent
experiments [22,23]; the remaining obstacle to a multimodemicrowave quantum memory is therefore the implementation of Hahn-echo refocusing sequences at the quantum
level in a hybrid quantum circuit. The object of this work is
precisely to identify the challenges posed by this task and todemonstrate experimentally that they can be solved. For
simplicity, we consider a protocol simpler than the fullquantum memory [14] but which constitutes an essentialbuilding block: the two-pulse echo (2PE). As depicted inFig. 1(a), the 2PE consists in storing weak pulses θi into thespin ensemble at times ti and applying a single refocusing
pulse at time τ, which triggers the emission of echo pulses
ei at times 2τ − ti (therefore, in reverse order) in thedetection waveguide [24].
Performing the 2PE at the quantum level imposes anumber of requirements that represent experimental challenges. For quantum states to be well defined, thermal
excitations should be absent from the system. This implies
both that the spin ensemble has a high degree of polarization and that the microwave field is in its ground statewith high probability, which can only be achieved if theexperiments are performed at millikelvin temperatures. At
these temperatures, however, spins tend to relax very
slowly towards their ground state, and an active spin resetis therefore needed in order to repeat the experimental

R
n

R

en

e

e

FIG. 1. Principle of the experiment. (a) Scheme of the multimode two-pulse echo (2PE) protocol applied to an ensemble of spins
placed in an electromagnetic cavity: successive low-power microwave pulses θi are stored in the spin ensemble. A refocusing pulse R
acts as time reversal for the spins and triggers the retrieval of the stored pulses as echoes ei in reverse order. Top and bottom time lines
show the applied and the reflected and echo signals, respectively. (b) Setup placed in a dilution refrigerator: the cavity is a lumpedelement parallel LC resonator in niobium coupled to a coplanar waveguide by a capacitor Cc. It consists of an interdigitated capacitor C
and a meander wire inductor L creating the ac magnetic field shown in the inset, for a 10 μW incident microwave power at resonance.
The spin ensemble consists of NV centers in a diamond monocrystal pressed on top of the inductor. Laser pulses can be shone on it
through an optical fiber glued to its top face. A tunable dc magnetic field BNV is applied parallel to the [110] direction of the crystal.
(c) Negatively charged NV centers in diamond consist of a nitrogen atom next to a vacancy of the diamond lattice, having trapped anelectron. Their electronic spin S ¼ 1 is coupled by hyperfine interaction to the nitrogen nuclear spin I ¼ 1 (for the 14 N isotope). Half ofthe electronic spins (subensemble denoted N-Orth. in blue) make an angle α ¼ 35.3° with BNV , whereas the other half (subensemble
Orth. in red) is orthogonal to the field. (d) NV simplified energy diagram (top) showing the ground 3 A and the excited 3 E electronic
states as well as the Zeeman and hyperfine structure of 3 A, with D=2π ¼ 2.8775 GHz the zero-field splitting. (bottom) Magnetic fielddependence of the allowed transitions for both N-Orth. (blue) and Orth. (red) subensembles, showing, respectively, a linear and aquadratic Zeeman effect. NVs can be optically repumped in their mS ¼ 0 ground state by application of green (532 nm) laser pulses
exciting the 3 A-3 E transition.

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MULTIMODE STORAGE AND RETRIEVAL OF MICROWAVE …
sequence at a reasonable rate (> 1 Hz) as required byexperiments at the single-photon level. Then, applying
refocusing pulses to the spins requires large microwave
powers potentially incompatible with the detection ofquantum fields. Finally, the echo emitted by the spinsshould faithfully restore the initial field, which implies thatthe echo recovery efficiency E, which we define as the ratioof the energy radiated during the echo to the energy of theincoming pulse, should be close to 1. To summarize,
reaching the quantum regime requires a mean excitation
per mode (both microwave and spin) nmw;sp ≪ 1, input
microwave fields with intracavity photon number n̄ ≈ 1,
and an echo efficiency E close to 1.
These stringent requirements have never been met in anexperiment, by far. The multimode character of the 2PE has
been recently benchmarked in the classical regime [25]with an ensemble of phosphorus donors in silicon at 10 K in
the three-dimensional microwave cavity of an electron
paramagnetic resonance spectrometer. That experimentreached nmw;sp ≈ 20, n̄ ≈ 1014 , and an echo recovery
efficiency E ≈ 10−10. Here, we use negatively charged
NV centers in diamond, which are color centers consistingof a substitutional nitrogen atom sitting next to a vacancy ofthe lattice [see Fig. 1(c)] with properties suitable for aquantum memory. Indeed, their spin triplet (S ¼ 1) electronic ground state has a long coherence time [9] and can be
optically repumped in the spin ground state jmS ¼ 0i [seeFigs. 1(c) and 1(d)] as a result of spin-dependent intersystem crossing from the electronic excited triplet state to ametastable singlet state [not shown in Fig. 1(d)] [26]. We
revisit the 2PE protocol with an ensemble of NV centers at
400 mK coupled to a planar superconducting resonator, in a
setup compatible with hybrid quantum circuits, with active
reset of the spin at the beginning of each experimental
sequence, and we demonstrate the storage of multiple
pulses at the picowatt level into orthogonal collectivemodes of the spin ensemble for 35 μs, 3 orders ofmagnitude longer than in earlier experiments [27]. Our
experiment reaches nmw ≈ 3, nsp ≈ 0.1, n̄ ≈ 100, andE ≈ 2 × 10−4 , and, therefore, comes closer to the quantum
regime than previous work by several orders of magnitude.
We quantitatively identify the present limitations and showthat they can be solved in future experiments, opening theway to the implementation of quantum memory protocols.
II. EXPERIMENTAL SETUP AND NV
HAMILTONIAN
The experimental setup is sketched in Fig. 1(b) (see also
the Supplemental Material [28]). A diamond crystal homogeneously doped with NV centers (½NV−  ≈ 2 ppm) isglued on top of the inductance of a planar superconducting
LC resonator cooled in a dilution refrigerator. For opticalpumping, 532 nm laser light is injected through a singlemode optical fiber, glued on top of the crystal, 1.5 mm~ NV isabove the resonator inductance. A magnetic field B

PHYS. REV. X 4, 021049 (2014)

applied parallel to the chip along the ½110 crystalline axis
[see Fig. 1(c)].
NV centers in their ground state are described [29] by
the Hamiltonian HNV =ℏ ¼ DS2z þ EðS2x − S2y Þ þ Az Sz I z þ~ NV · S~ þ Q½I 2z − IðI þ 1Þ=3, with S~ (~I) the spin operγeBator of the S ¼ 1 NV electronic spin (the I ¼ 1 nitrogen
nuclear spin), D=2π ¼ 2.8775 GHz the zero-field splitting
between states mS ¼ 0 and mS ¼ 1, Az ¼ −2.1 MHz thehyperfine coupling, and Q ¼ −5 MHz the nuclear quadrupole momentum [30]. Local electric field and strain couple
the spin eigenstates jmS ¼ 1i with strength E [31]. Theenergy eigenstates ji, shown in Fig. 1(d), are thus linear
combinations of states jmS ¼ 1i; in particular, at zeropﬃﬃﬃ
magnetic field, states ji ¼ ðjmS ¼ þ1i  jmS ¼ −1iÞ= 2
are separated in energy by 2E. In the experiment, we use
transitions between the spin ground state jmS ¼ 0i and thetwo excited states ji at frequencies close to the zero-field
splitting.
The resonator is capacitively coupled to measurement
lines through which microwave signals are applied, withthe amplitude and phase of the reflected field detected byhomodyne demodulation after amplification at 4 K. The
reflection coefficient S11 , shown in Figs. 2(a) and 2(b),yields the resonator frequency ωc =2π ¼ 2.88 GHz andquality factor Q ¼ 80. Such a low Q was chosen to avoid
spin relaxation by superradiant spontaneous emission after
excitation by the refocusing pulse [32]. Dips in jS11 j are due
to absorption by the NVs, as evidenced by their dependence
on BNV .
III. ACTIVE RESET OF THE SPINS
To demonstrate optical repumping of the NVs in
jmS ¼ 0i, we probe the spin polarization after a laser pulseof power PL and duration T L by measuring the absorptionof a microwave pulse at ωd =2π ¼ 2.884 GHz. In addition
to repumping the spins, the laser generates quasiparticles inthe superconductor and carriers in the silicon substrate. We
thus introduce a delay of 300 μs between the two pulses forthese excitations to relax. In order to start from a reproducible spin polarization, a strong microwave pulse isapplied before the laser pulse, which saturates all the spinsat the beginning of each sequence [see Fig. 2(c)].
The results are shown in Fig. 2(d) for PL ¼ 1.5 mW.
Without laser pulse, the reflected pulse amplitude isindependent of BNV , proving that the spins are efficiently
saturated by the initial microwave pulse. For nonzero T L ,absorption peaks with the triplet shape characteristic of theNV hyperfine structure are observed, indicating sizable NV
polarization. To quantify the effect, we convert the absorption signal into the imaginary part of the spin susceptibilityχ 00 ðT L ; BNV Þ [see Fig. 2(e) and the Supplemental Material[28]], which yields the relative spin polarization
pðT L Þ ¼ χ 00 ðT L ; BNV Þ=χ 00 ðT max ; BNV Þ, with T max the maximum repumping time. The polarization increases with T L
and then saturates [see Figs. 3(a) and 3b)], which shows

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300 s

PL
TL

p/pmaxFIG. 2. Spectroscopic signals and optical repumping. (a) Measured (open circles) and fitted (solid line) phase of the reflection
coefficient S11 showing the resonator resonance at ω0 =2π ¼ 2.88 GHz with quality factor Q ¼ 80, when the spins are saturated and do
not contribute to the signal. (b) Measured reflection coefficient modulus jS11 j around the center of the resonator line, showing theabsorption by the spins for different magnetic fields. Top line (6 mT, black) corresponds to all spins (Orth. and N-Orth.) being far detuned
and shows no absorption. Other lines show several absorption peaks moving with magnetic field (subensemble N-Orth.) or not(subensemble Orth). (c) Optical reset of the NV center spins. The spins are first saturated by a 20-μs-long microwave pulse with frequency
ωd and applied power −24 dBm; they are then optically repumped to their ground state with a laser pulse of power PL and duration T L .
After letting the system cool down during 300 μs, the reflected amplitude of an applied weak (−132 dBm) 20-ms-long measurement
pulse at ωd =2π ¼ 2.884 GHz is measured. (d) Reflected amplitude for PL ¼ 1.5 mW and different T L . The curves show the hyperfine
split mS ¼ 0 to mS ¼ 1 spectroscopic transitions of the N-Orth. subensemble, with an amplitude that increases with T L because ofincreasing spin repolarization. (e) Corresponding imaginary part χ 00 ðBNV Þ of the spin susceptibility. In addition, the dashed and dashdotted lines show, respectively, χ 00 ðBNV Þ measured at thermal equilibrium (30 mK, no saturating nor optical pulse) and calculated (see theSupplemental Material for methods and Figs. S3 and S4 [28]) and rescaled by a global factor to match the experiment at T L ¼ 4 s.

0.5

(a)

(b)

ω = ωdPL = 1.5 mW

ω = ωdTL = 6 s

spins at equilibrium

spins at equilibrium

0.0
0

2

4

6

8

0

TL (s)

0.25 0.50 0.75 1.00 1.25
PL (mW)

0.25

Amplitude (V)

(c)
0.24
0.23

MEASUREMENT

τ

µw
0.22

SPINS RESET

optical

∆Τ

0.21
5

10

15

20
∆T (min)

∆τ

25

30

35

40

FIG. 3. Spin reset efficiency and relaxation. (a),(b) Relative spinpolarization dependence on T L for PL ¼ 1.5 mW and on PL for
T L ¼ 6 s. The experimental sequence is shown in Fig. 2(c). (c) NV
spin relaxation time measurement. A series of Δτ ¼ 20 ms weak
microwave pulses (−120 dBm) at ωd =2π ¼ 2.884 GHz, separatedby τ ¼ 10 s, is applied following optical reset of the spins. Blue
dots are the average reflected amplitude of each pulse. A biexponential fit (red solid line) yields T 1;a ¼35s and T 1;b ¼395s.

that the spins reach the maximum polarization allowed by
optical pumping at 532 nm, close to 90% according toearlier work [33]. The refrigerator cold stage was heated to
400 mK due to laser power; all of the following results wereobtained under these conditions. Better alignment of thefiber with the resonator should reduce the power needed by
2 orders of magnitude.
Using the optical pumping, we measure the energy
relaxation of the spins. The spins are first repumped, after
which a series of a 20 ms resonant probe microwave
pulse separated by 10 s are applied. The average reflected
amplitude of each pulse is plotted in Fig. 3(c) and showsa biexponential response with time constants T 1;a ¼ 35 s
and T 1;b ¼ 395 s, similar to recent measurements [18].
These very long values confirm the need of actively
resetting the spins for operating a quantum memory.
IV. PULSED RESPONSE OF THE SPINSAs a first step towards the application of refocusing pulses
to the spins, we measure their time-domain response to
microwave pulses of varying power. The experiments are
performed at BNV ¼ 0 mT. The zero-field spin

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MULTIMODE STORAGE AND RETRIEVAL OF MICROWAVE …
susceptibility χ 00 ðωÞ [see Fig. 4(a)] shows two broad peaks
corresponding to the j0i → j−i and j0i → jþi transitions.
The width of these peaks is governed by the inhomogeneityof local electric fields and strain acting on the NVs, which
results in a broad distribution of E, causing the hyperfine
structure to be barely resolved, as seen in Fig. 4(a). On the
j0i → jþi transition, the spin absorption reaches a maximum at ωe =2π ¼ 2.8795 GHz, which we will use as thefrequency of all microwave pulses in the following. Squaremicrowave pulses of varying input power Pin are sent to thesample, and their reflected amplitude A is measured. The

PHYS. REV. X 4, 021049 (2014)

pﬃﬃﬃﬃﬃﬃ
data are shown in Figs. 4(b) and 4(c), rescaled by Pin, andcompared to the reflected amplitude of the same microwave
pulse with the spins initially saturated by a strong pulse. At
low power (the linear regime), after an initial transient whereresonator and spins exchange energy, A reaches half of thesaturated value in steady state, indicating that the spins
absorb ≈75% of the incoming power. The steady-state valueof A increases with incoming power, indicating reduced spin
absorption caused by progressive saturation of the ensemble.
Note that no clear Rabi oscillations are observed. This isdue to the spatial inhomogeneity of the microwave field
A

A

A

300 s

FIG. 4. (a) Measured (solid line) and computed (dash-dotted line) imaginary part χ 00 ðωÞ of the spin susceptibility at BNV ¼ 0 mT. The
calculated curve (see Supplemental Material [28]) was rescaled by a global factor to match the experiment. (b) Reflected field amplitude
A for a square input microwave pulse of power Pin. Solid lines are experimental data with Pin ¼ −90, −60, −55, and −50 dBm (blue,
green, yellow, and red, respectively), dashed lines are simulations. p
The
black
curve is obtained when spins have
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ
been saturated by an initial strong pulse. The curves have been rescaled by Pin =P0 for easier comparison, with P0 ¼ −90 dBm.
(c) In-phase (blue) and out-of-phase (green) quadrature of the reflected field for Pin ¼ −90 dBm. (d) Spin-echo sequence. An incoming
microwave pulse θ with power −60 dBm is followed by a delay τ and a 1-μs-long refocusing pulse (R) with power −20 dBm, yielding
an echo e at time 2τ. Saturation of the amplifiers (shown in red) limits the measurable amplitude to about 2 V. (e) Experimental (crosses)
and simulated and rescaled (open circles) area of the echo as a function of the refocusing pulse power PR. (f) Measured (crosses) decayof the echo maximum amplitude as a function of τ. Dashed and solid lines are an exponential fit yielding a characteristic timeT 2 ¼ 8.4 μs and a biexponential fit fðτÞ yielding T 2A ¼ 4.7 μs and T 2B ¼ 14.3 μs, respectively.

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generated by the planar resonator [see Fig. 1(b)], whichcauses a spread of Rabi frequency within the ensemble; inparticular, this prevents the application of precise π pulses toall the spins [34], which is an issue for Hahn-echo sequences.
In order to understand in detail the spin dynamics, we
compare the experimental data to the result of numericalsimulations. These simulations consist of a number ofmean-value equations along the lines of Ref. [14] andexplained in further detail in the Supplemental Material[28]. In particular, the inhomogeneity in both spin frequency and coupling strength is taken into account bydividing the ensemble into a sufficiently large set ofhomogeneous subensembles and integrating the equationsof motion for the resonator field and the spin componentsof all of the subensembles. The distribution of spin
frequencies follows from the spin susceptibility shown in
Fig. 5(a), and the distribution of coupling strengths depends
on the resonator-field vacuum fluctuations, whose spatial
distribution is calculated using the COMSOL simulation
package and exemplified in the inset of Fig. 1(b). The
actual distributions used are shown in Fig. S5 of the
Supplemental Material [28].
The simulations employed assume an ensemble of spin1=2 particles, which is an approximation in the case of NV
centers having a spin of 1. However, in the linear,nonsaturated regime this description is exact, and for the
nonlinear, saturated regime we expect the approximation tobe justified since the applied π pulse has a narrow frequency
bandwidth and is tuned predominantly to the j0i → jþitransition of the NV centers. In Figs. 4(b) and 4(c), themeasured and calculated reflected field are compared andshow a convincing agreement, without any adjustableparameter. This confirms the validity of the calculations,both in the linear and nonlinear regime, and proves, inparticular, that the frequency distribution used is correct.
V. SPIN ECHO AT HIGH POWER
Despite the impossibility of applying well-defined πpulses to the spins, we implement a spin-echo sequencewith an initial microwave pulse creating a transverse
magnetization, followed after τ by a refocusing pulse. Its
power PR ¼ −20 dBm is chosen such that spin saturationis reached within the pulse duration, as required for spinecho. The reflected signal amplitude is shown in Fig. 4(d),with the expected spin echo observed at 2τ. We study the
amplitude of this echo as a function of PR , and compare thiscurve to the result of the simulations. The agreement isquantitative, as shown in Fig. 4(e); in particular, the power
at which the echo amplitude saturates is well predicted by
the simulations. This shows further evidence of the validityof calculated coupling strengths and of the spin-1=2
approximation.
The dependence of the echo amplitude on τ is fitted
by a biexponential function fðτÞ ¼ A expð−2τ=T 2A Þþ
B expð−2τ=T 2B Þ, with two different coherence times

T 2A ¼ 4.8 μs and T 2B ¼ 14.3 μs, and A ¼ 0.78 and B ¼
0.22 [see Fig. 4(f)]. Such a dependence is expected for an
ensemble of NV centers in zero magnetic field. Indeed, thecoherence time of NV centers is limited by dipolarinteractions with the surrounding spin bath, either paramagnetic impurities (P1 centers) or 13 C nuclear spins. This
spin bath can be approximated as generating a fluctuating
magnetic field that blurs the phase of the NV center. In zeromagnetic field, an interesting situation occurs: the nuclear
spin state mI ¼ 0 becomes immune to first order tomagnetic fluctuations [31] because of the strain-induced
coupling between states mS ¼ 1, which gives rise to an
avoided level crossing, and thus to a transition frequency
independent of magnetic field to first order [see Fig. 1(d)].
This was shown in previous work to make the freeinduction decay time T 2 1 order of magnitude longer inzero magnetic field [31], and should equally lead to alonger Hahn-echo time T 2 . However, this is not true forstates with mI ¼ 1, which should, therefore, have ashorter decoherence time T 2 in zero magnetic field.
More details will be given in future work.
VI. MULTIMODE 2PE PROTOCOL AND
DISCUSSION
Finally, we implement the multimode 2PE protocol withweak microwave pulses. Six consecutive microwave pulses
with a varying phase and identical amplitude correspondingto ≈104 photons in the resonator are first absorbed by thespin ensemble, and a strong refocusing pulse is then applied
10 μs later [see Fig. 5(a)]. The sequence is averaged 104
times at a repetition rate of 1 Hz, made possible by theactive reset of the spins. As shown in Fig. 5(b), the six
pulses are recovered after the refocusing pulse up to 35 μs
after their storage, with an amplitude reduced by ∼102
compared to the incoming pulse, corresponding to ∼1
photon in the resonator. As expected, the pulses are
reemitted in reverse order [see Fig. 5(c)]. Note that thestrong refocusing pulse (∼109 photons in the cavity) does
not prevent detection of fields at the single-photon level few
microseconds later. We were able to detect a measurable
spin-echo signal for pulses containing up to 100 times
lower energy, thus populating the resonator with n̄ ≈ 100
photons on average [see Fig. 5(d)].
An important figure of merit is the field retrieval
efficiency E, defined as discussed in the Introduction as
the ratio between the energy recovered during the echo andthe energy of the incoming pulse. In the data shown in
Fig. 5(b), E is seen to decrease with τ due to spin
decoherence, following approximately the relation
Ee ¼ 0.03jfðτÞj2 , which yields E ¼ 2.4 × 10−4 for2τ ¼ 17 μs. Coming back to the figures of merit definedin the Introduction, our measurements reach nmw ≈ 3,
nsp ≈ 0.1, n̄ ≈ 100, and E ≈ 2 × 10−4 , many orders ofmagnitude closer to the quantum regime than previous
state-of-the-art experiments [25].

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MULTIMODE STORAGE AND RETRIEVAL OF MICROWAVE …
Reaching the quantum regime, however, requires a
recovery efficiency E close to 1, and, therefore, calls fora quantitative understanding of our measurement imperfections. For that purpose we perform simulations of themultimode 2PE protocol. As seen in Fig. 5(b), the measurements are well reproduced, although a 7 times higher
efficiency Et ¼ 0.21jfðτÞj2 is predicted. We attribute thediscrepancy between Ee and Et to the imperfect modelingof decoherence. Indeed, our simulations treat spin
decoherence in the Markov approximation. This is not
an adequate treatment since it is well known that the spinbath environment displays strong memory effects. In
particular, this Markov approximation is expected to
improperly describe the dynamics of a spin under theaction of a microwave drive, as happens during
the refocusing pulse. This non-Markovian bath causes
the Rabi oscillation of a single spin to decay faster than
the spin-echo damping time T 2 , as was observed inRef. [35], for instance. This effect is not included in our
simulations and might explain the remaining discrepancy
between theory and measurements. Overall, we infer fromthe simulations that Et would reach 0.2 for a sample with
infinite T 2 ; this number quantifies the reduced efficiency
caused by refocusing pulse imperfections and finite spin
absorption. In the measured efficiency Ee ≈ 2 × 10−4, finite
spin coherence causes a further 10−3 reduction, thus

PHYS. REV. X 4, 021049 (2014)

appearing as the main limitation of the field retrieval
efficiency in the present experiment.
According to the previous analysis, a 1 order ofmagnitude increase of the coherence time would be
sufficient to reach an echo efficiency ≈0.1, which would
enable first experiments in the quantum regime. This can beachieved [9] with samples having a reduced concentrationof nitrogen paramagnetic impurities as well as isotopic
enrichment of 12 C. Further improvements of the echo
efficiency will be reached thanks to better refocusing
pulses using rapid adiabatic passage [14,36], or by tailoring
the spin spatial distribution [37]. These combined advances
should make it possible to reach the figures of merit
required to implement a complete quantum memory protocol [13,14] at the single-photon level and to experimentally explore its fidelity. Optical pumping in a hybrid
circuit, as demonstrated here, is also a first step towards
the polarization of the nitrogen nuclear spins [38], and in
the longer term towards a nuclear-spin-based quantum
memory.
In conclusion, we implement the multimode storage andretrieval of microwave fields in an ensemble of NV centersin diamond at millikelvin temperatures, with active reset by
optical pumping and refocusing by a strong microwave
pulse. These results demonstrate that complex dynamical
control of spin ensembles is compatible with hybrid

300 sFIG. 5. Test of the 2PE protocol for multimode storage of few-photon pulses. (a) Experimental sequence including a spin reset
pulse, a train of six microwave pulses θi (i ¼ 1; …; 6) with an identical amplitude (corresponding to ∼104 photons in the resonator)and different phases φ1 ¼ φ2 ¼ φ4 ¼ −π=4 and φ3 ¼ φ5 ¼ φ6 ¼ π=4, and a 50 dB stronger refocusing pulse R with phaseφr ¼ 0.1 rad. (b) Amplitude of the measured (solid line) and calculated (dash-dotted line) output signal showing the reflected pulses
θi (after partial absorption by the spins) and R (its amplitude being trimmed by amplifier saturation, shown in red), as well as the six
reemitted echoes ei (magnified by a factor of 5). Inset: Comparison between the energies of the reflected θi pulses with the spins
saturated (black line) or reset in their ground state (blue line) shows that about 75% of the incident power is absorbed by the spins.
(c) In‐phase (blue solid line) and Out‐of‐Phase (purple solid line) quadratures I and Q of the output signal, showing that the ei pulses(magnified by 10) are recovered with phase −ðφi − φr Þ, as expected. (d) Spin echo e of ∼0.02 photons in the resonator for a lowpower incoming θ pulse populating the resonator with only ∼100 photons. The refocusing pulse (dashed line) was suppressed in theroom-temperature detection chain by a microwave switch to avoid saturating the follow-up amplifiers.

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C. GREZES et al.

PHYS. REV. X 4, 021049 (2014)

quantum circuits, thus enabling the long-term storage ofquantum information in electronic or nuclear spin ensemble
quantum memory.
ACKNOWLEDGMENTS
We acknowledge technical support from P. Sénat, D.
Duet, J.-C. Tack, P. Pari, and P. Forget, as well as useful
discussions within the Quantronics group and with A.
Dréau, J.-F. Roch, T. Chanelière, and J. Morton. We
acknowledge support from the French National Research
Agency (ANR) with the QINVC project from CHISTERA
program, the European project SCALEQIT, and theC’Nano IdF project QUANTROCRYO. Y. K. is supportedby the Japanese Society for the Promotion of Science(JSPS). B. J. and K. M. acknowledge support from theVillum Foundation.

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