Dynamics of a system of two coupled quibts in interaction with a thermal bath: A comparative study using different models for the system-bath interaction
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).
We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.
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.
We study in this thesis composite quantum systems under the influence of external environments.In the first part of this work, we investigate a two qubit interacting system having one of them isolated and the other coupled to a thermal bath.We analyze the effect of the temperature of the bath on the dynamics of the two qubit system.In order to do that, we consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a "phenomenological" approach, in which the master equation consists of a dissipative term added to the unitary evolution term.We show that in the strong coupling regime between the subsystems (qubits), the expected thermal equilibrium steady state for the two-qubit system naturally arises in the framework of the microscopic model, while in the phenomenological approach it is obtained a steady state density operator which is not correct.Furthermore, the differences are even more profound in the weak coupling regime, when the models give rise to opposite behaviors with regard to the linear entropy of qubit 1.At the context of quantum systems coupled to environments with few degrees of freedom, we solve analytically the matter-radiation interaction model known as two atom Tavis-Cummings Model.With the solutions at hand, achieved in general circumstances until the present not found in literature, in which the constituent atoms may be coupled with different strengths to the field and also have different frequency detunings, we study the effects that arise from the interaction of a small environment (atom in a statistical mixture state) with the other atom coupled to an oscillator (cavity mode).We show that nonclassical features associated to the main system may be significantly degraded by the action of the small environment, if atom 2 is resonantly coupled to the field.We also demonstrate that the nonclassical behaviour of the system may be restored if we detune the field from the transition frequency of atom 2, the environment.
Abstract The dissipative dynamics of non-coupled two qubits interacting with independent reservoir is studied by solving the non-Markovian master equation. In order to examine the effectiveness of the Nakajima-Zwanzig and time-convolutionless master equations in the description of quantum correlation dynamics, different coupled regimes are investigated. The comparison between the above two master equation methods for investigating the dynamics of quantum discord is also made. Finally, we further confirm that the two master equations should be applied in different regimes of qubits coupled to their reservoirs, respectively.
A system evolving unitarily does not dephase or thermalize by definition. Yet, if one considers a part of a unitary system, situation is different. Here we analyze an isolated set of coupled qubits taking one qubit at a time as a subsystem, and writing self-consistently a weak-coupling master equation for it. Weakly anharmonic oscillators and ideal qubits (two-level systems) demonstrate dephasing, i.e. the diagonal elements of the density matrix reach a steady-state in the long-time limit, and the off-diagonal elements of ideal qubits decay exponentially. For the linear coupling between the qubits, only the degenerate ones interact, and the system does not reach thermal distribution. However, non-linearity, in our analysis in form of three-wave mixing, ensures a thermal distribution in the long time limit, where the temperature is determined uniquely by the energy in the initial non-thermal state. Finally, we present a potential experimental scheme based on a superconducting quantum circuit.
We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation (RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.