Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser

In the observation of multiple thresholds in the cavity-quantum electrodynamics microlaser there was deviation from the result predicted by uniform atom-cavity coupling theory, notably a frequency-pushing behavior. We analyze in the semiclassical limit the tilted injection of atoms, originally used to achieve a spatially uniform atom-cavity coupling, and show that the deviation originates from the interference between the induced dipole moments associated with two traveling-wave components of a standing-wave cavity mode. The criteria for sufficiently reduced interference and thus uniform atom-cavity interactions are derived in analytic considerations and verified by numerical calculation. Our analysis is well supported by experimental data.

Figure 1

(Color online) Illustration showing how the steady-state detuning curve is determined. There are five stable branch solutions in this case.

Figure 2

Mode function for atoms injected into the cavity at two different positions $\left(k{z}_0=0,\pi /2\right)$ with a tilt angle with Doppler shift of $\delta /2\pi =22.8\text{MHz}$ at a speed of $v=750\text{m}/\text{s}$, which are typical experimental parameters.

Figure 3

(Color online) Density plot of the difference of the cross term for $k{z}_0=0$, $\pi /2$ as a function of $\Delta \tau$ and $\delta \tau$. Dashed lines $\Delta =\pm \delta$ are shown for comparison.

Figure 4

(Color online) Density plots of emission probabilities for the antinode $\left[\left(\text{a}\right)–\left(\text{d}\right)\right]$ and the node $\left[\left(\text{e}\right)–\left(\text{h}\right)\right]$. A top-hat mode profile is assumed. From the first row to the fourth, $\delta /2\pi$ are 0, 15, 30, and 45 MHz, respectively. Typical parameters in the experiment, $v=750\text{m}/\text{s}$ (monovelocity) with $g/2\pi =380\text{kHz}$ and ${\Gamma }_c/2\pi =150\text{kHz}$, are used.

Figure 5

(Color online) Density plots of $P_{\mathit{em}}$ for a Gaussian mode profile. The same parameters and plot conventions are used as in Fig. 4. From the first row to the third $\delta /2\pi$ are 0, 15, and 30 MHz, respectively.

Figure 6

(Color online) Density plots of $P_{\mathit{em}}$ for $\delta /2\pi =15\text{MHz}$ at $k{z}_0=0$. (a) By the exact calculation and (b) by the approximate calculation of Ref. [11].

Figure 7

Detuning curves for (a) $\delta /2\pi =15\text{MHz}$ and (b) $\delta /2\pi =35\text{MHz}$. Circle: experiments, line: theoretical curves which are obtained for the mean intracavity atom number of $N=800$ in (a) and $N=900$ in (b).