Solid State Spin-Wave Quantum Memory for Time-Bin Qubits

Mustafa Gündoğan, Patrick M. Ledingham, Kutlu Kutluer, Margherita Mazzera, and Hugues de Riedmatten

Phys. Rev. Lett. 114, 230501 – Published 12 June 2015

Abstract

We demonstrate the first solid-state spin-wave optical quantum memory with on-demand read-out. Using the full atomic frequency comb scheme in a $\Pr^{3 +} ∶ Y_{2} {SiO}_{5}$ crystal, we store weak coherent pulses at the single-photon level with a signal-to-noise ratio $> 10$ . Narrow-band spectral filtering based on spectral hole burning in a second $\Pr^{3 +} ∶ Y_{2} {SiO}_{5}$ crystal is used to filter out the excess noise created by control pulses to reach an unconditional noise level of $(2.0 \pm 0.3) \times 10^{- 3}$ photons per pulse. We also report spin-wave storage of photonic time-bin qubits with conditional fidelities higher than achievable by a measure and prepare strategy, demonstrating that the spin-wave memory operates in the quantum regime. This makes our device the first demonstration of a quantum memory for time-bin qubits, with on-demand read-out of the stored quantum information. These results represent an important step for the use of solid-state quantum memories in scalable quantum networks.

Received 13 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.114.230501

Authors & Affiliations

Mustafa Gündoğan¹, Patrick M. Ledingham^1,*, Kutlu Kutluer¹, Margherita Mazzera^1,†, and Hugues de Riedmatten^1,2

¹ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
²ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain

^*Present address: Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom.
^†margherita.mazzera@icfo.es

Coherent Spin Control at the Quantum Level in an Ensemble-Based Optical Memory

Pierre Jobez, Cyril Laplane, Nuala Timoney, Nicolas Gisin, Alban Ferrier, Philippe Goldner, and Mikael Afzelius

Phys. Rev. Lett. 114, 230502 (2015)

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Vol. 114, Iss. 23 — 12 June 2015

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Images

Figure 1
(a) Quantum memory setup. The memory (MC) and filter (FC) crystals are located inside a liquid-free cooler (Oxford V14) operating at a temperature of 2.5 K. They are both 3 mm long and doped with a $\Pr^{3 +}$ concentration of 0.05%. The control and input beams are steered towards the memory with an angle of $\sim 1.5 °$ , leading to leading to an extinction ratio of $10^{- 5}$ . The beam diameters on the crystal are 280 and $90 μ m$ for strong and input modes, respectively. The weak coherent states are prepared by attenuating bright pulses with variable neutral density filters (NDFs). A portion of the input beam is picked up before the NDF and sent to a photodiode (PD1) for the calibration of the mean photon number per pulse. A mechanical shutter is used to protect the single-photon detector (SPD) during the memory and filter preparation. HWP: half-wave plate. AOM: acousto-optical modulator. DG: diffraction grating. The dashed red beam indicates the filter preparation mode. (b) Hyperfine splitting of the first sublevels of the ground ${{}^{3}H}_{4}$ and the excited ${{}^{1}D}_{2}$ manifold of $\Pr^{3 +}$ in $Y_{2} {SiO}_{5}$ .
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Figure 2
(a) Time histograms of the retrieved photons measured for different input photon numbers when a transparency window 2 MHz wide is prepared in the filter crystal. The input ( $μ_{in} = 0.9$ ) and the control pulses, as measured in photon counting and from a reference photodiode (PD2 in Fig. 1), respectively, are also displayed. The chosen $0.7 μ s$ wide detection window is indicated by the dashed lines about the three-level echo; it includes $\sim 80 %$ of the counts in the full echo mode. (b) Signal-to-noise ratio (SNR) as a function of the number of input photons for different filter widths. Circles: 2 MHz. Squares: 14 MHz. The error bars (smaller than the data points) are evaluated with Poissonian statistics. The black dotted line indicates the limit of detection $SNR = 1$ . The dashed lines are linear fits of the experimental data. (c) Decay of the SNR as a function of the spin-wave storage time $T_{S}$ with average photon number $μ_{in} = 1$ . From the fit with a Gaussian profile, the spin inhomogeneous broadening $γ_{in} = (26 \pm 1) kHz$ can be extrapolated. By comparing the SNR that we measure at a storage time $T_{S} = 7.8 μ s$ with the extrapolation at $T_{S} = 0 μ s$ , we can evaluate the decoherence term $η_{C}$ to be about 75%.
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Figure 3
(a) Pulse sequence to measure the time-bin qubit coherence. We apply two partial write pulses with a relative phase $Δ β$ in order to split each pulse into two temporally separated echoes. If the delay between the time bins $| e ⟩$ and $| l ⟩$ is equal to the time difference between the two write pulses, we can overlap the late echo of the early bin, $| e l ⟩$ , with the early echo of the late bin, $| l e ⟩$ . The output of the memory (occurring after the single read pulse $r$ ) has three time bins, ${| e e ⟩, | e l ⟩ + | l e ⟩, | l l ⟩}$ . An interference will occur in the central time bin if the coherence is preserved. The input pulses, located at $| e ⟩$ and $| l ⟩$ , have a relative phase difference of $Δ α$ . (b) Interference fringes obtained integrating over the central output time bin (in this case $Δ t_{d} = 0.5 μ s$ ) as a function of the relative phase difference $Δ β$ for $μ_{q} = 1.5$ . Circles: $Δ α = 90 °$ , $V = (71.6 \pm 6.8) %$ . Squares: $Δ α = 135 °$ , $V = (73.4 \pm 3.5) %$ .
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Figure 4
Total fidelity versus input photon number per qubit, $μ_{q}$ . The light orange squares are the data points with an error bar of 1 standard deviation. The orange dotted line is a fit to the data points using Eq. (5) in Ref. [41], with the corresponding shaded area being the 1 standard deviation of the error in this fit. The solid blue (dashed green) line is the classical limit obtained by a measure-and-prepare strategy for our memory efficiency of $η_{sw} = 2.2 %$ ( $η_{sw} = 100 %$ ) when testing the memory with weak coherent states [25]. The dash-dotted line is the classical limit for testing the memory with a single-photon Fock state ( $F = 2 / 3$ ).
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