Strong Coupling of a Mechanical Oscillator and a Single Atom

We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven high-finesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox from atomic physics for coherent manipulation, preparation, and measurement of micromechanical and nanomechanical oscillators.

Figure 1

(a) Strong coupling of the motion of a single atom to a vibrational degree of freedom of a micron-sized membrane can be achieved in a two mode cavity (for details see text). (b) Cavity response as a function of frequency. Two cavity modes are driven by two lasers of frequencies ${\omega }_1$ and ${\omega }_2$, with red and blue detuning, respectively. (c) The two frequencies drive two atomic transitions, e.g., the $D_{1,2}$ lines of Cs, both with red detuning, causing ac Stark shift of the ground state. (d) (Left-hand side) The atom is trapped in the potential from the two optical lattices. (Right-hand side) The membrane is placed at a point of steepest slope of the intensity profiles. (e) A small displacement of the membrane will shift the cavity resonances [cf. dashed line in (b)] resulting in a spatial shift of the trap potential for the atom, and thus an effective linear atom-membrane coupling as in Eq. (1).

Figure 2

(a) Wigner functions of atom and membrane (upper and lower panels, respectively). At $t=0$ (left-hand panels) the atom is in a squeezed state (9 dB) and the membrane in a thermal state with a mean number of phonons $\overline{n}=5$. An exact solution of the equation of motion (2) with losses $\Gamma ={\Gamma }_c,{\Gamma }_m,{\Gamma }_{at}$ at rate $\Gamma =0.1G$ shows that after a time $Gt=\frac{\pi }{2}$ (right-hand panels) the states are exchanged, up to a trivial rotation in phase space by 90°. (b) Squeezing transferred to membrane (maximized over time), versus loss rate $\Gamma$, for the indicated values of initial atomic position fluctuations.