Theory of robust subrecoil cooling by stimulated Raman adiabatic passage

We demonstrate one-dimensional robust Raman cooling in a three-level $\Lambda$-type atom, where the velocity-selective transfer is carried out by a STIRAP pulse. In contrast to the standard Raman method, the excitation profile is insensitive to variations in the pulse duration, whereas its position and width are nevertheless under control. Two different cooling variants are examined and we show that subrecoil temperatures are attainable in both cases.

Figure 1

(a) A three-level $\Lambda$-type atom interacting with a pair of contrapropagating laser beams. The pump laser links the initial state $|1\rangle$ with an intermediate state $|2\rangle$, whereas the Stokes laser links the intermediate state with the final state $|3\rangle$. (b) Both the pump and Stokes pulse have a Gaussian profile in time, overlapping during period $\Delta \tau$.

Figure 2

The eigenfrequencies of pure atomic states $|a_1\rangle$ and $|a_3\rangle$ (dashed lines) cross at point ${\delta }_{\mathrm{eff}}=0$. The avoided level crossing for the eigenstates (solid lines) leads to a corresponding change between the eigenstates and pure states.

Figure 3

The time evolution of the dressed-state frequencies (solid line) on the pulse-overlapping region $\Delta \tau$. The dashed lines represent the frequencies of the pure states. In dependence on $\Delta \delta$, one gets the following cases: (a) ${\delta }_{\mathrm{eff}}>0$, (b) ${\delta }_{\mathrm{eff}}<0$ during this period, (c) ${\delta }_{\mathrm{eff}}=0$ at a specific time. (c) Represents adiabatic transfer from the $|a_1\rangle$ state to $|a_3\rangle$ state.

Figure 4

(a) The excitation probability of atoms in state $|1\rangle$ against velocity $v$ by STIRAP pulses of different coupling parameters according to set (23). (b) The velocity spread $\Delta v$ decreases from the initial $3v_{\mathrm{rec}}$ to $0.1v_{\mathrm{rec}}$ of cooled ensemble.

Figure 5

(a) The excitation probability of atoms in state $|1\rangle$ against velocity $v$ by STIRAP pulse (24a) with the maximum at the resonant velocity $v_0=-0.25v_{\mathrm{rec}}$. (b) The velocity spread $\Delta v$ decreases from the initial $3v_{\mathrm{rec}}$ to $0.1v_{\mathrm{rec}}$ of cooled ensemble.