**Phase-locked time-and-frequency resolved homodyne detection & measuring the frequency response of an optical cavity** - Katanya Brianne Kuntz

I will discuss the latest results from two experiments. First, I will discuss a simple, novel technique to measure the frequency response (free spectral range and linewidth) of an optical cavity up to 10 GHz from the optical carrier frequency without the need for a wide bandwidth photodetector. Our technique involves a fibre amplitude (intensity) modulator and a low-frequency power meter, both of which are readily available laboratory equipment.
Then I will discuss an experiment designed to characterise phase-coherent time-and-frequency resolved homodyne detection. This detection scheme can measure two optical frequency modes defined as the “symmetric” and “anti-symmetric” sideband modes. These modes are superposition states of upper and lower sideband frequencies, which are separated symmetrically in the frequency domain about the optical carrier frequency. The “symmetric” sideband mode is analogous to the amplitude quadrature, while the “anti-symmetric” sideband mode is analogous to the phase quadrature of light.
We apply phase-locked time-and-frequency resolved homodyne detection to a discretely phase modulated coherent state, and conduct MaxLik reconstruction of two distinct states: a coherent state in the “anti-symmetric” mode, and a vacuum state in the “symmetric” mode. The discrete nature of the modulation signal defines a temporal window, while the precise modulation frequency defines the demodulation frequency. We apply fixed-phase demodulation in post-processing of the captured homodyne data, which allows reconstruction of either sideband mode from a single data set.