Figure 1

Calculated maximum fidelities for fluorescence state detection of a single ${}^{87}\mathrm{Rb}$ atom with a cavity ($\eta =20\%$) and with a high numerical aperture (NA) objective ($\eta =0.6\%$), where $\eta$ is the detection probability of a scattered photon. Fidelities are limited by an insufficient number of detected photons, optical pumping, and detector dark counts. Unidirectional probe light expels the atom from an optical dipole trap after scattering $\approx 100$ photons (dashed line) for a typical trap depth of 2 mK. The novel regime of cavity-enhanced fluorescence readout introduced in this Letter is indicated by a black circle. A state-detection fidelity of 99.98% is feasible with less than 100 scattered photons.Reuse & Permissions

Figure 2

(a) Experimental apparatus. A single ${}^{87}\mathrm{Rb}$ atom is trapped in an optical cavity at the focus of a standing-wave dipole trap. A CCD-camera system monitors the position of the atom (inset: CCD-camera image of a single intracavity atom, image size $15\mu \mathrm{m}\times 25\mu \mathrm{m}$). For optical cooling and state preparation of the atom, laser beams near resonant with the $5S_{1/2}\leftrightarrow 5P_{3/2}$ transitions are applied orthogonal to the cavity axis and retroreflected with a $\mathrm{lin}\perp \mathrm{lin}$ polarization ($\lambda /4$: quarter wave plate). For atomic state detection, a probe laser resonant with the $F=2\leftrightarrow F^{\prime }=3$ transition is applied either orthogonal to the cavity axis for fluorescence state detection or along the cavity axis for differential transmission measurements. Photons emitted into the cavity output mode are detected by a single photon counting module (SPCM). (b) Energy level diagram of the ${}^{87}\mathrm{Rb}$ $D_2$ transition, not to scale.Reuse & Permissions

Figure 3

Cavity-enhanced fluorescence state detection. Shown are measured probability distributions for the number of detected photons $N$ per probe interval. The atom is either prepared in the $F=2$ (open histogram) or in the $F=1$ hyperfine ground state (filled histogram). The atom is illuminated with a $85\mu \mathrm{s}$ pulse of probe light orthogonal to the cavity axis and resonant with the $F=2\leftrightarrow F^{\prime }=3$ transition. Identifying probe intervals with $N=0$ as the $F=1$ state and intervals with $N\ge 1$ as the $F=2$ state (dashed discrimination line) yields a hyperfine state-detection fidelity of $99.4\pm 0.1\%$ (uncertainty is statistical), mainly limited by detector dark counts and state preparation errors. The bright state photon number distribution is nearly Poissonian, but broadened because atomic position and Stark-shift uncertainties lead to shot-to-shot variations of the mean number of scattered photons (Mandel $Q$ parameter $Q=0.5$).Reuse & Permissions

Figure 4

Fidelity as a function of atomic detuning for state detection by fluorescence and differential transmission. (a) The state-detection fidelity is robust against atomic detuning for the fluorescence technique (black solid line: calculated fidelity for on average $N=8$ detected photons for the $F=2$ state; black dots: measured fidelity). For the differential transmission technique, the fidelity decreases rapidly with detuning (solid gray line: calculated fidelity for on average $N=80$ detected photons for the $F=1$ state; gray dots: measured fidelity). (b) Differential transmission histograms measured at low (${\Delta }_a=0\mathrm{MHz}$) and higher (${\Delta }_a/2\pi =20\mathrm{MHz}$) atomic detuning for $300\mu \mathrm{s}$ transmission probe intervals. The atom is prepared in the $F=2$ (open histogram) or $F=1$ state (filled histogram). We choose discrimination levels (vertical dashed lines) which optimize the fidelity and measure a state-detection fidelity of $99.0\pm 0.5\%$ at ${\Delta }_a=0\mathrm{MHz}$ and a fidelity of $64\pm 2\%$ at ${\Delta }_a/2\pi =20\mathrm{MHz}$ (uncertainty is statistical).Reuse & Permissions