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International Journal of Theoretical Physics

Purity and Correlation of a Cavity Field Interacting with a SC Charge Qubit with a Lossy Cavity

M. Sebawe Abdalla, A.‐S. F. Obada, A.‐B. A. Mohamed, Eied Mahmoud Khalil

Published Nov 26, 2013• 9 citations
Publisher

Abstract

A single-mode microwave cavity field, coupled to its reservoir, interacting generally with a superconducting charge qubit is considered. Using a certain canonical transformation for the qubit states, the system is transformed into the usual Jaynes-Cummings model. The solution of the master equation of this system, in the case of a high- Q cavity is obtained. The temporal evolution of the population inversion is explored. The effects of cavity damping on the purity of the qubit, the field and the global system state are studied. It is found that due to the coupling between the system and environment, the purity is lost. The entanglement is compared with total correlation. It is found that, with the damping parameter, the asymptotic value of the correlation measure is not null, since the global system evolves to a classically correlated state. The negativity is used as an indicator of the degree of entanglement between the qubit and the field. The results indicate the sensitivity of these aspects to change of the damping parameter.

DOI
10.1007/s10773-013-1929-0

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A single-mode microwave cavity field, coupled to its reservoir, interacting generally with a superconducting charge qubit is considered. Using a certain canonical transformation for the qubit states, the system is transformed into the usual Jaynes-Cummings model. The solution of the master equation of this system, in the case of a high- Q cavity is obtained. The temporal evolution of the population inversion is explored. The effects of cavity damping on the purity of the qubit, the field and the global system state are studied. It is found that due to the coupling between the system and environment, the purity is lost. The entanglement is compared with total correlation. It is found that, with the damping parameter, the asymptotic value of the correlation measure is not null, since the global system evolves to a classically correlated state. The negativity is used as an indicator of the degree of entanglement between the qubit and the field. The results indicate the sensitivity of these aspects to change of the damping parameter.
A system of a superconducting charge qubit with gate change ne≠12 interacting with a single-mode microwave cavity field, coupled to its reservoir, is introduced. The system is transformed into the usual Jaynes–Cummings model by canonical transformation. Analytical and numerical results under certain parametric conditions are obtained by means of which we analyze the influence of the damping terms and the detuning on the dynamics of Wehrl entropy and purity loss of the states. The results indicate the sensitivity of these aspects to change either in the decay or in the detuning parameters. An interesting relation between the correlation and decoherence effect is observed.
The system of a superconducting charge qubit interacting with a field in the case of lifting the restriction of the degeneracy point (⁠|ng=12n_{g}=\frac {1}{2}ng​=21​|⁠) is considered. Two different kinds of canonical transformation are used to transform the Hamiltonian of this system into the Jaynes–Cummings model. We use the coherence angle of the qubit coherent state to examine the effects of lifting the restriction of the degeneracy point on the qubit inversion. This helps us to see the variation in the collapse and revival phenomenon. Meanwhile, we also consider the degree of entanglement using the definition of purity, in addition to a discussion on the variance and entropy squeezing. AMS Subject Classification A34,A61
The temporal evolution of entanglement for a single-mode field interacting with a two-level atom via intensity-dependent coupling in the off-resonant case has been studied, where the leakage of photon through the cavity is taken into account. The effects of cavity damping on the coherence properties of the atom and the field are studied. The amount of entanglement is compared with the total correlations. It is found that the atom–field system is inhibited from going into a pure state in the off-resonant case.
An analytical description of a superconducting (SC) phase qubit coupled to a torsional resonator, which is damped by a dispersive reservoir, is presented based on the master equation. Therefore, the effect of the qubit phase damping on the dynamical behavior of the entanglement, purity loss and qubit inversion are investigated. It is found that the collapse and revival phenomena of qubit inversion are very sensitive not only to the damping parameter but also to the frequency detuning and the qubit distribution angle of the initial state. It is interesting to note that the purity of the state of the SC-qubit, which is measured by von Neumann entropy, can be completely lost due to the dispersive reservoir parameter. Because of the existence of dispersive reservoir, the von Neumann entropy cannot be a measure for the entanglement in open system. So, the negative eigenvalue of the partially transposed density matrix of qubit-resonator system is used to quantify the entanglement. For certain parameter sets, it is possible to control the degree and the dynamics of entanglement between the qubit and the torsional resonator.
In a system of two charge-qubits that are initially prepared in a maximally entangled Bell's state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast.
We investigate the entanglement dynamics of a quantum system consisting of three Superconducting charge qubits (SCQs) interacting with a single-mode cavity field. Considering the Rotating wave approximation (RWA) and the resonance condition, we give the effective Hamiltonian of the system involving cavity decay. The dynamical evolution is studied in terms of the entanglements in the different bipartite partitions of the system, as quantified by the square concurrence. With the choice of the appropriate initial states, a four-qubit W-entangled state can be obtained. We study the effect of cavity decay on various square concurrences in the system, the results show that the peak value of the square concurrence declines with the increase of cavity decay when the other parameters are fixed, but the cavity decay does not change the period of the square concurrence. We also find a natural entanglement transfer and entanglement invariant under evolution of the effective Hamiltonian.