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Journal of Physics Conference Series

Dynamics in a system of four qubits in two cavities

Duong Hai Trieu

Published Sep 1, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/187/1/012032

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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.
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated. The exact dynamic solutions in the general condition are obtained via Laplace transform. The simple analytical solutions are obtained in several particular cases, which demonstrate the clear and simple physical picture for the quantum state transition of the system. In the large detuning or hoppling case, the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode. In the large coupling case, the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities. In the case of λ ≈ Δ ≫ g , the quantum states transition of qubits is accompanied by the excitation of the cavity, and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.
The problem of the complete transfer of quantum states and entanglement in a four-qubit system composed of two single-mode cavities and two two-level atoms is investigated. The transfer of single and double excitation states is discussed for two different coupling configurations between the qubits. In the first, the coupling is mediated by the atoms that simultaneously couple to the cavity modes. In the second configuration, each atom resides inside one of the cavities and the coupling between the cavities is mediated by the overlapping field modes. A proper choice of basis states makes it possible to identify states that could be completely transferred between themselves. Simple expressions are derived for the conditions for the complete transfer of quantum states and entanglement. These conditions impose severe constraints on the evolution of the system in the form of constants of motion. The constrains on the evolution of the system imply that not all states can evolve in time, and we find that the evolution of the entire system can be confined into that occurring among two states only. Detailed analysis show that in the case where the interaction is mediated by the atoms, only symmetric superposition states can be completely and reversibly transferred between the atoms and the cavity modes. In the case where the interaction is mediated by the overlapping field modes, both symmetric and antisymmetric superposition states can be completely transferred. We also show that the system is capable of generating purely photonic NOON states, but only if the coupling is mediated by the atoms, and demonstrate that the ability to generate the NOON states relies on perfect transfer of an entanglement from the atoms to the cavity modes.
The dynamics of a system composed of two coupled cavities, each containing a single two-level atom, is studied over a wide range of detuning and coupling values. A description of the field in terms of delocalized modes reveals that the detuning between the atoms and these modes is controlled by the coupling between the cavities; this detuning in turn governs the nature of the dynamics. If the atoms are highly detuned from both delocalized field modes, the dynamics become dispersive and an excitation may be transferred from the first atom to the second without populating the field. In the case of resonance between the atoms and one of the delocalized modes, state transfer between the atoms requires intermediate excitation of the field. Thus, the interaction between the two atoms can be controlled by adjusting the coupling between the cavities.
The transferred energy between two (three) radiators localized in two (three) cavities in interaction through an evanescent field is investigated. In the good-cavity limit the exact solution of the Schrödinger equation for this system is obtained. An interesting problem appears when the located excitation in one atom from one distinguished cavity is transferred to a second atom from another cavity. We analyze analytically and numerically the dynamics of the transferred energy as a function of the coupling constant between the cavities. Another interesting problem is the trapping condition for two atoms flying through different coupled cavities. For subsystems consisting of two atomic levels, we know that, only a dynamic trapping condition can be found. In this paper, we show that due to the coupling of the cavities, the trapping condition for two atoms flying through different cavities becomes possible. This effect depends on the coupling constants between the cavities and the dipole interaction between the radiators and cavity modes. A similar problem is studied in the bad-cavity limit, when the lifetime of photons in the cavity is smaller than the decay time of excited atoms. In this case, we write the analytical solution of the master equation and show its entanglement. We obtain that entangled states arise from non-entangled initial states of the atoms. The exact description of such a system opens up new possibilities for the processing of quantum information with two optical cavities.
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.