Atom interference in a gray optical lattice

Atomic wave packets are coherently split into two components evolving on different adiabatic potentials of a near-resonant gray optical lattice. The components follow separated paths and overlap periodically. Wave-packet interference is observed at times when the components overlap. The wave-packet splitting and recombination mechanisms are quantum projection and nonadiabatic coupling. Experimental results are in agreement with the results of a detailed theoretical model.

Figure 1

Sloshing-type wave-packet motion and wave-packet interference in a one-dimensional gray optical lattice of ${}^{87}\mathrm{Rb}$ $5S_{1∕2}$, $F=2$ atoms. (a) Adiabatic potentials $E_i$ in units of the recoil energy $E_{\mathrm{R}}=h\times 3.628\mathrm{kHz}$ vs lattice position $z$ and qualitative illustration of the wave-packet dynamics. The three displayed potentials originate in the three magnetic substates with even $m$; the odd-$m$ potentials are not important and are omitted. The potentials are for lattice intensity $I=8\mathrm{mW}∕{\mathrm{cm}}^2$, lattice detuning $+38\mathrm{MHz}$ from the $5S_{1∕2}$, $F=2\to 5P_{1∕2}$, $F^{\prime }=2$ transition (wavelength $\lambda =795\mathrm{nm}$). A magnetic field of $100\mathrm{mG}$ parallel to the lattice beams is applied. (b) Signatures of the sloshing-type motion and the wave-packet interference in experimental data.

Figure 2

(a) Power exchange $\Delta P$ vs time $t$ for $B_{\parallel }=100\mathrm{mG}$ and lattice intensities $I$ as indicated. For clarity, the slow sloshing oscillations have been subtracted from the signal. The arrows mark the signal maxima that have been used to determine the frequency of the fast oscillations. (b) Average electric-dipole force $⟨F⟩$ for the same lattice obtained with quantum Monte Carlo wave-function simulations.

Figure 3

Frequencies of the sloshing oscillations (${\nu }_{\text{slosh}}$; circles) and the wave-packet interference signal (${\nu }_{\mathrm{wp}}$; squares) for the indicated values of $B_{\parallel }$ as a function of lattice intensity $I$.

Figure 4

Linear gray-scale plots of the magnitudes of the delayed coherences ${\tilde{\psi }}_2(z,t)$ (panel “a”) and ${\tilde{\psi }}_1(z,t)$ (panel “b”) vs position $z$ and time $t$ for lattice parameters as in Fig. 1a. At time $t=0$, the lattice is shifted by $0.1\lambda$. The $z$ scales cover three lattice periods. The wave packets are split in the region marked $S$ and recombined in the region $R$.

Figure 5

Linear grayscale plot of the magnitude of the coherence $\mid {\rho }_{12}(z,t)\mid$ between AP 1 and AP 2 vs position $z$ and time $t$ over one lattice period. Wave-packet interference occurs within the regions enclosed by the dashed lines.