Abstract
We demonstrate an exact mapping of a class of models of two interacting qubits in thermal reservoirs to two separate problems of spin–boson-type systems. Based on this mapping, exact numerical simulations of the qubits dynamics can be performed, beyond the weak system–bath coupling limit and the Markovian approximation. Given the time evolution of the system population and coherences, we study as an application the dynamics of entanglement between the pair of qubits immersed in boson thermal baths, showing a rich phenomenology, including an intermediate oscillatory behavior, the entanglement sudden birth, sudden death and revival. We find that the occurrence of entanglement sudden death in this model depends on the portion of the zero and double excitation states in the subsystem initial state. In the long-time limit, analytic expressions are presented at weak system–bath coupling, for a range of relevant qubit parameters.
Highlights
Understanding the dynamics of a dissipative quantum system is a prominent challenge in physics, as a quantum system is never perfectly isolated from a larger environment
We show how the dynamics can be followed within a simpler construction: While we take into account the zero excitation and double excitation states, under certain initial conditions their dynamics can be separated from the evolution of the single-excitation states
We simulated the time evolution of two qubits immersed in thermal environments, considering a class of initial states for the subsystem
Summary
Understanding the dynamics of a dissipative quantum system is a prominent challenge in physics, as a quantum system is never perfectly isolated from a larger environment. Steady-state entanglement generation by dissipation has been recently observed in atomic ensembles [24] These studies have assumed non-interacting qubits, and the system dynamics has been typically followed within quantum master equation approaches (e.g., the Redfield equation or Lindblad formalism [25]), by invoking the weak system-bath coupling approximation. The model has turned into the anisotropic XYZ-type model with flip-flop (σx) coupling between the system and reservoirs In this form, the model describes energy exchange between the qubits and the baths, unlike the original Hamiltonian [Eq (3)] which delineates dephasing effects.
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