Realization of a bipolar atomic Šolc filter in the cavity-QED microlaser

We report experimental realization of a rudimentary atomic Šolc filter, recently proposed by Hong et al. [Opt. Express 17, 15455 (2009)]. It is realized by employing a bipolar atom-cavity coupling constant in the cavity-QED microlaser operating with a TEM${}_{10}$ mode in a strong coupling regime. The polarity flip in the coupling constant dramatically changes the photoemission probability of a two-level atom relative to unipolar coupling, resulting in multiple narrow emission bands in the detuning curve of the microlaser mean photon number. The observed resonance curves are explained well by a two-step, three-dimensional, geodesic-like motion of the Bloch vector in the semiclassical limit.

Figure 1

(a) Atom-cavity coupling $g(t)$ (solid line) that an atom experiences while traversing the TEM${}_{10}$ mode with a dotted line indicating an idealized flat-top profile with the same pulse area (for $t<0$ or $t>0$) as the actual TEM${}_{10}$ mode. (b) Schematic for the experimental setup: M, mirror; C, cavity mode; P, pump beam; $\theta$, atomic beam tilt angle; B, barium atomic beam; BS, beam splitter; APD, avalanche photo-diode for photon counting of the output signal; and CCD, charge-coupled device for mode imaging.

Figure 2

(a) Detuning curves of the microlaser output for various vertical positions of the atomic beam. (b) Transverse profiles of TEM${}_{01}$ and TEM${}_{10}$ modes when they are lasing, taken with a CCD camera. The cavity was locked at the maximum intensity of each mode. (c) The detuning curves at three atomic beam positions, A, B, and C. For A and C, the detuning curve for TEM${}_{01}$ mode is observed, whereas for B, only the TEM${}_{10}$ mode undergoes lasing. Tiny shoulder-like structures on the right sides of each lasing peak of TEM${}_{01}$ mode are small contributions from the nearby (separated by 5 MHz) TEM${}_{10}$ mode.

Figure 3

(a) In the Bloch sphere, the state vector (blue arrow), initially upward, can move in the downward direction by two successive rotations around a direction-switching torque vector (red arrow) for the bipolar coupling constant. (b) The gain function of Eq. (1) is plotted as a function of a normalized detuning $\delta$ and a normalized Rabi frequency $\eta$. (c) Actual Bloch vector trace. (d) The gain function accounting for the actual mode profile and the velocity distribution. The flat-top coupling constant $g_0$ is chosen to give the same $m=1$ gain peak conditions as the actual coupling constant.

Figure 4

(a) Detuning curves of the microlaser mean photon number for the TEM${}_{10}$ mode for various numbers of atoms $N$. The green and gray arrows indicate the Doppler shift of resonance and the two-peak separation, respectively. Inset: Quantum jumps to the $m=3$ layer solutions were observed with a large atom number at a small tilt angle ($k={10}^3$). An $m=1$ layer solution is also shown (blue dashed curve) for comparison. At this high gain, the two opposite traveling wave components become partially overlapped due to bichromatic interaction between them [30]. (b) The heights of peaks A and B in the detuning curve as the atom number. Grey dashed curve (for $N=78$) in (a) and solid lines in (b) are the fits by the semiclassical theory including the atomic velocity distribution and the actual mode profile. (c) The separation between peaks C and D versus the atomic beam tilt angle, measured with a slightly larger mean velocity of atoms than (a).