Optimization and readout-noise analysis of a warm-vapor electromagnetically-induced-transparency memory on the Cs $D_1$ line

Quantum memories promise to enable global quantum repeater networks. For field applications, alkali-metal vapors constitute an exceptional storage platform, as neither cryogenics, nor strong magnetic fields are required. We demonstrate a technologically simple, in principle satellite-suited quantum memory based on electromagnetically induced transparency on the cesium $D1$ line, and focus on the tradeoff between end-to-end efficiency and signal-to-noise ratio, both being key parameters in applications. For coherent pulses containing one photon on average, we achieve storage and retrieval with end-to-end efficiencies of ${\eta }_{\text{e2e}}=13\left(2\right)\%$, which correspond to internal memory efficiencies of ${\eta }_{\text{mem}}=33\left(1\right)\%$. Simultaneously, we achieve a noise level corresponding to ${\mu }_1=0.07\left(2\right)$ signal photons. This noise is dominated by spontaneous Raman scattering, with contributions from fluorescence. Four-wave mixing noise is negligible, allowing for further minimization of the total noise level.

Figure 1

Overview of the experiment. (a) Three-level $\mathrm{\Lambda }$ system with signal (control) laser frequency red-detuned by $\mathrm{\Delta }$ from the respective hyperfine transitions of the Cs $D1$ line. A pump laser initially prepares the $F=3$ ground state ($|g\rangle$). Both ground states $|g\rangle$ and $|s\rangle$ are naturally long lived. (b) Schematic memory-experiment setup. EOM: electro-optic modulator; AFG: arbitrary function generator; ATT: attenuator; SOA: semiconductor optical amplifier; CP1, CP2: calcite prisms; Cs: vapor cell inside magnetic shielding; $\lambda /2$, $\lambda /4$: wave plates; APD: single-photon counting avalanche photodiode; AOM: acousto-optic modulator. (c) Signal and control pulse sequence (not to scale). The signal pulse enters the memory shortly after the first control pulse and is written into the memory by it, while the second control pulse reads out the information $80-200\mathrm{ns}$ later. (d) Exemplary arrival time histogram of detected photons in a memory experiment integrated for $60\mathrm{s}$ for an incoming coherent state with a Gaussian envelope containing ${\left|\alpha \right|}^2=1.0\left(1\right)$ photons on average (blue), for blocked input signal (${\left|\alpha \right|}^2=0$) (red), as well as the resulting noise-corrected signal (yellow). The storage time is $t_{\mathrm{storage}}=140\left(1\right)\mathrm{ns}$ as measured from the maximum of the input signal to the global maximum of the retrieval pulse. The shaded area shows the detection window of width $t_{\text{max}}-t_{\text{min}}$ used for further analysis of the end-to-end efficiency ${\eta }_{\mathrm{e}2\mathrm{e}}$ of the memory setup and the signal-to-noise ratio SNR. We use $t_{\text{max}}=155\mathrm{ns}$ (black dashed line), being a good compromise between ${\eta }_{\mathrm{e}2\mathrm{e}}$ and SNR (inset).

Figure 2

End-to-end efficiency (${\eta }_{\text{e2e}}$) and signal-to-noise ratio (SNR). ${\eta }_{\text{e2e}}$ (blue circles) and SNR (green squares) of the memory as a function of signal pulse width $\mathrm{\Delta }{t}_S$ (a), control pulse energy $E_C$ (b), and laser detuning $\mathrm{\Delta }$ (c). The values selected for the measurements are $\mathrm{\Delta }{t}_S=25\mathrm{ns}$, $E_C=560\left(50\right)\mathrm{pJ}$, and $\mathrm{\Delta }=2300\left(100\right)\mathrm{MHz}$ red detuning from the atomic resonance, with only the respective parameter being varied.

Figure 3

Noise analysis. (a) Noise detected on the APD, while scanning one of the etalons used for spectral filtering over two free spectral ranges (FSR) (shaded area corresponds to one FSR), while keeping the other etalon on resonance with the signal frequency. Large peaks at $-16.4\mathrm{GHz}$ and $9.2\mathrm{GHz}$ detuning correspond to leaked control-laser light, and small peaks close to the signal frequency (and at $25.6\mathrm{GHz}$ detuning) originate from atomic noise (fluorescence, SRS and FWM). Vertical dashed lines indicate the signal (blue) and control (red) frequencies and vertical black solid lines indicate the limits of one FSR. (b) Exemplary measurement of total noise counts (the two different data sets were taken on different days) per retrieval attempt as a function of the energy in the control pulse $E_C$ for $\mathrm{\Delta }=334\mathrm{MHz}$ (red detuning), and corresponding fits of the different noise components: fluorescence, spontaneous Raman scattering (SRS), and four-wave mixing (FWM). (c) Systematic study of the measured total noise counts and the corresponding fitted noise components at retrieval as a function of the control laser detuning $\mathrm{\Delta }$. Negative values of $\mathrm{\Delta }$ correspond to blue detuning from resonance. The noise is mainly dominated by SRS and florescence, while FWM is negligible in this setting.