Homodyne detection: measuring the quantum fluctuations of light
Directly measuring the electric field of light at optical frequencies is incredibly challenging because it oscillates far too rapidly for any detector to follow. Instead, we can rely on techniques that allow me to infer the properties of the field indirectly.
Visible light, like the orange light at 5 \times 10^{14} Hz, oscillates much too quickly for direct measurement. Even the fastest detectors we have available average the signal over a picosecond, effectively smoothing out the rapid oscillations and giving a zero reading.
The key idea is to measure the correlation between the signal field and a strong local oscillator. The signal field can be written as:
\mathbf{E}^{(+)}(\mathbf{r}, t) = i\mathbf{e}_\lambda \mathscr E^{(1)}_\lambda \mathbf{a}_\lambda e^{i(\mathbf{k}_\lambda \cdot \mathbf{r} - \omega_\lambda t)}
In homodyne detection, this signal field is mixed with a strong local oscillator (LO) field. The LO can be thought of as a coherent state with a large amplitude. The key is that the LO’s phase can be controlled. When the signal and LO are mixed fields on a beamsplitter, the resulting light is detected by a photodetector.
The current from the photodetector is proportional to the square of the electric field. This current contains terms that oscillate at the difference frequency between the signal and the LO. By carefully controlling the LO’s phase, we can select which quadrature of the signal field we measure. This means we can measure quantities related to \mathbf{a}_\lambda and \mathbf{a}_\lambda^\dagger.
With homodyne detection, we can access information about the phase of the light field, which is not possible with direct intensity measurements. This allows me to characterize the quantum state of light, including its fluctuations.For example, it can be used to study squeezed states of light, where the noise in one quadrature is reduced below the standard quantum limit at the expense of increased noise in the other. This is a powerful technique we use to explore the quantum world of light.
For more insights into this topic, you can find the details here.