Nonlinear Faraday rotation and detection of superposition states in cold atoms

We report on the observation of nonlinear Faraday rotation with cold atoms at a temperature of $~100$ $\mu$K. The observed nonlinear rotation of the light polarization plane is up to $0.1$ rad over the $1$-mm-size atomic cloud in approximately $10$-mG magnetic field. The nonlinearity of rotation results from long-lived coherence of ground-state Zeeman sublevels created by a near-resonant light. The method allows for creation, detection, and control of atomic superposition states. It also allows applications for precision magnetometry with high spatial and temporal resolution.

Figure 1

(a) The setup of the experiment for the balanced polarimeter arrangement. M, mirrors; PBS, polarizing beam splitters; PD, photodetectors; $\lambda /2$, $\lambda /4,$ wave plates. Direction of the magnetic field $B$ necessary for the observation of the Faraday rotation is indicated. (For FS scheme the $\lambda /2$ plate is removed and PD2 is not used). (b) Energy level structure with the Zeeman coherences established by a linearly polarized light resonant with the $F=3\to F^{\prime }=4$ transition.

Figure 2

Linear (wide) and nonlinear (narrow) Faraday rotation resonances centered at $B=0$. Signals were recorded at the time $\tau =2$ ms after switching on the probing beam. The probe power is 64 $\mu$W. At that power the NFR resonance is substantially power broadened but is well visible in comparison with the LFR. The slope of the central part is $\approx 0,6$ rad/G.

Figure 3

Evolution of the Faraday rotation with increasing light intensity of the probe beam showing the nonlinear increase and power broadening of the central resonance.

Figure 4

Time evolution of linear (wide) and nonlinear (narrow) Faraday rotation resonances in FS arrangement where the signal is proportional to magneto-optical rotation angle squared. Probe power is 18 $\mu$W.

Figure 5

Time dependence of the nonlinear Faraday rotation with a 45-mG magnetic field at two different probe beam powers (4 $\mu$W, magnified eight times, and 16 $\mu$W) compared to the time dependence of the linear Faraday rotation at 3 G and 16 $\mu$W.

Figure 6

NFR with amplitude modulated light (AMOR). The narrow central resonance is a typical NFR zero-field resonance and the two high field resonances at $\pm 3$ G result from amplitude modulation of the light with ${\Omega }_m=2.8$ MHz.