Parametric Amplification and Noise Squeezing in Room Temperature Atomic Vapors

We report on the use of parametric excitation to coherently manipulate the collective spin state of an atomic vapor at room temperature. Signatures of the parametric excitation are detected in the ground-state spin evolution. These include the excitation spectrum of the atomic coherences, which contains resonances at frequencies characteristic of the parametric process. The amplitudes of the signal quadratures show amplification and attenuation, and their noise distribution is characterized by a strong asymmetry, similar to those observed in mechanical oscillators. The parametric excitation is produced by periodic modulation of the pumping beam, exploiting a Bell-Bloom-like technique widely used in atomic magnetometry. Notably, we find that the noise squeezing obtained by this technique enhances the signal-to-noise ratio of the measurements up to a factor of 10, and improves the performance of a Bell-Bloom magnetometer by a factor of 3.

Figure 1

Schematics of the apparatus: a circularly polarized amplitude-modulated pump beam creates atomic coherences in the ground states of the Cs atoms by resonant ($F=3$) and indirect pumping ($F=4$). The generated collective atomic spin precesses orthogonally to the applied static magnetic field. A linearly polarized probe beam is used to extract information on the atomic precession via Faraday-like, nondestructive measurements.

Figure 2

Amplitude dependence of the $F=4$ atomic coherences oscillating at (a) ${\omega }_M$, and (b) ${\omega }_L$ on the pump beam amplitude modulation frequency ${\omega }_M$, recorded with a pump beam intensity of $61\mu \mathrm{W}/{\mathrm{cm}}^2$. All measurements were made with a probe beam power of $20\mu \mathrm{W}/{\mathrm{cm}}^2$, and ${\omega }_L/2\pi =270\mathrm{Hz}$. The solid red line represents the signal obtained by numerically solving Eq. (2). In the inset the amplitude of a parametric peak (${\omega }_M=2/3{\omega }_L$) is shown as a function of the pump beam intensity.

Figure 3

(a) Amplitude of the in-phase (open squares) and out-of-phase (filled dots) components of the magneto-optical rotation signal oscillating at frequency ${\omega }_L$ as a function of the pump beam intensity, with ${\omega }_M=2{\omega }_L$ and probe beam intensity of $24\mu \mathrm{W}/{\mathrm{cm}}^2$. Solid lines are numerically calculated for the same parameters of Fig. 2. (b) Variance of the quadrature amplitudes over 350 measurements for the in-phase (open squares) and out-of-phase (filled dots) components as a function of the pump beam intensity. For comparison, the variance measured with a modulation frequency of $4{\omega }_L$ is also reported (open triangles and gray diamonds).

Figure 4

(a) Signal-to-noise ratio of the signal quadratures measured for ${\omega }_M=2{\omega }_L$ as a function of the pump beam intensity. The out-of-phase quadrature (closed dots) shows an improved SNR with respect to the in-phase quadrature (open squares), and to the case of no modulation (gray diamonds). (b) Corresponding noise scaling with signal amplitude.

Figure 5

Signal-to-noise ratio of a Bell-Bloom magnetometer, as a function of the pump beam intensity. Similar to the case of modulation at $2{\omega }_L$, the out-of-phase quadrature (closed dots) is increased with respect to the in-phase quadrature (open squares) for intensities larger than roughly $15\mu \mathrm{W}/{\mathrm{cm}}^2$. Note that, as expected, the overall magnetization is higher when hitting the Bell-Bloom resonance with respect to other modulation frequencies.