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arXiv:quant-ph/0504223 · Journal of Optics B Quantum and Semiclassical Optics

Perspectives for a mixed two-qubit system with binomial quantum states

Mahmoud Abdel‐Aty

Published Feb 13, 2004• 23 citations
arXivHTMLPDF

Abstract

The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an alternative view of how to think about this problem. We consider mixed states of two qubits and obtain an exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multiphoton transition. We consider the situation for which the field may start from a binomial state. Employing this solution, the significant features of the entanglement when a second qubit is weakly coupled to the field and becomes entangled with the first qubit, is investigated. We also describe the response of the atomic system as it varies between the Rabi oscillations and the collapse–revival mode and investigate the atomic inversion and the Q -function. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multi-photon process is involved. Finally, we obtain illustrative examples of some novel aspects of this system and show how the off-resonant case can sensitize entanglement to the role of initial state setting.

DOI
10.1088/1464-4266/6/4/003

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The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an alternative view of how to think about this problem. We consider mixed states of two qubits and obtain an exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multiphoton transition. We consider the situation for which the field may start from a binomial state. Employing this solution, the significant features of the entanglement when a second qubit is weakly coupled to the field and becomes entangled with the first qubit, is investigated. We also describe the response of the atomic system as it varies between the Rabi oscillations and the collapse–revival mode and investigate the atomic inversion and the Q -function. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multi-photon process is involved. Finally, we obtain illustrative examples of some novel aspects of this system and show how the off-resonant case can sensitize entanglement to the role of initial state setting.
An exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (ions or atoms) within a perfect cavity for the case of multiphoton transition and in the presence of both the Stark shift and phase shift is obtained. Employing this solution, the significant features of the entanglement when a second qubit is allowed to interact with cavity mode and becomes entangled with the first qubit are investigated in the context of the measure defined by negative eigenvalues for the partial transposition of the density operator. The effects of Stark shift, distance between the two qubits, and an instantaneous phase shift experienced by the second qubit on the entanglement and probability amplitudes are indicated. It has been shown that the entanglement as well as the intensity are markedly affected by different parameters when the nonlinear two-photon process is involved. Moreover, the quasiprobability distribution function is investigated before and after the sudden phase shift experienced by the second qubit. We believe that this may throw some light on the question of the entanglement of multi-qubit systems.
Abstract In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.
In this paper, we study the entanglement between two two-level atoms (qubits) when they interact simultaneously with a single-mode thermal field through exchanging k photons. We demonstrate the entanglement of the bipartite by making use of the concurrence. Contrary to previous studies, we deduce an exact form of the wave function of the system for various types of initial atomic states. We show that the asymmetric case (i.e., nonidentical atoms) can generate amounts of entanglement much greater than those of the symmetric one. These amounts are sensitive to the value of the transition parameter k and the type of initial atomic states. We present a novel phenomenon: for a particular type of Bell states, the initial entanglement can be trapped through the evolution of the system. This would be of a great interest in the framework of quantum memory.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.
We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed system, implemented as two two-level atoms interacting with a single-mode cavity field. The dynamical evolutions of the entanglement and entropy are controlled via time-dependent cavity–atom couplings. Our theoretical findings lead us to propose an alternative measure of entanglement, which could be used to develop a much needed correlation measure for more general multi-partite quantum systems.
Our aim is to present an analytical solution for the quantum optics model that has two two-level atoms interacting together and interacting with an intensity-dependent quantized field. The quantized field is initially in binomial state and based on the Lamb–Dicke parameter and associated Laguerre polynomials. While two atoms are symmetric and initially in superposition state. Besides, the quantum entanglement between the quantum system components under the effect of the parameters of detuning, coupling, binomial, Lamb–Dicke and the initial state of the model is discussed. Several phenomena have been clearly observed and analyzed, such as entanglement sudden death (ESD) followed by entanglement sudden birth (ESB) in the concurrence and the negativity curves, and long-lived quantum coherence in the von Neumann entropy curve. In addition, the presence of revivals and collapses in the atomic population inversion curves has been figured out. Our analysis aims to help the scientists to determine the critical values required of quantum system parameters to control entanglement dynamics.