Observation of Optomechanical Strain in a Cold Atomic Cloud

We report the observation of optomechanical strain applied to thermal and quantum degenerate ${}^{87}\mathrm{Rb}$ atomic clouds when illuminated by an intense, far detuned homogeneous laser beam. In this regime the atomic cloud acts as a lens that focuses the laser beam. As a backaction, the atoms experience a force opposite to the beam deflection, which depends on the atomic cloud density profile. We experimentally demonstrate the basic features of this force, distinguishing it from the well-established scattering and dipole forces. The observed strain saturates, ultimately limiting the momentum impulse that can be transferred to the atoms. This optomechanical force may effectively induce interparticle interactions, which can be optically tuned.

Figure 1

Strain measurements. Absorption image of a thermal cloud after long expansion times with (b) and without (a) an electrostriction pulse. The cloud aspect ratio changes from unity to 2.1. We used a laser beam shone along the $\widehat{y}$ axis with intensity $8\times {10}^3\mathrm{mW}/{\mathrm{cm}}^2$, detuning 47 GHz and pulsed for 0.5 ms. (c) A BEC after an electrostriction pulse and long expansion time. Even for a strong impulse and large aspect ratio the BEC remains partly condensed, showing a bimodal distribution in the axial direction (d). (e) Oscillations in the cloud size along one transverse direction (axial direction shown in inset) induced by an electrostriction pulse as a function of a variable waiting time in the trap after applying the pulse. A pure transverse breathing mode is observed, fitting to a decaying oscillation (solid line) of twice the trap frequency.

Figure 2

Scaling of strain with detuning $\mathrm{\Delta }$. A thermal cloud AR after an electrostriction pulse and free expansion, red circles (blue crosses), correspond to a red (blue) detuned electrostriction laser. Fits to the data (solid lines) indicate a scaling of the force as $1/{\mathrm{\Delta }}^{\alpha }$, with $\alpha =1.09(5)$ [$\alpha =1.05(9)$] for the red (blue) detuned electrostriction laser. A prediction (dashed line) based on a force that scales as $1/{\mathrm{\Delta }}^2$ is shown as well. The error in $\alpha$ corresponds to a 95% confidence level. We used a cloud with a temperature of $1.1\mu \mathrm{K}$ and a laser with intensity $1.1\times {10}^4\mathrm{mW}/{\mathrm{cm}}^2$, pulsed for 0.5 ms.

Figure 3

Strain for clouds of different sizes. Measured cloud aspect ratio after an electrostriction pulse and free expansion for different cloud sizes (circles), and the theoretical prediction (line, scaled strain). All data points correspond to thermal clouds besides the first one, which includes a small condensed fraction. Smaller clouds consist of fewer atoms, but the ${\mathrm{AR}}_n$ (normalized AR [27]) is independent of the number of atoms as can be seen in the inset. We used a laser with intensity $7.4\times {10}^3\mathrm{mW}/{\mathrm{cm}}^2$ and detuning 73 GHz, pulsed for 0.25 ms.

Figure 4

Strain saturation with electrostriction laser intensity $I$, detuning $\mathrm{\Delta }$ and pulse duration ${\tau }_p$. (a) Saturation with laser intensity $I$ for different pulse durations ${\tau }_p$ (left graph). After scaling the results by ${\tau }_p^2$ (right) they collapse to a single curve. (b) Saturation with laser intensity $I$ for different detunings $\mathrm{\Delta }$ (left graph). After scaling the results by ${\mathrm{\Delta }}^2$ (right) they collapse to a single curve. (c) When plotted as a function of the momentum impulse ${\sigma }_P^{\mathrm{es}}$, all measurements collapse together. The laser intensity is changed between $0-9\times {10}^3\mathrm{mW}/{\mathrm{cm}}^2$, the detuning $\mathrm{\Delta }$ between $(-167)-(+152)\mathrm{GHz}$, and the pulse duration ${\tau }_p$ between 0.1 and 0.6 ms. ${\sigma }_P^{\mathrm{th}}$ is the width of the thermal momentum distribution prior to the electrostriction impulse.