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Progress of Theoretical and Experimental Physics

Entanglement of a cavity field interacting with a superconducting charge qubit

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

Published Aug 1, 2013• 3 citations
Publisher

Abstract

The system of a superconducting charge qubit interacting with a field in the case of lifting the restriction of the degeneracy point (⁠|$n_{g}=\frac {1}{2}$|⁠) 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

DOI
10.1093/ptep/ptt056

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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
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.
We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.
We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.
The dynamics of entanglement of two superconducting charge qubit system interacting with a squeezed coherent state were examined by means of linear entropy. The influence of the relative phase of the two qubits' levels and squeezing parameter on the time evolution of linear entropy was discussed. The results showed that the linear entropy almost tends to zero at half the revival time when the two qubits were initially in the maximally entangled state. It was also showed that a greater number of oscillations of the linear entropy were observed with the increasing of squeezing parameter and the sustainment time of the maximum entropy was increased. There was no change in the maximum value of the linear entropy. Moreover,the relative phase of the two qubits' levels decreased the degree of entanglement between the two qubits and the field.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.