Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM${}_{10}$ cavity mode

We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical microcavity. The single atom strongly couples to the high-order transverse vacuum TEM${}_{10}$ mode, instead of the usual TEM${}_{00}$ mode, and the parameters of the system are $(g_{10},\kappa ,\gamma )=2\pi \times (20.5,2.6,2.6)\hspace{0.5em}\text{MHz}$. The atoms simply fall down freely from the magneto-optical trap into the cavity modes, and the trajectories of the single atoms are linear. The transmission spectra of atoms passing through the TEM${}_{10}$ mode are detected by single-photon counting modules and are well fitted. Thanks to the tilted cavity transverse TEM${}_{10}$ mode, which is inclined to the vertical direction $~$${45}^{°}$, it helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atom trajectory. An atom position with a high precision of $0.1\hspace{0.5em}\mu \text{m}$ in the off-axis direction (axis $y$) is obtained, and a spatial resolution of $5.6\hspace{0.5em}\mu \text{m}$ is achieved in a time interval of $10\hspace{0.5em}\mu \text{s}$ along the vertical direction (axis $x$). The average velocity of the atoms is also measured from the atom transits, which determines independently the temperature of the atoms in a magneto-optical trap, $186\pm 19\hspace{0.5em}\mu \text{K}$.

Figure 1

Experiment scheme. The atoms fall down freely from the magneto-optical trap (MOT) and pass through the higher transverse modes in the cavity. The optimum coupling constant $g_0$ is larger than cavity decay rate $\kappa$ and atom decay rate $\gamma$, so the interaction between the atom and cavity mode reaches the strong coupling regime.

Figure 2

Cavity transmission spectra vs the atom’s positions in the $x$ axis for a TEM${}_{10}$ mode for various off-axis distances $y$ ($y=0,\pm 10\hspace{0.5em}\mu \text{m},\pm 20\hspace{0.5em}\mu \text{m}$) between the atoms’ trajectories and the center of the mode. The detuning between the probe light and atom transition is ${\Delta }_{\mathit{ca}}=0$ MHz, and the detuning between the probe light and atom transition is also ${\Delta }_{\mathit{pa}}=0$ MHz. $g_0=2\pi \times 23.9$ MHz, $w_0=23.8\hspace{0.5em}\mu$m, $\gamma =2\pi \times 2.6$ MHz, and $\kappa =2\pi \times 2.6$ MHz; all the parameters are used according to our experimental system.

Figure 3

Cavity transmission vs the scanning of the probe frequency. The inset shows the TEM${}_{00}$, TEM${}_{10}$, and TEM${}_{01}$ modes. Splitting $~82.5$ MHz between TEM${}_{10}$ and TEM${}_{01}$ mode is observed. Three images, from the left-hand side to the right-hand side, are the 2D intensity distributions of TEM${}_{00}$, TEM${}_{10}$, and TEM${}_{01}$ modes directly detected by a CCD camera, respectively.

Figure 4

The cavity transmission spectra of a single atom coupled to the tilted TEM${}_{10}$ mode of a high-finesse optical cavity. The red dots are the experimental data and the green solid curves are theoretical fitting according to expression (1). (a) $y=-16.3\pm 0.1\hspace{0.5em}\mu$m, $v=0.39\pm 0.01$ m/s. (b) $y=0\pm 0.2\hspace{0.5em}\mu$m, $v=0.42\pm 0.01$ m/s. (c) $y=18.0\pm 0.1\hspace{0.5em}\mu$m, $v=0.42\pm 0.01$ m/s. The right-hand side figures (d), (e), and (f) show the unique atom trajectories corresponding to (a), (b), and (c), respectively. ${\Delta }_{\mathit{pa}}=0$ MHz. ($g_0=2\pi \times 23.9$ MHz, $w_0=23.8\hspace{0.5em}\mu$m, $\gamma =2\pi \times 2.6$ MHz and $\kappa =2\pi \times 2.6$ MHz.)

Figure 5

The velocities of atoms at the cavity at different arrival times. The result is obtained from 200 times of atom transits based on the strong coupling between atoms and the cavity mode.