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arXiv:1111.2358 · Physical Review A

Atom-mediated effective interactions between modes of a bimodal cavity

F. O. Prado, F. S. Luiz, J. M. Villas-Bôas, Augusto M. Alcalde, Eduardo I. Duzzioni, L. Sanz

Published Nov 21, 2011• 14 citations
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Abstract

We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering $N$ independent atoms trapped inside a high-finesse optical cavity.

DOI
10.1103/physreva.84.053839

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We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering NNN independent atoms trapped inside a high-finesse optical cavity.
A new conditional scheme for entangling the two quantized modes of a bimodal high-Q cavity field is presented. We show that, injecting one at time k atoms inside the cavity, it is possible to guide the field toward k-dependent linear combinations of k + 1 bimodal Fock states, each one possessing the same total number of photons. The two simple cases corresponding to the passage of one or two atoms only through the resonator are considered. Their practical feasibility against cavity losses, spontaneous emission and other sources of imprecision of the experimental set-up is discussed. Two examples illustrating the usefulness of and the interest toward the creation of such a local entanglement, are reported. The first one relates the specific features of these bimodal entangled states to the occurrence of a non-classical correlation effect in the dynamics of a two-level atom interacting with the entangled cavity. The second one demonstrates that the peculiar entanglement initially stored in the cavity in accordance with our method, provides an effectively exploitable resource to entangle two spatially separated cavities.
In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even when considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.
We show that it is possible to use an atom–cavity reservoir to prepare the two-mode squeezed and entangled states of a hybrid system of an atomic ensemble and an optical field, which do not directly interact with each other. The essential mechanism is based on the combined effect of a two-mode squeezing interaction and a beam–splitter interaction between the system and the reservoir. The reservoir mechanism is important for quantum networking in that it allows an interface between a localized matter-based memory and an optical carrier of quantum information without direct interaction. (Some figures may appear in colour only in the online journal)
Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.
We propose the methods of generating multipartite entanglement by considering the interaction of a system of N two-level atoms in M cavities of high quality factor with a strong classical driving field. It is shown that, with the cavity detuning, the applied driving field detuning and vacuum Rabi coupling, we can produce an entangled coherent state in two single-mode cavities and generate the entangled coherent cluster states in two bimodal vacuum cavities. Tuning these parameters also allows us to acquire the anti-Jaynes–Cummings (AJC) interaction, with which we can generate the maximally two-photon entangled states, and the two-atom and the two-photon entangled cluster states.
The coherent evolution of the atom–cavity state in bimodal (cavity) experiments has been analysed for a realistic time dependence in detuning the atomic transition frequency. Apart from a 'smooth switch' of the atomic resonance from one to the second mode of a bimodal cavity, we considered also an additional (effective) interaction between the field modes of the cavity, known as a 'communication channel'. Comparison of our model computations has been made especially with the measurements by Rauschenbeutel et al (2001 Phys. Rev. A 64 050301) who demonstrated for the first time the entanglement of the field modes in a bimodal cavity. It is shown that the agreement between the (theoretically) predicted and experimental phase shifts can be improved by allowing a 'communication' between the two field modes during a short but finite switch of the atomic transition frequency from one mode to the other. We therefore suggest that the details of the atom–cavity detuning should be taken into account for the future interpretation of bimodal cavity experiments.