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arXiv:cond-mat/0411376 · Physical Review B

Effects of a nonlinear bath at low temperatures

Hanno Gassmann, Christoph Bruder

Published Jul 1, 2005• 3 citations
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Abstract

We use the numerical flow-equation renormalization method to study a nonlinear bath at low temperatures. The model of our nonlinear bath consists of a single two-level system coupled to a linear oscillator bath. The effects of this nonlinear bath are analyzed by coupling it to a spin, whose relaxational dynamics under the action of the bath is studied by calculating spin-spin correlation functions. As a first result, we derive flow equations for a general four-level system coupled to an oscillator bath, valid at low temperatures. We then treat the two-level system coupled to our nonlinear bath as a special case of the dissipative four-level system. We compare the effects of the nonlinear bath with those obtained using an effective linear bath, and study the differences between the two cases at low temperatures.

DOI
10.1103/physrevb.72.035102

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Reduced equations of motion for a two-level system strongly coupled to a harmonic oscillators bath are constructed by extending the hierarchy of equations introduced by Tanimura and Kubo [J. Phys. Soc. Jpn. 58 (1989) 101]. The set of equations treats the bath in a nonperturbative manner and is applicable to a low-temperature system with taking into account the correlation time of noise. By numerically calculating linear absorption spectra for different temperatures, we demonstrate that the present theory is not afflicted with the dynamical positivity problem that occurs at low temperatures without the rotating wave approximation. Remarkable changes are found in the spectra when the temperature is lower than the resonant energy of the two-level system.
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We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness--Bloch--Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
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