Storage and retrieval of microwave fields at the single-photon level in a spin ensemble

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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, and P. Bertet

Phys. Rev. A 92, 020301(R) – Published 7 August 2015

Abstract

We report the storage of microwave pulses at the single-photon level in a spin-ensemble memory consisting of $10^{10}$ nitrogen-vacancy centers in a diamond crystal coupled to a superconducting $L C$ resonator. The energy of the signal, retrieved $100 μ s$ later by spin-echo techniques, reaches $0.3 %$ of the energy absorbed by the spins. This $0.3 %$ storage efficiency is quantitatively accounted for by simulations. This figure of merit is sufficient to envision first implementations of a quantum memory for superconducting qubits.

Received 8 April 2015

DOI:https://doi.org/10.1103/PhysRevA.92.020301

Authors & Affiliations

C. Grezes¹, B. Julsgaard², Y. Kubo¹, W. L. Ma^3,4, M. Stern¹, A. Bienfait¹, K. Nakamura⁵, J. Isoya⁶, S. Onoda⁷, T. Ohshima⁷, V. Jacques⁸, D. Vion¹, D. Esteve¹, R. B. Liu³, K. Mølmer², and P. Bertet¹

¹Quantronics Group, Service de Physique de l'Etat Condensé, DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA Saclay, 91191 Gif-sur-Yvette, France
²Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
³Department of Physics, Centre for Quantum Coherence, and Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China
⁴State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
⁵Energy System Research Institute, Fundamental Technology Department, Tokyo Gas Co., Ltd., Yokohama 230-0045, Japan
⁶Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan
⁷Japan Atomic Energy Agency, Takasaki 370-1292, Japan
⁸Laboratoire Aimé Cotton, CNRS, Université Paris-Sud and ENS Cachan, 91405 Orsay, France

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Vol. 92, Iss. 2 — August 2015

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Images

Figure 1
(a) Experimental setup and principle of the experiment. An ensemble of $\sim 10^{10}$ spins is inductively coupled to a planar superconducting $L C$ 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 coupling capacitance. Microwave pulses are produced by mixing a continuous microwave source with dc pulses generated by an arbitrary wave form generator (AWG). They drive the spins via the microwave current induced in the resonator inductance. The reflected microwave signal (including the emitted echo) is amplified at low temperature and demodulated at room temperature, yielding its amplitude $A (t)$ and phase $ϕ (t)$ . (b) The spins are nitrogen-vacancy color centers in diamond, which consist of a nitrogen impurity next to a vacancy of the diamond lattice. A dc magnetic field $B_{NV}$ applied parallel to the chip along the $[110]$ crystalline axis so that only NV centers whose axis are nonorthogonal to the field (shown in blue in the figure) are Zeeman shifted and contribute to the signal. Laser pulses can be sent onto the diamond via a direct optical access to the cryostat mixing chamber. (c) NV centers energy levels in a weak magnetic field. The electronic ground state is a spin triplet $S = 1$ , with a zero-field splitting $D / 2 π = 2.88$ GHz, coupled by hyperfine interaction to the ${}^{14}N$ nuclear spin triplet $I = 1$ . This splits each of the $| m_{S} = 0 〉 \to | m_{S} = + 1 〉$ transitions into a triplet of lines.
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Figure 2
(a) Phase $ϕ$ of the resonator reflection coefficient $S_{11} (ω)$ measured with a vector network analyzer (blue dots), yielding $ω_{r} / 2 π = 2.915$ GHz and $Q = 650$ (red line is a fit to the data). (b) $S_{11} (ω)$ as a function of $B_{NV}$ around $1.8$ mT, showing the NV centers as a triplet of absorption dips. The inset shows $| S_{11} | (B_{NV})$ at $ω / 2 π = 2.915$ GHz; blue dots are data, and red line is a fit to a sum of three Lorentzians with linewidth $0.012$ mT. (c) Measured spin polarization for a laser pulse of power $P_{L} = 280 μ W$ as a function of its duration $T_{L}$ , renormalized to its maximal value. Dashed red and black lines indicate the laser pulse durations $T_{L} = 0.2$ and $0.1$ s used in the experiments shown in Figs. 3 and 4, corresponding to relative polarizations $p / p_{max} = 0.72$ and $0.62$ .
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Figure 3
(a) Hahn echo sequence. The spins are first reset in their ground state by a laser pulse of power $280 μ W$ and duration $0.2$ s. A first $1 μ s$ microwave pulse $θ$ at $ω_{r}$ , of power $- 71$ dBm, induces a transverse magnetization which decays within $T_{2}^{*}$ . A $1 - μ s$ -long microwave refocusing pulse ( $R$ ) of power $- 20$ dBm is applied at $τ = 50 μ s$ , which rephases the spins at $2 τ$ . The microwave amplitude (blue curve) shows both the reflection of the two microwave pulses driving the spins (with their amplitude trimmed by saturation of our detection chain, as indicated in red), as well as the echo emitted at $2 τ$ upon rephasing of the spins. (b) Measured decay of the echo amplitude $A$ as a function of $2 τ$ (open circles). Calculated decay due to a bath of 213 ppm of ${}^{13}C$ (dashed orange curve), $0.6$ ppm of $P 1$ centers causing spectral diffusion (dotted green line), $0.2$ ppm of NV centers causing instantaneous diffusion (dash-dotted blue line), and the combination of the three contributions (solid red line). The theory curves have been scaled in amplitude according to the data. An exponential fit (black solid line) yields a coherence time $T_{2} = 84 μ s$ .
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Figure 4
Spin echo at the few-photon level. The experimental sequence is the same as in Fig. 3, but with an initial microwave pulse having a power corresponding to (a) 60 and (b) one photon inside the resonator. The signal was averaged over $3 \times 10^{4}$ (a) and $5 \times 10^{5}$ (b) sequences, with a repetition rate of 5 Hz (a) and 10 Hz (b), limited by the laser pulse duration. Blue solid lines are experimental data, and red dashed-dotted lines are the results of simulations as explained in the text. The signal-to-noise ratio, defined as the ratio between signal intensity integrated over the echo duration and the corresponding noise intensity, is 4 for the 60-photon pulse (a) and $1.5$ in the one-photon pulse (b).
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