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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Transfer of quantum states in a four-qubit system

Smail B. Bougouffa, Z. Ficek

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The complete transfer of quantum states and entanglement mediated by either atoms or the overlapping cavity field modes in a four-qubit system composed of two single-mode cavities and two two-level atoms is discussed.
DOI
10.1364/cqo.2013.m6.53

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There have recently been interests in transferring entanglement between two quantum systems in different Hilbert spaces. In particular, the study of entanglement transfer from a continuous-variable to a qubit system has a primary importance due to practical implications. A continuous-variable system easily propagates entanglement while a qubit system is easy to manipulate. We investigate conditions to entangle two two-level atoms for a broad-band two-mode squeezed field driving the cavities where the atoms are.
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 problem of a controlled transfer of an entanglement initially encoded into two two-level atoms that are successively sent through two single-mode cavities is investigated. The atoms and the cavity modes form a four-qubit system and we demonstrate the conditions under which the initial entanglement encoded into the atoms can be completely transferred to other pairs of qubits. We find that in the case of non-zero detuning between the atomic transition frequencies and the cavity mode frequencies, no complete transfer of the initial entanglement is possible to any of the other pairs of qubits. In the case of exact resonance and equal coupling strengths of the atoms to the cavity modes, an initial maximally entangled state of the atoms can be completely transferred to the cavity modes. Complete transfer of the entanglement is restricted to the cavity modes, with transfer to the other pairs being limited to 50%. We find that complete transfer of an initial entanglement to other pairs of qubits may take place if the initial state is not the maximally entangled state and the atoms couple to the cavity modes with unequal strengths. Depending on the ratio between the coupling strengths, optimal entanglement can be created between the atoms and one of the cavity modes.
We examine the time evolution of entanglement between two qubits of a system of four qubits. The system is composed of two separate cavities each containing a single two-level atom. The qubits of the system are the two atoms and the two cavity modes. We show that during the transfer of an initial entanglement from atoms to the cavity modes, an additional entanglement is induced between the atoms and the cavity modes. Thus, during the evolution, the system effectively behaves as a six qubit system. In addition, we study the entanglement evolution for an imperfect matching of the atoms to the cavity modes. We show that the imperfect matching can force a stable entangled state to evolve in time and may produce a continuous entanglement in time.