Relaxation of interacting open quantum systems

Abstract

We consider the transition from the description of a closed quantum system consisting of an open quantum system and a reservoir to the description of the open quantum system alone by eliminating the reservoir degrees of freedom by averaging over them. An approach based on the Lindblad master equation for the density matrix is used. A general scheme is developed for deriving the Lindblad superoperator that emerges after averaging the von Neumann equation over the reservoir degrees of freedom. This scheme is illustrated with the cases of radiation of a two-level atom into free space and the dynamics of the transition of a two-level atom from a pure state to a mixed state due to interaction with a dephasing reservoir. Special attention is paid to the open system consisting of several subsystems each of which independently interacts with the reservoir. In the case of noninteracting subsystems, the density matrix is a tensor product of the subsystem density matrices, and the Lindblad superoperator of the system is a sum of Lindblad superoperators of those subsystems. The interaction between the subsystems results not only in the emergence of the corresponding term in the Hamiltonian of the combined system but also in the nonadditivity of the Lindblad superoperators. This is often overlooked in modern literature, possibly leading, as is shown in this methodological note, to serious errors; for example, the second law of thermodynamics could be violated.

Universal lasing condition

“…This emission acts as an external driving force, causing the atom to oscillate at a unified frequency. On the other hand, dephasing processes occurring due to interaction with the environment (for details, see 22 , 48 ) cause the phase of oscillations to be disturbed. If the action of all atoms upon each single atom can overcome dephasing, atoms start to synchronize and emit coherently with each other, which leads to a substantial increase in the atom-field interaction and lasing.…”

“…the linewidth of the atom). The relaxation of polarization is mainly caused by dephasing processes such as the interactions between atoms and the phonons inside the active medium 21 , 22 , and is thus determined by the properties of the active medium. is the population inversion of the mth active atom.…”

Quantum Embedded Superstates

“…In the first case, one should consider non‐Markovian dynamics of the system + reservoir, [ 69 ] in the second case, one should use the global master equation by decomposing the system's operators on the eigenbasis of system's Hamiltonian. [ 70,71 ]…”

Dephasing-assisted entanglement in a system of strongly coupled qubits

“…The last statement can be elucidated in the Born-Markov approximation by means of a master equation in the Lindblad form. As the Lindblad approach gives an answer consistent with thermodynamic laws, using eigenstates of the whole system is necessary [35,36]. In the case of well-separated eigenstates, the Lindblad superoperator describes the transitions between eigenstates.…”

“…In the case of well-separated eigenstates, the Lindblad superoperator describes the transitions between eigenstates. Because the eigenstate of the interacting subsystem is a superposition of isolated subsystem eigenstates, mentioned Lindblad superoperators will result in a cross-relaxation process when relaxation of one subsystem leads to relaxation of the others [35,37]. Recently, construction of the correct master equation for the system of coupled TLSs, interacting with different types of reservoirs, was actively investigated [38][39][40].…”