# Supersensitive estimation of the coupling rate in cavity optomechanics with an impurity-doped Bose-Einstein condensate

## TL;DR

This paper introduces a method for highly precise estimation of coupling strength in a hybrid optomechanical system with a Bose-Einstein condensate and impurity, achieving Heisenberg scale sensitivity under certain conditions.

## Contribution

The authors propose a novel scheme for supersensitive coupling estimation in a hybrid system, demonstrating robustness with coherent states and a measurement approach that saturates the quantum Cramér-Rao bound.

## Key findings

- Heisenberg scale sensitivity achievable with low photon numbers
- Coherent state input is more robust against photon loss than squeezed state
- Measurement scheme can saturate the quantum Cramér-Rao bound

## Abstract

We propose a scheme to implement a supersensitive estimation of the coupling strength in a hybrid optomechanical system which consists of a cavity-Bose-Einstein condensate system coupled to an impurity. This method can dramatically improve the estimation precision even when the involved photon number is small. The quantum Fisher information indicates that the Heisenberg scale sensitivity of the coupling rate could be obtained when the photon loss rate is smaller than the corresponding critical value in the input of either coherent state or squeezed state. The critical photon decay rate for the coherent state is larger than that of the squeezed state, and the coherent state input case is more robust against the photon loss than the squeezed state case. We also present the measurement scheme which can saturate the quantum Cram\'er-Rao bound.