Single-atom detection with optical cavities

We present a thorough analysis of single-atom detection using optical cavities. The large set of parameters that influence the signal-to-noise ratio for cavity detection is considered, with an emphasis on detunings, probe power, cavity finesse, and photon detection schemes. Real device operating restrictions for single photon counting modules and standard photodiodes are included in our discussion, with heterodyne detection emerging as the clearly favorable technique, particularly for detuned detection at high power.

Figure 1

Single-atom detection with an optical cavity showing (a) schematic diagram of cavity setup. (b) Typical photon counts for a detection event. The dashed line indicates the threshold for an atom detection event.

Figure 2

(Color online) SNR $S$ for resonant atom detection with ideal photon counting. The cavity has a length of $100\mu \mathrm{m}$ and waist $20\mu \mathrm{m}$. ${\kappa }_{\mathrm{in}}={\kappa }_{\mathrm{out}}$, ${\kappa }_{\text{loss}}=0$, $\gamma =2\pi \times 6\mathrm{MHz}$, $\tau =20\mu \mathrm{s}$. Panel (b) corresponds to a cross section along the dashed line in (a), showing the positions of optimum SNR. The dashed line indicates the SNR and solid line the power as a function of cavity finesse. Panel (c) corresponds to the solid line at $\mathcal{F}={10}^4$ and (d) to a cross section along the dotted line in (a) at $\text{flux}=10\text{photons}∕\mu \mathrm{s}$.

Figure 3

Energy spectrum for resonant dressed states. Detunings reduce for high levels of excitation.

Figure 4

Relative photon transmission $T$ for the atom-cavity system as a function of probe detuning. Dashed traces are for the empty cavity and solid lines represent the dressed modes. The cavity finesse $\mathcal{F}$ is (a), (b) ${10}^3$; (c), (d) $\mathcal{F}={10}^4$; and (e), (f) ${10}^5$. The left plot for each value of $\mathcal{F}$ is for a driving flux of $1\text{photon}∕\mu \mathrm{s}$, the right is for $200\text{photons}∕\mu \mathrm{s}$.

Figure 5

(Color online) SNR $S$ for a range of cavity and atom detunings. $\mathcal{F}={10}^4$, other parameters as in Fig. 2. The probe power is (a) $\sim 40\text{photons}∕\mu \mathrm{s}$, (b) $\sim 6300\text{photons}∕\mu \mathrm{s}$. (c) SNR as a function of probe power positions in detuning space marked A ($\Delta =0\kappa$, $\theta =0\gamma$), B ($\Delta =\kappa$, $\theta =10\gamma$), and C ($\Delta =-\kappa$, $\theta =25\gamma$) in (a) and (b). (d) Normalized cavity transmission $T$ at a probe power of ${10}^4\text{photons}∕\mu \mathrm{s}$. The atom shifts the cavity resonance from the dashed to solid line, giving a signal represented with the short arrow.

Figure 6

(Color online) Schematic representation of heterodyne photodetection.

Figure 7

(Color online) A comparison of the SNR, $S$ (solid) and $S_{\mathrm{het}}$ (dashed), for atom detection with (a) ideal photon counting and ideal heterodyne detection and (b) an APD with 50% QE and a saturation flux of $20\text{photons}∕\mu \mathrm{s}$, and a realistic heterodyne setup using 95% efficient photodiodes. Traces at high power are for detection at the detuned position C in Fig. 5. Parameters as for Fig. 5.

Figure 8

Variation in QE and false detection count rate with discriminator position. Solid traces are the normalized photon counts for the empty cavity (fine) and the cavity containing an atom (thick). Dashed traces correspond to the QE (thick) and false counts (fine) as the position of the discriminator is varied. The SNR is (a) $\sim 17$, (b) $\sim 1.5$.