Cavity-free quantum optomechanical cooling by atom-modulated radiation

We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that, by suitably driving $\mathrm{\Lambda }$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Thereby, we can manipulate heating and cooling effects. Particularly, we develop an optomechanical cooling strategy that can mutually cancel the heating effect of the outgoing and incoming radiation, rendering the motional ground state attainable by net cooling. Our proposal complements other efforts in quantum cooling of macroscopic objects since it requires neither a cavity nor perfect alignment.

Figure 1

Configuration of our system. Two radiation beams, Control (upper, orange) and Probe (lower, green), are applied to and reflected from an oscillating mirror. A diluted atomic cloud (red oval) is trapped at the overlap of the outgoing Control and incoming Probe beams.

Figure 2

Level diagram of a $\mathrm{\Lambda }$-level atom.

Figure 3

Atomic cloud is modeled as an array of atom that the radiation passes through each in sequence. For a general atomic cloud, we can divide the cloud into parallel slices (gray rectangles), and each slice consists of a negligible number of atoms. For simplicity, in this work we consider each slice contains exactly one atom and the slices are indexed according to the distance from the mirror. Our model remains valid if the atoms in each slice are weakly interacting, which is a usual assumption for diluted cloud.

Figure 4

Illustration of cooling strategies. (a) BS-enhancing strategy: atomic parameters are chosen to convert blue sideband correlation with mirror from outgoing Control to incoming Probe. The correlation contained by the Probe mode will enhance the BS cooling effect. Nevertheless, red sideband of both outgoing Control and outgoing Probe will be dissipated and induce TMS heating. (b) TMS-suppressing strategy: atomic parameters are chosen to convert red sideband correlation with mirror from outgoing Control to incoming Probe. Due to a time delay, the correlation contained by the Probe mode will suppress TMS heating. However, blue sideband of both Control and Probe is unaffected. Its dissipation will induce net cooling on the mirror.

Figure 5

Typical behavior of spectral function $J\left(\omega \right)$. Blue: real (solid) and imaginary (dashed) part of $J\left(\omega \right)/\left|J\right(\nu \left)\right|$. The parameters are ${\mathrm{\Omega }}_p={\mathrm{\Omega }}_c=4\nu$ and ${\gamma }_p+{\mathrm{\Gamma }}_p={\gamma }_c+{\mathrm{\Gamma }}_c=0.3\nu$. The detuning $\mathrm{\Delta }$ is chosen to satisfy (20), in order to facilitate the atom interaction with blue sideband radiation. The interaction with red sideband is suppressed, as we can see $\left|J\right(\nu \left)\right|\gg \left|J\right(-\nu \left)\right|$. Red: real (long-dashed) and imaginary (dotted) part of $J\left(\omega \right)/\left|J\right(-\nu \left)\right|$, of which the atomic parameters are the same as those of the blue lines, except $\mathrm{\Delta }$ is chosen to satisfy (23).