Compass state: Effect of squeezing and displacement on the Fock space

TL;DR

This paper explores superpositions of squeezed and displaced number states, analyzing their phase space structure and metrological potential, achieving high fidelity with compass states and comparable measurement variance.

Contribution

It introduces a class of non-classical states with high fidelity to compass states and evaluates their metrological usefulness, especially for damping parameter estimation.

Findings

State fidelity exceeds 99% with compass states.

Variance in small shift measurements is comparable to compass states.

Potential for damping parameter estimation in metrology.

Abstract

We investigate a broad class of non-classical states, composed of superposed squeezed and displaced number states. The phase space structure is analysed, keeping in mind, Heisenberg limited sensitivity in parameter estimation. Appropriate squeezing and displacement parameters are identified, wherein state fidelity in comparison to metrologically sensitive compass state, is more than 99$\%$. Also, the variance in small shifts measurements, is found equal for both proposed and compass states. They show similar behaviour with change in average photon number. In metrological application, number variance of the compass state being small for low coherent amplitude, suggests its potential to estimate damping parameter.