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Journal of the Optical Society of America B

On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity

Seyedeh Robabeh Miry, Mohammad Kazem Tavassoly, R. Roknizadeh

Published Jan 13, 2014• 9 citations
Publisher

Abstract

The proposed schemes in this paper involve the interaction of a two-level atom with single- or two-mode quantized cavity fields (for different purposes) in the presence of a classical field. Indeed, following the path of Solano et al. in [Phys. Rev. Lett.90, 027903 (2003)], the behavior of the entire atom-field system may be described by the Jaynes–Cummings (JC)- and anti-Jaynes–Cummings (anti-JC)-like models. It is illustrated that, under specific conditions, the effective Hamiltonian of the system can be switched from a JC- to an anti-JC-like model. During the process, the two-level atom in the cavity is alternately affected by the above two effective interactions. Ultimately, after the occurrence of the desired interactions in appropriate setups, the cavity field will arrive at a specific superposition of number states, a fixed number state, and in particular, two-mode binomial field states. Moreover, the entanglement property of the two-mode binomial state is investigated by evaluating the entropy criterion. While there exist various proposals for preparation of number states and their superpositions in the literature, our scheme has the advantage that it is independent of the detection of the atomic state after the interaction occurs.

DOI
10.1364/josab.31.000270

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The proposed schemes in this paper involve the interaction of a two-level atom with single- or two-mode quantized cavity fields (for different purposes) in the presence of a classical field. Indeed, following the path of Solano et al. in [Phys. Rev. Lett.90, 027903 (2003)], the behavior of the entire atom-field system may be described by the Jaynes–Cummings (JC)- and anti-Jaynes–Cummings (anti-JC)-like models. It is illustrated that, under specific conditions, the effective Hamiltonian of the system can be switched from a JC- to an anti-JC-like model. During the process, the two-level atom in the cavity is alternately affected by the above two effective interactions. Ultimately, after the occurrence of the desired interactions in appropriate setups, the cavity field will arrive at a specific superposition of number states, a fixed number state, and in particular, two-mode binomial field states. Moreover, the entanglement property of the two-mode binomial state is investigated by evaluating the entropy criterion. While there exist various proposals for preparation of number states and their superpositions in the literature, our scheme has the advantage that it is independent of the detection of the atomic state after the interaction occurs.
Following the approach of Solano et al (2003 Phys. Rev. Lett. 90 027903) we propose a scheme for a generation of a few classes of entangled (nonlinear) coherent states. To achieve this purpose, the interaction of a spatially narrow collection of two-level atoms with a quantized field in a high-Q factor cavity in the presence of a strong-driving classical field is studied. We perform appropriate Hamiltonians describing the atom-field interaction by focusing on two particular forms of intensity-dependent functions which are directly related to su (1, 1) and su (2) Lie algebras. It is shown that the dynamical evolution of the considered systems can generate bipartite, tripartite (nonlinear) and more complicated entangled states corresponding to the mentioned groups depending on the number of atoms in the cavity. In the processes of the abovementioned generation schemes, even and odd nonlinear coherent states are produced. In the end, in a particular circumstance with the two-mode quantized field we can turn easily from Jaynes–Cummings to anti-Jaynes–Cummings interactions which brings us to the maximally entangled number state . Finally, to quantify the degree of entanglement of the produced states, the measures of von Neumann and linear entropies are applied.
We study in detail entanglement properties of the Jaynes-Cummings model assuming a two-level atom (qubit) interacting with the first NNN levels of an electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model, the number operator is the conserved quantity that allows for the exact diagonalization of the Hamiltonian and thus we study states that commute with this conserved quantity and whose structure is preserved under the Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are bound entangled states that satisfy the symmetries imposed by the conservation of the number of excitations when N>3N>3N>3. Furthermore we show that \emph{the Jaynes-Cummings interaction can be used to generate bound-entanglement} between the atom and the mode.
In this paper, we study the evolution of two two-level atoms interacting with a single-mode quantized radiation field, namely, the two-atom multiphoton Jaynes–Cummings model (JCM). We assume that the field and the atoms are initially prepared in the superposition of displaced number states and excited atomic states, respectively. For this system, we investigate the atomic inversion, Wigner function, phase distribution and entanglement. We show that for symmetric (asymmetric) atoms, the system can generate asymmetric (symmetric) cat states at a quarter of the revival time. Furthermore, the degrees of entanglement for the field–atoms and the one-atom–remainder tangles depend on the rate of energy flow between the parties. The interference in phase space decreases the degree of entanglement in the bipartite.
This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes–Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare bases, related by the unitary transformation, becomes particularly simple. It is shown how to generate (the highly non-classical) entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage of the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation, a measurement is required, leaving the field in either of two orthogonal entangled coherent states.
We present a way to engineer an effective anti-Jaynes-Cumming and a Jaynes-Cumming interaction between an atomic system and a single cavity mode and show how to employ it in reservoir engineering processes. To construct the effective Hamiltonian, we analyze the interaction of an atomic system in a $\ensuremath{\Lambda}$ configuration, driven by classical fields, with a single cavity mode. With this interaction, we first show how to generate a decoherence-free displaced squeezed state for the cavity field. In our scheme, an atomic beam works as a reservoir for the radiation field trapped inside the cavity, as employed recently by S. Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)] to generate an Einstein-Podolsky-Rosen entangled radiation state in high-QQQ resonators. In our scheme, all the atoms have to be prepared in the ground state and, as in the cited article, neither atomic detection nor precise interaction times between the atoms and the cavity mode are required. From this same interaction, we can also generate an ideal squeezed reservoir for atomic systems. For this purpose we have to assume, in addition to the engineered atom-field interaction, a strong decay of the cavity field (i.e., the cavity decay must be much stronger than the effective atom-field coupling). With this scheme, some interesting effects in the dynamics of an atom in a squeezed reservoir could be tested.
We present a scheme for transferring quantum state between atom and cavity field in Jaynes–Cummings model (JC) in the aid of spin-echo-like technique. It is based on the facts that the atom in a cavity can induce the generation of modified coherent states (MCSs), which can be shown to be macroscopically distinguishable, and the anti-commutation relation between the Hamiltonian and the z-component Pauli matrix. We show that this scheme is applicable for a class of cavity field states. The application on two-cavity system provides an alternative scheme for preparation of non-local superpositions of quasi-classical light states. Numerical simulation shows that the proposed schemes are efficient.