Electromagnetically-induced-transparency control of single-atom motion in an optical cavity

We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)–like interference in an atomic $\Lambda$-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.

Figure 1

(a) Schematic of the experimental setup. A single cesium atom is trapped inside a high-finesse optical cavity and illuminated by a control laser along the dipole trap axis. A probe laser is coupled into the cavity mode and its transmission is detected by a single-photon detector. (b) Relevant bare energy levels (black) of atom and cavity, Rabi frequencies, and detunings of lasers and cavity mode. (c, d) Dressed states (gray) and scattering processes leading to cooling. Vibrational excitations are shown explicitly. Straight (curvy) arrows represent coherent (incoherent) transitions which lead to a change in energy by one vibrational quantum $\hslash \omega$. Open arrows identify the process which mediates the mechanical action. (c) Cooling (heating) transition due to the recoil of fluorescence photons. Inset: Excitation spectrum, determining the corresponding rate, as a function of the probe frequency. This process is diffusive and can be suppressed using EIT. (d) Cooling transition due to the mechanical effect of the cavity field [horizontal (blue) arrows]. Inset: Corresponding transition rate [solid (blue) curve]. The dashed (red) curve corresponds to heating. The double Fano structure is a consequence of the strong atom-cavity coupling [27]. Diffusion and cooling or heating add up to give the rates $A_{\pm }^{\left(j\right)}$.

Figure 2

(a) Cooling rate $\Gamma$, calculated for a fixed cavity-atom detuning ${\Delta }_{\mathrm{CA}}=2\pi \times 16$ MHz according to [27]. The horizontal dashed-dotted line corresponds to ${\delta }_{\mathrm{LC}}=0$. Solid black lines indicate the frequencies of the dressed states $|\pm \rangle ,|\circ \rangle$. Away from the avoided crossing at ${\delta }_{\mathrm{LC}}=0$ the dressed states $|\pm \rangle$ are coherent superpositions of $|g_2,1_{\mathrm{c}}\rangle$ and $|e,0_{\mathrm{c}}\rangle$ which are coupled by the cavity field, whereas state $|\circ \rangle$ asymptotically coincides with $|g_1,0_{\mathrm{c}}\rangle$. Boxed region: Region corresponding to the detail shown in Fig. 3. (b) Measurement of the single-atom survival probability as a function of the probe-cavity detuning ${\delta }_{\mathrm{PC}}$ for the case ${\delta }_{\mathrm{LC}}=0$ and for two holding times $t$ inside the cavity. The parameter space corresponds to the horizontal dashed-dotted line in (a).

Figure 3

(a) Calculated cooling rate along the cavity axis (blue shading) and heating rate along the control laser axis (red shading). Solid lines indicate the dressed-state energies of $|\circ \rangle$ and $|+\rangle$, while the dashed diagonal line corresponds to ${\delta }_{\mathrm{PL}}=0$, where $A_{\pm }$ are given by Eq. (4). Horizontal and vertical dashed-dotted lines correspond to the measurements in (b) and (c), respectively. (b) Survival probability of one atom as a function of the probe-cavity detuning ${\delta }_{\mathrm{PC}}$ for five values of ${\delta }_{\mathrm{LC}}$ as indicated in (a) for a holding time of $t=1$s (black lines). Dashed vertical lines indicate the condition ${\delta }_{\mathrm{PL}}=0$. For comparison, the lighter (red) line indicates the survival probability as a function of the probe-atom detuning ${\Delta }_{\mathrm{PA}}$ for the case of EIT cooling outside the cavity. (c) Survival probability of one atom at probe-cavity resonance ${\delta }_{\mathrm{PC}}=0$ as a function of ${\delta }_{\mathrm{LC}}$ for three holding times: $t=0.02$, $0.3$, and 15 s (red, black, and blue lines, respectively).

Figure 4

Microwave sideband spectra of EIT-cooled [filled (blue) circles] and molasses-cooled (open black circles) atoms in the standing-wave dipole trap. For this, the cooled atoms were prepared in the Zeeman sublevel $|F=4,m_F=-4\rangle$ and transferred to $|F=3,m_F=-3\rangle$ using a microwave pulse of fixed power and duration. The transfer probability was determined by state-selective detection of atoms in $F=3$ and plotted as a function of the detuning ${\delta }_{\mathrm{MW}}$ of the microwaves from the cesium clock transition frequency. The peak at ${\delta }_{\mathrm{MW}}\approx -1$ MHz corresponds to the carrier transition $m\to m$. The sideband transitions $m\to m-1$ and $m\to m-2$ are strongly reduced in the EIT case, indicating a high occupation of the vibrational ground state.