Abstract
We study a quantum harmonic oscillator linearly coupled through the position operator to a first bath and through the momentum operator 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 or 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.
Highlights
The study of the quantum dissipation and the decoherence dynamics in atomic and mesoscopic systems is fueled by the perspective of engineering the reservoirs in order to preserve quantum coherence [1,2,3,4,5]
For the quantum damped harmonic oscillator, it is known that the quantum fluctuations of the operator to which the bath is coupled are squeezed and those of its conjugate variable are enhanced in such a way that the Heisenberg uncertainty principle holds
The paper is organized as follows: in section 2, we introduce the model Hamiltonian for the quantum harmonic oscillator coupled to two baths and derive the expressions for the fluctuations of q and p
Summary
The study of the quantum dissipation and the decoherence dynamics in atomic and mesoscopic systems is fueled by the perspective of engineering the reservoirs in order to preserve quantum coherence [1,2,3,4,5]. The decay dynamics of decoherence and relaxation can be always underdamped despite the fact that the strength of the dissipative interaction increases This state of affairs was termed ‘quantum frustration’ and was analysed for an open quantum system realized by a harmonic oscillator [23,24,25,26] or a single spin [27,28,29,30,31]. These findings can be understood by considering the two baths as two detectors continuously coupled to the system and measuring simultaneously two non-commutating observables. A short summary and perspective are given in the last section 6
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
