Identical damped harmonic oscillators described by coherent states

TL;DR

This paper analyzes quantum coherence dynamics in damped harmonic oscillators, exploring coherence measures, superposition effects, and quantum statistics, revealing basis-dependent coherence decay and boson-fermion statistical differences.

Contribution

It provides analytical insights into coherence evolution in quantum damped oscillators, including superposition effects and quantum statistical influences on coherence and particle correlations.

Findings

Coherence remains constant in position and momentum bases but decays in energy basis.

Quantum coherence increases with separation between superposed states.

Bosonic and fermionic statistics significantly affect single-particle coherence and correlations.

Abstract

Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the master equation, we take a single coherent state and compute analytically the relative entropy of coherence, $C_r$, in the energy, position and momentum bases. Although $C_r$ is constant in both the position and the momentum bases, it is a decreasing function of time in the energy basis becoming zero at long times, revealing its role as the preferred basis. Then, quantum coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation, in the complex plane, between the two superposed states. It is seen that the quantum coherence increases with this separation. Furthermore, quantum coherence of superposition is compared to that of decomposed states in the superposition. Finally, considering a system of two non-interacting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states, the joint detection probability and the mean square separation of particles. Our computations show that the single-particle coherence for antisymmetric states is always less than that of symmetric ones. Furthermore, boson anti-bunching and fermion bunching is seen in this open system. This behavior of bosons is the matter-wave analogue of photon anti-bunching seen in a modified Hanbury Brown-Twiss (HBT) interferometer.