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arXiv:1402.0335 · Journal of the Optical Society of America B

Distributed manipulation of two-qubit entanglement with coupled continuous variables

Li-Tuo Shen, Rongxin Chen, Huai‐Zhi Wu, Zhen‐Biao Yang

Published Jan 16, 2015• 2 citations
arXivHTMLPDF

Abstract

We study the dynamics of two qubits separately sent through two coupled resonators, each initially containing a coherent-state field. We present analytical arguments and numerically approximate solutions for the qubit-field system under different two-qubit initial states, photon-hopping strengths, and detunings. In the far off-resonant regime, the maximal entanglement of two qubits can be generated with the initial qubit state in which one qubit is in the excited state and the other is in the ground state, and the initially maximal two-qubit entanglement can be frozen and fully revived even for large mean photon number. When the qubits are both initially in their excited states or ground states, qubit–qubit entanglement birth and death apparently appear in the regime where the photon-hopping strength is close to qubit-field detuning, and its peaks do not decrease monotonically as the interaction time increases. It is interesting to observe that when there is photon hopping between two fields, the field–field entanglement can be larger than 1 and increases as the initial amplitude of the coherent state grows. Our present setup is fundamental for distributed quantum information processing and applicable to different physical qubit-resonator systems.

DOI
10.1364/josab.32.000297

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We study the dynamics of two qubits separately sent through two coupled resonators, each initially containing a coherent-state field. We present analytical arguments and numerically approximate solutions for the qubit-field system under different two-qubit initial states, photon-hopping strengths, and detunings. In the far off-resonant regime, the maximal entanglement of two qubits can be generated with the initial qubit state in which one qubit is in the excited state and the other is in the ground state, and the initially maximal two-qubit entanglement can be frozen and fully revived even for large mean photon number. When the qubits are both initially in their excited states or ground states, qubit–qubit entanglement birth and death apparently appear in the regime where the photon-hopping strength is close to qubit-field detuning, and its peaks do not decrease monotonically as the interaction time increases. It is interesting to observe that when there is photon hopping between two fields, the field–field entanglement can be larger than 1 and increases as the initial amplitude of the coherent state grows. Our present setup is fundamental for distributed quantum information processing and applicable to different physical qubit-resonator systems.
The dynamical evolution of a quantum system composed of two coupled cavities, each containing a two-level atom and a single-mode thermal field, is investigated under different conditions. The entanglement between the two atoms is controlled by the hopping strength and the detuning between the atomic transition and the cavities. We find that when the atomic transition is far off-resonant with both the eigenmodes of the coupled-cavity system, the maximally entangled state for the two atoms can be generated with the initial state in which one atom is in the ground state and the other is in the excited state. When both the two atoms are initially in the excited state, the entanglement exhibits periodical sudden birth and death. By choosing appropriate parameter values, the initial maximal entanglement of the two atoms can be frozen. The relation between the concurrence and the cooperative parameter is calculated.
How to analytically deal with the general entanglement dynamics of separate Jaynes–Cummings nodes with continuous-variable fields is still an open question, and few analytical approaches can be used to solve their general entanglement dynamics. Entanglement dynamics between two separate Jaynes–Cummings nodes are examined in this article. Both vacuum state and coherent state in the initial fields are considered through the numerical and analytical methods. The gap between two nonidentical qubit-field coupling strengths shifts the revival period and changes the revival amplitude of two-qubit entanglement. For vacuum-state fields, the maximal entanglement is fully revived after a gap-dependence period, within which the entanglement nonsmoothly decreases to zero and partly recovers without exhibiting sudden death phenomenon. For strong coherent-state fields, the two-qubit entanglement decays exponentially as the evolution time increases, exhibiting sudden death phenomenon, and the increasing gap accelerates the revival period and amplitude decay of the entanglement, where the numerical and analytical results have an excellent coincidence.
How to analytically deal with the entanglement and coherence dynamics of separated Jaynes–Cummings nodes with continuous-variable fields is still an open question. We here generalize this model to a more common situation including either a small or large qubit-field detuning, and obtain two new analytical formulas. The X-state simplification, Fock-state shortcut and detuning-limit approximation work together in an amazingly accurate way, which agrees with the numerical results. The new formulas almost perfectly predict the two-qubit entanglement dynamics both in sudden death and rebirth phenomenon for detuning interactions. We find that when both the qubit-field detuning and amplitude of coherent states are large enough, the maximal entanglement and coherence peaks can be fully and periodically retrieved, and their revival periods both increase linearly with the increasing detuning.
Abstract The intrinsic decoherence effects on a flux qubit coupled to a resonator through a two-photon interaction where the resonator field is initially in coherent and even coherent states are investigated. The qubit-resonator entanglement and coherence loss (mixedness) of the system and its subsystems are examined using entropy and negativity. The ability of the qubit-resonator interaction to generate quantum coherence (qubit-resonator entanglement and mixedness) is shown to be dependent on the initial cavity non-classicality, detuning, and decoherence. For larger values of the qubit-resonator detuning, the initial resonator non-classicality can enhance the generation and stability of quantum coherence. The decoherence degrades the qubit-resonator entanglement and destroys the sudden death-birth entanglement.
In this paper, we primarily investigate the generation of quantum entanglement triggered by a single photon between two qubits or multiple qubits and analyze the impact of decoherence of the light field. In the model of single-photon interaction with two qubits, we first study the effect of the initial excited-state weight of the qubits on the entanglement triggered by a single photon. We find that the greater the initial excited-state weight, the smaller the maximum quantum entanglement triggered by the single photon between the two qubits. Specifically, when both qubits are in the excited state, a single photon cannot trigger quantum entanglement between the two qubits. We then examine the impact of the initial coherence of the two qubits on the entanglement triggered by a single photon, and find that a single photon can trigger the maximum quantum entanglement between two qubits when both qubits initially have maximum coherence. In the model of single-photon interaction with multiple qubits, in the limit of a large number of qubits, we find that when the initial excited-state weight of each qubit is larger than the ground-state weight, or when all qubits are initially in the ground state, a single photon cannot trigger quantum entanglement between any two qubits in the multiqubit system. Interestingly, we find that a single photon can trigger quantum entanglement between any two qubits from at least 2000 qubits. Moreover, in this limit, the maximum quantum entanglement between any two qubits in the multiqubit system triggered by a single photon changes with the initial-state parameters and almost no longer depends on the number of qubits. Finally, we discuss the effect of decoherence of the light field, and we find that a higher decoherence strength of the light field weakens the generation of quantum entanglement between qubits in both the single-photon interaction with two qubits and the single-photon interaction with multiple qubits models. However, interestingly, the initial coherence of the qubits can resist the impact of decoherence, especially when the two nonidentical qubits, both having maximum coherence, can maintain the maximum quantum entanglement between the two qubits at 0.5 even as the decoherence strength of the light field increases.
We study the dynamics of a closed system of four qubits in two coupled cavities. Each cavity contains two qubits which interact with it's quantum field and photons which may hop between the cavities. The state of the system is first expressed in delocalized modes and then is expressed in the system of local bases. Exact general solutions are obtained for one-excitation state with arbitrary initial condition. We consider in detail two cases of large and small hopping at resonance. In the case of resonance and large hopping the state of the first qubit may also be transferred to the second qubit in the same cavity without excitation of the field. Such transfer of states minimizes decoherence due to photon loss.