Three-Photon Correlations in a Strongly Driven Atom-Cavity System

The quantum dynamics of a strongly driven, strongly coupled single-atom-cavity system is studied by evaluating time-dependent second- and third-order correlations of the emitted photons. The coherent energy exchange, first, between the atom and the cavity mode, and second, between the atom-cavity system and the driving laser, is observed. Three-photon detections show an asymmetry in time, a consequence of the breakdown of detailed balance. The results are in good agreement with theory and are a first step towards the control of a quantum trajectory at larger driving strength.

Figure 1

(a) A calculated quantum trajectory of $⟨a^{†}a⟩$ (red) and $⟨a^{†2}{a}^2⟩$ (blue). (b) A zoom reveals coherent oscillations at different frequencies accompanied by irreversible quantum jumps due to spontaneous emission (▽) and cavity decay (▴). (c) Experimental setup: Single ${}^{85}\mathrm{Rb}$ atoms pass through the cavity mode. Probe light and stabilization light are separated using an interference filter (IF). The probe light is split by beam splitters (BS) into four equal parts each directed onto a single-photon counting module (SPCM). (d) Energy levels of the strongly coupled atom-cavity system with the dressed eigenstates $|n,\pm ⟩=(|n,g⟩\pm |n-1,e⟩)/\sqrt{2}$ and the coupling (green arrows) induced by the probe laser.

Figure 2

(a) $g^{(2)}(\tau )$ for different driving strengths (from top to bottom $\eta =1.9\kappa$, $2.7\kappa$, $3.5\kappa$, $3.9\kappa$, $4.5\kappa$) in the experiment (black) and theory (red). (b) The two oscillation frequencies $\omega$ (▴) and $\Omega$ (●) as a function of the driving strength. $\omega$ is constant with an average $\overline{\omega }/2\pi =29\mathrm{MHz}$ (dashed blue line) close to the maximum vacuum Rabi frequency of $2g_0/2\pi =32\mathrm{MHz}$. $\Omega$ increases with $\eta$. Up to a driving strength of $3\kappa$ (dashed red line) it can be described by a two-level model with $\Omega =\sqrt{2}\eta$ (solid red line).

Figure 3

(a) $g^{(3)}(\pm \tau ,0)$ ($\eta =4.5\kappa$). The vacuum Rabi oscillations at a frequency of $2g_0$ are visible (red arrow) as a weak modulation for negative times (red, ●) whereas the quantum Rabi oscillations at a frequency of $2\sqrt{2}{g}_0$ are visible (blue arrow) as a weak modulation for positive times (blue, ○). (b) A sample quantum trajectory shows the same characteristic frequencies for the observables $⟨a^{†}a⟩$ (red) and $⟨a^{†2}{a}^2⟩$ (blue).

Figure 4

$g^{(3)}({\tau }_1,{\tau }_2)$ in the experiment (a) and theory (b) ($\eta =3.9\kappa$). To reduce noise, it was convoluted with a two-dimensional Gaussian filter with a width (FWHM) of 7 ns. An intuitive explanation for the pronounced, time-asymmetric peak marked by the dashed lines is given in the text.