QND measurements of photon number in monolithic microcavities

TL;DR

This paper demonstrates that monolithic microcavities can perform quantum nondemolition measurements of photon number with precision surpassing the standard quantum limit by leveraging Kerr nonlinearity and optimal measurement strategies.

Contribution

It provides an exact solution for QND photon number measurement in microcavities, accounting for losses and nonlinear effects, and identifies conditions for surpassing the standard quantum limit.

Findings

Achieves measurement imprecision below the standard quantum limit

Provides an explicit conditional quantum state for the signal field

Designs optimal homodyne measurement to mitigate self-phase modulation effects

Abstract

We revisit the idea of quantum nondemolition measurement (QND) of optical quanta via a resonantly enhanced Kerr nonlinearity taking into account quantum back action and show that the monolithic microcavities enable QND measurement of number of quanta in a weak signal field using a spatially overlapping classical probe field. Due to the cross-phase modulation effect, the phase of the probe field acquires information about the signal number of quanta without altering it. We find the exact solution to the Heisenberg equations of motion of this system and calculate the measurement error, accounting for the optical losses in the measurement path. We identify a realistic approximation to obtain the explicit form of the final conditional quantum state of the signal field, accounting for the undesirable self-phase modulation effect and designing the optimal homodyne measurement of the probe beam to evade this effect. We show that the best modern monolithic microcavities allow achieving the measurement imprecision several times better than the standard quantum limit.