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Physical Review A

X state and quantum and classical correlations of two driven qubits with dissipation

Octavio Castaños

Published Jun 4, 2012• 3 citations
Publisher

Abstract

We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with all the modes of the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms. When the atoms have the same coupling with the laser field, it is shown that their steady-state density operator is approximately an $X$ state and this is used to obtain simple approximate analytic expressions for steady-state quantum and classical correlations which are characterized as functions of the laser field intensity and the distance between the two atoms. Moreover, the values of both the laser field intensity and the distance between the two atoms that maximize correlations are identified.

DOI
10.1103/physreva.85.062103

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We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with all the modes of the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms. When the atoms have the same coupling with the laser field, it is shown that their steady-state density operator is approximately an XXX state and this is used to obtain simple approximate analytic expressions for steady-state quantum and classical correlations which are characterized as functions of the laser field intensity and the distance between the two atoms. Moreover, the values of both the laser field intensity and the distance between the two atoms that maximize correlations are identified.
We consider two two-level atoms fixed at different positions, driven by a monochromatic laser field, and interacting collectively with the vacuum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and their steady-state is obtained analytically for two configurations, one in which the atoms are in equivalent positions and another in which they are not. The steady-state populations of the energy levels of the free atoms, entanglement, quantum discord and degree of mixed-ness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that driving both atoms with the laser field is inefficient for the generation of steady-state correlations when they are in equivalent positions. On the contrary, inequivalent positions lead to the possibility of considerable steady-state entanglement and left/right quantum discord. It is shown that an X-state can be obtained for high laser field intensities for both configurations. This allows the comparison of two measures of quantum discord. The behaviour and relationships between correlations are studied and several limiting cases are investigated.
We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and the steady-state is obtained analytically for a configuration of the atoms. The steady-state populations of the energy levels of the free atoms, entanglement, quantum and geometric discords and degree of mixedness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that there is a possibility of considerable steady-state entanglement and left/right quantum discord and that these can be controlled either by increasing/decreasing the intensity of the laser field or by increasing/decreasing the distance between atoms. It is shown that the system of two atoms can be prepared in a separable mixed state with non-zero quantum discord that turns into an XXX-state for high laser field intensities. The behavior and relationships between the different correlations are studied and several limiting cases are investigated.
The quantum correlations of two qubits in a microcavity with dissipation and a single quantized mode of the electromagnetic field are studied. In order to study our physical system, the Tavis-Cummings model and the formalism of the master equation of the density operator under the Born-Markov approximations will be used. The cavity mode will be coupled with an external pulsed laser and the master equation of the density operator that describes the evolution of the system will be solved numerically. The concurrence, the quantum mutual information, and the quantum discord are determined for the system of two qubits. The correlations are studied as a function of the dimensionless quantity $\tau = gt $ when the intensity of the laser cavity coupling varies, and two initial conditions are considered in the weak coupling regime in which the dynamic evolution of these correlations was studied.
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.
We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.
The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat 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 effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.