Dissipation-induced enhancement and squeezing of quantum fluctuations

TL;DR

This paper investigates how a quantum harmonic oscillator's fluctuations can be simultaneously enhanced and squeezed through competing dissipation channels, revealing quantum frustration effects at low temperatures.

Contribution

It provides analytic formulas for oscillator fluctuations under dual dissipation, highlighting the novel regime where both quadratures are amplified due to quantum frustration.

Findings

Fluctuations are suppressed when one bath dominates.

Squeezing occurs when a single dissipative interaction dominates.

Both quadratures can be enhanced simultaneously in the balanced dissipation regime.

Abstract

We study a quantum harmonic oscillator linearly coupled through the position operator $\hat{q}$ to a first bath and through the momentum operator $\hat{p}$ to a second bath yielding an Ohmic-Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations ${\langle \Delta \hat{q}^2 \rangle}_0$ or ${\langle \Delta \hat{p}^2 \rangle}_0$ appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration. In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling.