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arXiv:1210.4298 · Physical Review A

Atoms versus photons as carriers of quantum states

Smail B. Bougouffa, Z. Ficek

Published Aug 14, 2013• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.022317

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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.
The temporal evolution of two coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons. The general state of the system is a linear superposition of symmetric and antisymmetric states with the symmetric states controlled by two of the four eigenfrequencies and the antisymmetric states by the other two. The system undergoes Rabi oscillations between the two symmetric (antisymmetric) states. There is state transfer between the cavities when both atoms are in the ground state and two photons are exchanged. In addition, there is also Rabi ``flopping'' whereby one atom is in the excited state and the other in the ground state and the roles are reversed in a periodic fashion by the exchange of two photons. The generation of entanglement can be explicitly given as a function of time. Models of coupled cavities are of interest in distributed quantum information and computation.
We investigate a system composed of NNN coupled cavities and two-level atoms interacting one at a time. Adjusting appropriately the atom-field detuning, and make the hopping rate of photons between neighboring cavities, AAA, greater than the atom-field coupling ggg (i.e. A>>gA>>gA>>g), we can eliminate the interaction of the atom with the nonresonant normal modes reducing the dynamics to the interaction of the atom with only a single-mode. As an application of this interaction, we analyze the transmission of an arbitrary atomic quantum state between distant coupled cavities. In the ideal case, we obtain a flexible and perfect quantum communication. Considering the influence of dissipation an interesting parity effect emerge and we obtain NNN maximum in which it is still possible to achieve a quantum communication more efficient than a purely classical channel between the ends. We also studied important sources of imperfections in procedure execution.
In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength ggg and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of ggg and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.
We analyze the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time-dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behavior which can be mapped onto the single atom Jaynes-Cummings model. Exploring the main features of this system we propose simple and fairly robust methods for entangling atoms independently of the cavity, for quantum state mapping, and for implementing SWAP and controlled-NOT (CNOT) gates with atomic qubits.