Transverse mode revival of a light-compensated quantum memory

A long-lived quantum memory was developed based on light-compensated cold ${}^{87}\mathrm{Rb}$ atoms in a dipole trap. The lifetime of the quantum memory was improved by 40 folds, from 0.67 to 28 ms with the help of a compensation laser beam. Oscillations of the memory efficiency due to the transverse mode breathing of the singly excited spin wave have been clearly observed and clarified with a Monte Carlo simulation procedure. With detailed analysis of the decoherence processes of the spin wave in cold atomic ensembles, this experiment provides a benchmark for the further development of high-quality quantum memories.

Figure 1

A schematic of the setup. (a) The memory light modes are arranged in a collinear configuration, along the axial direction of the hollow beam. The light modes of the write, read, write-out photon $S_w$, and read-out photon $S_r$ are all focused single-mode Gaussian beams. At the focus, the diameter for the write and read is 550 $\mu$m and that for the signal beams is 130 $\mu$m. (b) An absorption image of the atoms in the dipole trap (with false color). The dipole trap holds $~3\times {10}^6$ atoms at $30\hspace{0.5em}\mathrm{ms}$ after sub-Doppler cooling, in a shape with length $3\hspace{0.5em}\mathrm{mm}$ and diameter $190\hspace{0.5em}\mathrm{\mu }\mathrm{m}$. (c) The loss of atoms in the optical trap. Within the first $100\hspace{0.5em}\mathrm{ms}$, the hot atoms quickly escape from the trap, and an exponential fitting gives the decay constant of $160\hspace{0.5em}\mathrm{ms}$. After that, the atom number slowly decays with a constant of $580\hspace{0.5em}\mathrm{ms}$. (d) Relevant atomic levels. A pair of clock states, $|F=2,m_F=0\rangle$ and $|F=1,m_F=0\rangle$, are chosen as the memory states to suppress dephasing from inhomogeneous magnetic field. BS, 50:50 beam splitter; PBS, polarizing beam splitter; DM, dichroic mirror.

Figure 2

(a) Retrieve efficiency at short time scale. (b) The wavelength of the trapping beam is 775 nm and that of the compensation beam is 780 nm. Without compensation, dominated dephasing mechanism is differential light shift from the trapping laser, and an exponential fitting gives a lifetime of $0.67\pm 0.03\hspace{0.5em}\mathrm{ms}$. When the compensation laser is turned on, the decay constant becomes $1.44\pm 0.09\hspace{0.5em}\mathrm{ms}$.

Figure 3

Oscillation of retrieve efficiency due to dynamical mode breathing. (a) Retrieve efficiency curve when the signal mode is at the center of the trap and the spin wave is generated by off-resonance Raman scattering. (b) Retrieve efficiency curve when the signal mode is 60 $\mu$m above the center of the trap, and the spin wave is generated by the EIT process. The transverse spatial mode of the singly excited spin wave at different storage times is simulated with a Monte Carlo procedure and shown below the retrieve efficiency curves. The triangle points are the overlapping integral calculated directly from the initial spatial mode and the evolved spatial mode. The squared dots are obtained by considering atom loss and the dephasing time obtained in Fig. 4. The color depth shows the density of the atoms and is rescaled for each figure to make the distribution more visible.

Figure 4

Memory efficiency at long time scale. By a least-square fitting with an exponential function to the measured data, a decay constant of $28\pm 2.5$ ms is obtained.