Light storage on the time scale of a minute

Light storage on the minute scale is an important capability for future scalable quantum information networks spanning intercontinental distances. We employ an ultracold atomic gas confined in a one-dimensional optical lattice for long-term light storage. The differential ac Stark shift of the ground-level microwave transition used for storage is reduced to a sub-Hz level by the application of a magic-valued magnetic field. The $1/e$ lifetime for storage of coherent states of light is prolonged up to 16 s by a microwave dynamic decoupling protocol.

Figure 1

Essential elements of the experimental setup. A 2D-MOT produces a cold atomic beam to load a 3D-MOT in the differentially pumped glass cell with antireflection-coated windows. The 3D-MOT is used to produce a dense sample of cold ${}^{87}$Rb atoms in a 1D optical lattice formed by two 1064 nm ${\Omega }_L$ fields. Atomic levels used in the experiment are shown in the inset. A probe pulse ${\Omega }_p$ is converted into an atomic spin wave by adiabatically switching off the control field ${\Omega }_c$. After a storage period $T_s$ the spin wave is retrieved into a phase-matched direction by turning the probe field back on. The lattice confines the atoms in the field maxima, minimizing spin-wave motional dephasing. The differential ac Stark shift produced by the lattice is nulled by setting the bias magnetic field to a “magic” value. A dynamic decoupling sequence of the microwave $\pi$ pulses on the clock transition is used to extend storage time.

Figure 2

Number of lattice-trapped atoms $N_a$ as a function of the holding time $t_H$. The data are for atoms prepared in $5S_{1/2},F=1$ (diamonds), $5S_{1/2},F=2$ (circles), and $5S_{1/2},F=1$ when the dynamic decoupling sequence is applied (triangles). The data are fit with an exponential function $\propto$$\exp (-t_H/\tau )$ starting from $t_H=5$ s, with the best-fit values of $\tau =169\left(14\right)$, 15(1), and $20\left(1\right)$ s for atoms in $F=1$, $F=2$, and $F=1$ with DD, respectively.

Figure 3

Measured light-storage lifetimes as a function of sensitivity to the magnetic field for three long-lived coherences. Error bars represent uncertainties from the exponential fits. The inset shows the retrieved pulse energy $E$ as a function of the magnetic field. The pulse is retrieved after 5, 7, and 2 s for $(0,0)$, $(-1,1)$, and $(1,-1)$ coherences, respectively. The Gaussian fits yield corresponding magic field values $B^{\left(0\right)}=4.27$, $B^{(-)}=5.43$, and $B^{\left(0\right)}=6.04$ G.

Figure 4

Retrieved pulse energy $E$ as a function of storage time, normalized to its value at 38 ms, for the “magic” magnetic field values for the three long-lived coherences, $(0,0)$ (circles), $(-1,1)$ (diamonds), and $(1,-1)$ (squares). The storage efficiencies at 38 ms are 0.14, 0.06, and 0.05, respectively, for the three coherences. The solid lines are exponential fits to the data. The extracted $1/e$ lifetimes are 4.8(1), 6.9(4), and 2.5(1) s for the clock, $(-1,1)$, and $(1,-1)$ transitions, respectively.

Figure 5

Lifetime as a function of the applied DD sequence frequency $f_{\text{DD}}$. The longest lifetime of 16 s is observed for $f_{\text{DD}}=60$ Hz. Higher $f_{\text{DD}}$ result in lower lifetimes attributed to the accumulation of rotation errors.

Figure 6

Retrieved pulse energy $E$ as a function of storage time, normalized to its value at 38 ms, with (diamonds) and without (squares) the DD sequence applied. The solid curves are exponential fits.