Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 $\pm$ 7 $\text{kHz}/\sqrt{\text{Hz}}$ with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.

Figure 1

A Gaussian laser beam passes through a Sagnac interferometer consisting of a 50:50 BS, a mirror, and a prism. The prism weakly perturbs the direction of the beam as the frequency of the laser source is modulated, denoted by the red and blue beam paths. We monitor the position of the light entering the dark port of the interferometer. We lock the input power to the interferometer using a power measurement before the BS. The majority of the light exits the interferometer via the bright port and is collected with an isolator for use in an experiment.

Figure 2

The position of the postselected beam profile is measured as we modulate the input laser frequency of the interferometer. The modulation oscillates as a sine wave at 10 Hz and the signal from the split detector is frequency-filtered and amplified. The error bars are given by the standard deviation of the mean. The minimum frequency change measured here is around 743 kHz with an effective integration time of 30 ms. The weak value amplification is approximately 79.

Figure 3

We show the noise spectrum for a passive system (green, solid trace) and for a driven system (blue, dashed trace), where the laser frequency modulation is 7.4 MHz at 10 Hz. We see that the first harmonic of the signal is about 5 dB down from the fundamental and the third harmonic is nearly 25 dB down. For a 7.4-MHz change in laser frequency, we see that the noise is approximately 35 dB below the signal, demonstrating the low-noise nature of this measurement.