Quantum-enhanced magnetometer with low-frequency squeezing

We report the demonstration of a magnetometer with noise-floor reduction below the shot-noise level. This magnetometer, based on a nonlinear magneto-optical rotation effect, is enhanced by the injection of a squeezed vacuum state into its input. The noise spectrum shows squeezed noise reduction of about $2\pm 0.35$ dB spanning from close to 100 Hz to several megahertz. We also report on the observation of two different regimes of operation of such a magnetometer: one in which the detection noise is limited by the quantum noise of the light probe only, and one in which we see additional noise originating from laser noise which is rotated into the vacuum polarization.

Figure 1

Experimental setup. The squeezer prepares an optical field with reduced noise properties which is used as a probe for the magnetometer. SMPM fiber depicts single-mode polarization-maintaining fiber, $\lambda /2$ is half-wave plate, PhR is phase-retarding wave plate, PBS is polarizing beam splitter, GP is Glan-laser polarizer, and BPD is balanced photodetector. Axes $x$ and $y$ coincide with horizontal and vertical polarization axes of all PBSs in our setup; axis $z$ is along beam propagation direction. Insets show the polarization of the squeezed-vacuum (Sq. vac) field and the laser field before the magnetometer cell (a) and right before the last PBS (b).

Figure 2

Comparison of the noise power spectral density of the laser residual intensity noise detected by a single photodiode (a) and balanced PD (b) for different laser intensities. Intensity of the laser doubles between subsequent traces (i)–(iii). The bottom trace (iv) corresponds to the dark noise of the detector.

Figure 3

Sample of the magnetometer response to the longitudinal magnetic field. The narrow feature at zero field is due to repeated coherent interactions of atoms with the light field. Cell temperature is $40{}^{\circ }$C, density is $6\times {10}^{10}$ atoms/cm${}^3$, and probe power is 6 mW.

Figure 4

Magnetometer response (solid) and probe transmission (dashed) vs atomic density. Density uncertainties due to temperature fluctuations correspond to the size of the markers. Laser power is 6 mW. Cell temperatures range from $25{}^{\circ }\text{C}\mathrm{to}70{}^{\circ }\text{C}$ in $5^{\circ }\text{increments}$.

Figure 5

Magnetometer quantum-noise-floor spectra with polarization-squeezed (light trace) and shot-noise-limited probe (dark trace) fields taken at different temperatures or atomic densities of the magnetometer. (a) 25 ${}^{\circ }$C ($N=1.3\times {10}^{10}$ cm${}^{-3}$), (b) 35 ${}^{\circ }$C ($N=3.6\times {10}^{10}$ cm${}^{-3}$), (c) 50 ${}^{\circ }$C ($N=1.5\times {10}^{11}$ cm${}^{-3}$), (d) 55 ${}^{\circ }$C ($N=2.2\times {10}^{11}$ cm${}^{-3}$), (e) 60 ${}^{\circ }$C ($N=3.4\times {10}^{11}$ cm${}^{-3}$), and (f) 70 ${}^{\circ }$C ($N=7.4\times {10}^{11}$ cm${}^{-3}$). Laser probe power is 6 mW. Spectrum analyzer resolution bandwidth is 28.6 Hz; the resulting trace is averaged over 300 traces.

Figure 6

Magnetometer quantum noise spectrum with polarization-squeezed (a) and shot-noise-limited (b) probe fields taken at a magnetometer cell temperature of 35 ${}^{\circ }$C. The inset shows the low-frequency part of the noise spectrum (0–5 kHz). The arrow marks the frequency of magnetic field modulation at 220 Hz. Laser probe power is 6 mW. Spectrum analyzer resolution bandwidth is 0.9 Hz.

Figure 7

Noise suppression level vs atomic density normalized to shot-noise level for several noise frequencies. Positive values indicate noise suppression, negatives indicate noise amplification. This level is found by averaging the coherent probe noise level subtracted from the squeezed probe noise level over 100 points (2 kHz) centered around the chosen noise frequency. The average uncertainty of $\pm 0.35$ dB is not included in the plot for clarity. Laser probe power is 6 mW.

Figure 8

NMOR magnetometer sensitivity as a function of the atomic density with polarization-squeezed (a) and coherent (b) (shot-noise-limited) optical probes. Error bars are smaller than the size of the markers. Laser probe power is 6 mW. Detection frequency is 500 kHz.