Spectrum of the Cavity-QED Microlaser: Strong Coupling Effects in the Frequency Pulling at Off Resonance

We report the first experimental observation of the cavity-QED microlaser spectrum, specifically the unconventional frequency pulling brought by a strong atom-cavity coupling at off resonance. The pulling is enhanced quadratically by the atom-cavity coupling to result in a sensitive response to the number of pumping atoms (2.1 kHz per atom maximally). Periodic variation of the pulling due to the coherent Rabi oscillation is also observed as the number of pumping atoms is increased across multiple thresholds.

Figure 1

(a) Schematic of the experimental setup. The polarizations, denoted by red arrows, of the microlaser and the cavity stabilization laser are orthogonal to each other. PBS: polarizing beam splitter, BS1: high transmission beam splitter, BS2: nonpolarizing beam splitter, APD: avalanche photodiode, SPCM: single photon counting module, LO: local oscillator. (b) The typical second-order correlation function $g_h^{(2)}(t)$ of the heterodyne signal. (c) The spectrum obtained by Fourier-transforming $g_h^{(2)}(t)$ in (b). The red solid curve is a fit with a Voigt integral function [18].

Figure 2

(a) The mean photon number in the cavity obtained by scanning the cavity resonance frequency. Indicated by the red circle is the fixed cavity frequency for the example of (b). (b) At the fixed cavity frequency the spectral contents of the microlaser emission is obtained by PCSOCS. The red dashed line indicates the cold cavity frequency which is offset from the probe frequency (gray dashed-dotted line). The black dotted line is the center frequency of the microlaser. (c) The frequency pulling extracted from the analysis like (b) as a function of the cavity-atom detuning for the selected values of $g/g_0$ indicated in the panel. The symbols correspond to the experiment, and the curves to the theory. (d) The linewidth obtained by fitting the spectra for $g=g_0$ (empty square). The theoretical curves are obtained by considering the nondispersive effect only (blue dotted line), including the differential pulling induced by $\Delta n$ (green dashed-dotted line), including the differential pulling induced by $\Delta N$ (red dashed line) and including the effect of both $\Delta N$ and $\Delta n$ (black solid line). (e) The mean photon number on resonance as we increase the effective coupling constant. (f) The amount of the frequency pulling as a function of $g/g_0$ at the detuning ($-3.6\mathrm{MHz}$) denoted with a yellow bar in (c). The filled circles are from the experiment. The solid curves in (e) and (f) are from the quantum theory. The velocity of the atom follows a Gaussian distribution with $\overline{v}=680\mathrm{m}/\mathrm{s}$ and $\Delta v_{\mathrm{FWHM}}/\overline{v}\simeq 0.35$. The associated Doppler shift is 20.5 MHz.

Figure 3

(a) The magnitude of the frequency pulling at a fixed detuning of 4.6 MHz investigated within the first branch solution. The mean velocity $\overline{v}$ of atoms is $680\mathrm{m}/\mathrm{s}$ with the inhomogeneous spread $\Delta v_{\mathrm{FWHM}}/v_c\simeq 0.35$ for this particular data. (circles: experiment, solid curve: theory, dotted line: linear fit) (b) The magnitude of the pulling (black circles: experiment, solid curve: theory) and the mean photon number (gray circles: experiment, dashed curve: theory) at a detuning of 3.3 MHz, here investigated up to the third branch solution. (c) The detuning curve of the mean photon number (gray circles) and the frequency pulling (squares: 1st, upright triangles: 2nd, inverted triangles: 3rd branch solution) with $\overline{N}=1500$, at which the third branch solution is possible near resonance. (d) The spectrum taken at a detuning of 3.3 MHz [marked by the dashed box in (c)] is fitted by two Gaussian functions (dashed lines: individual Gaussian profiles, solid line: complete fitting). From (b) to (d) the atomic beam has $\overline{v}=720\mathrm{m}/\mathrm{s}$, $\Delta v_{\mathrm{FWHM}}/\overline{v}=0.40$, and the associated Doppler shift is 21.5 MHz.