Gravity-Sensitive Quantum Dynamics in Cold Atoms

We subject a falling cloud of cold cesium atoms to periodic kicks from a sinusoidal potential created by a vertical standing wave of laser light. By controllably accelerating the potential, we show quantum accelerator mode dynamics to be highly sensitive to the effective gravitational acceleration when close to specific, resonant values. This quantum sensitivity to a control parameter is reminiscent of that associated with classical chaos and promises techniques for precision measurement.

Figure 1

Phase-space plots for Eq. (3), when $2\pi \gamma /{\mathrm{k̵}}^2=1/1\Rightarrow \gamma =(2\pi +ϵ{)}^2/2\pi$, and $\tilde{k}=|ϵ|0.8\pi$ for $ϵ=-0.88$ (a), $-0.02$ (b), 0.03 (c), and 0.6 (d). This corresponds to $T=57.4$, 66.5, 67, and $73\mu \mathrm{s}$. For (a),(b) the island corresponds to a $(\mathfrak{p},\mathfrak{j})=(1,1)$ QAM, and for (c),(d), to a $(\mathfrak{p},\mathfrak{j})=(1,-1)$ QAM.

Figure 2

Density plots of experimental momentum distributions for different effective gravity $g$ corresponding to (a) $r/s=1/1$ (after 15 kicks), (b) $r/s=1/2$ (30 kicks), (c) $r/s=1/3$ (45 kicks), and (d) $r/s=1/4$ (60 kicks), as $T$ is varied near the half-Talbot time $T_{1/2}=66.7\mu \mathrm{s}$, from 60.5 to $74.5\mu \mathrm{s}$ in steps of $0.128\mu \mathrm{s}$. In each case the QAM corresponds to $\mathfrak{j}/\mathfrak{p}=r/s$; subplot (i) corresponds to $w\simeq -8.5\times {10}^{-4}$ (deviation from resonant $g$ is $\sim -8.6\times {10}^{-2}{\mathrm{m}\mathrm{s}}^{-2}$), subplot (ii) to $w\simeq 0$, and subplot (iii) to $w\simeq 8.5\times {10}^{-4}$ (deviation from resonant $g$ is $\sim 8.6\times {10}^{-2}{\mathrm{m}\mathrm{s}}^{-2}$). Overlaid lines, labeled ($\mathfrak{p},\mathfrak{j}$), indicate QAM momenta predicted by Eq. (6). Population arbitrarily normalized to maximum value $=1$, and momentum defined in a frame falling with $g$. Note the significantly greater population at high momentum (up to $50\hslash G$) near $T_{1/2}$ in (d)(i) and (d)(iii), compared to (a)(i) and (a)(iii).