Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout

We prepare and detect the hyperfine state of a single ${}^{87}\mathrm{Rb}$ atom coupled to a fiber-based high-finesse cavity on an atom chip. The atom is extracted from a Bose-Einstein condensate and trapped at the maximum of the cavity field, resulting in a reproducibly strong atom-cavity coupling. We use the cavity reflection and transmission signal to infer the atomic hyperfine state with a fidelity exceeding 99.92% in a readout time of $100\mu \mathrm{s}$. The atom is still trapped after detection.

Figure 1

(a) Schematic of the experiment. A fiber-based high-finesse cavity (length $39\mu \mathrm{m}$) sustains a Gaussian ${\mathrm{TEM}}_{00}$ mode with approximately $3.4\mu \mathrm{m}$ waist. The cavity is doubly resonant to a dipole trap laser and a probe laser. Two APDs record cavity reflection and transmission. (b) Relevant level scheme of a single ${}^{87}\mathrm{Rb}$ atom trapped in the linearly $\pi$ polarized dipole trap. The cavity sustains two modes with orthogonal polarizations, $\pi$ and $\perp$. We use probe light near resonant to the $F=2\to F^{\prime }=3$ transition of the D2 line. A single atom is extracted from a small reservoir using weak MW pulses. (c) Typical experimental trace of cavity reflection and transmission with a single ${}^{87}\mathrm{Rb}$ atom coupled to the cavity. Quantum jumps between the hyperfine ground states lead to sudden, simultaneous changes in both signals.

Figure 2

(a) Histogram of counts in transmission during $20\mu \mathrm{s}$ after the first microwave pulse. The full black and dashed red lines are Poissonian fits with expectation values of 0.3 and 22, respectively. The clear dip between the two peaks allows us to use a thresholding technique to signal the preparation of a single atom. (b) Distribution of the number of required MW pulses to prepare an atom. The line is a fit assuming a reservoir with a Poissonian distribution.

Figure 3

Normal-mode spectrum of a single atom coupled to the cavity. Large red points are the measured transmission. The thick line is the steady-state solution of the master equation for $g_0/2\pi =240\mathrm{MHz}$ and ${\Delta }_{ac}=0$. The gray area bounds the solutions when varying $g_0/2\pi$ by $\pm 10\mathrm{MHz}$ and ${\Delta }_{ac}/2\pi$ by $\pm 10\mathrm{MHz}$. The small blue dots are the measured empty cavity transmission together with a Lorentzian fit.

Figure 4

Two-dimensional distributions of counts registered during $60\mu \mathrm{s}$ in reflection and transmission with an atom prepared in $F=1$ (upper graphs) and $F=2$ (lower graphs). The left graphs are calculated distributions. The right graphs show the associated measurements. The color scale logarithmically encodes $p(c_R,c_T)$. The solid black lines represent the threshold used to differentiate $F=2$ from $F=1$ atoms.