Heating rates for an atom in a far-detuned optical lattice

We calculate single-atom heating rates in a far-detuned optical lattice, in connection with recent experiments. We first derive a master equation, which includes a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the total heating rate (which corresponds to the increase of the total mechanical energy of the atom in the lattice), and the ground-band heating rate (which corresponds to the increase of energy within the ground energy band of the lattice). The total heating rate remarkably is independent of the atomic state and of the sign of the laser detuning. In contrast, the ground-band heating rate in the deep lattice limit is strongly suppressed for blue-detuned lattices with respect to red-detuned lattices.

Figure 1

The atomic level scheme considered in this work, typical for alkali-metal atoms.

Figure 2

Sketch of the different heating processes in a lattice: intraband processes (1) and interband processes (2).

Figure 3

Initial ground-band heating rate ${\mathit{dE}}_{\mathrm{GB}}/\mathit{dt}$ for an atom prepared in the ground Bloch state of the optical lattice, for a red lattice (red, upper lines) and for a blue lattice (blue, lower lines), as a function of the lattice depth in recoil units $U_0/E_{\mathrm{rec}}$. Here, the coefficient $C=3/2$, and the lattice is isotropic: $U_{0,\mu }=U_0$ for all spatial directions $\mu =x,y,z$ in Eq. (32) for a red lattice and in Eq. (33) for a blue lattice. Solid lines: Numerical evaluation of Eq. (30). Dashed lines: Asymptotic expressions Eqs. (40) and (42). The ground-band heating rate is expressed in units of the total heating rate Eq. (25).