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International Journal of Quantum Information

Dispersive reservoir influence on the superconducting phase qubit

H. A. Hessian, A.‐B. A. Mohamed, Ali H. Homid

Published Oct 1, 2015• 4 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749915500562

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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 this article, an analytical description is presented based on the master equation. This master equation is formed from the system of superconducting phase qubit which is coupled to a torsional resonator and damped by a dispersive reservoir. An analytical approach for searching of some physical phenomena on the qubit system is presented, such as qubit inversion, purity and negativity. In addition, these phenomena are discussed for the resonance and off-resonance cases for many different initial states. From computational results, it is found that the mentioned phenomena depend on the dispersive reservoir parameter which leads to their death. However, the complete destruction of system coherence in the presence of dispersive reservoir leads to the death of entanglement between the qubit and torsional resonator.
Control of purity and entanglement of two two-qubits dispersively coupled to a field with a reservoir are investigated. Initially the qubits are entangled, while the field is either in a coherent state or a statistical mixture of two coherent states. For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially transposed density matrix. A measure related to the mutual entropy, namely the index of entropy, is employed to measure the entanglement. Its results agree well with the negativity. It is found that the entanglement and purity have strong sensitivity to phase damping. The asymptotic behaviour of the states of the field, the two two-qubits, and the total system fall into mixed states.
In the present manuscript, we consider a quantum system of two super-conducting (SC) qubits that move at relativistic speeds and each qubit coupled to a resonator mode (RM). Here, the relativistic motion of the SC-qubits results from the modulation of the time-varying coupling between the SC-qubits and the resonator for which the system resembles the rotating approximation and anti-Jaynes-Cummings (JC) dynamics. We study the time variation of some interesting current quantumness measures with respect to the time-varying coupling (TVC) considering von Neumann entropy, negativity and Mandel parameter. We illustrate the dynamical behavior of the SC-qubits–RMs entanglement, SC-qubit–SC-qubit entanglement and photon statistics of the RMs at relativistic motion in the absence and presence of dissipative environment.
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.
Taking the intrinsic decoherence effect into account, we investigate the entanglement dynamics of a superconducting charge qubit in a single-mode optical cavity. Concurrence, as the measure of entanglement of the coupled field-junction system, is calculated. In comparison, we also consider the entanglement of the system by using the entanglement parameter based on the ratio between mutual entropy and partial Von-Neumann entropy to investigate how the intrinsic decoherence affects the entanglement of the coupling system. Our results show that the evolution of the entanglement parameter has the behaviour similar to the concurrence and it is thus the well measure of entanglement for the mixed state in such a coupling system.
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.