Master equations for the density operator. (Reservoir theory)

Anton Sergeevich Trushechkin

One of the main methods for describing the dynamics of open quantum systems is the method of quantum master equations. These equations describe the dynamics of the reduced density operator of a system interacting with a reservoir. In this case, averaging is performed over the degrees of freedom of the reservoir, which does not allow one to describe the dynamics of reservoir observables. In this paper we show that applying the Zwanzig projection operator method, which is used in deriving quantum master equations, one can also derive dynamic equations for reservoir observables. As an example, we derive dynamic equations for the average number of quanta (photons, phonons) of a bosonic reservoir in the approximation of its weak coupling to the system in the case of the dipole interaction Hamiltonian.

Xiang‐Guo Meng, Ji‐Suo Wang, Bao‐Long Liang

Anna KOWALEWSKA-KUDè Aszyk

The generalized master equation for a two-level atom driven by a strong classical e eld and damped into a 'tailored' reservoir with a non-e at density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed e rst and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modie cations introduced by a strong e eld and/or by the reservoir with the non-e at density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the e uorescence and probe absorption spectra are obtained and illustrated graphically.

A. Kowalewska-Kudłaszyk, R. Tanaś

The generalized master equation for a two-level atom driven by a strong classical field and damped into a ‘tailored’ reservoir with a non-flat density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with the non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the fluorescence and probe absorption spectra are obtained and illustrated graphically.