J. G. Peixoto de Faria

Entanglement versus energy in the entanglement transfer problem

We study the relation between energy and entanglement in an entanglement transfer problem. We first analyze the general setup of two entangled qubits (a and b) exchanging this entanglement with two other independent qubits (A and B). Qubit a (b) interacts with qubit A (B) via a spin exchange-like unitary evolution. A physical realization of this scenario could be the problem of two-level atoms transferring entanglement to resonant cavities via independent Jaynes-Cummings interactions. We study the dynamics of entanglement and energy for the second pair of qubits (tracing out the originally entangled ones) and show that these quantities are closely related. For example, the allowed quantum states occupy a restricted area in a phase diagram entanglement vs. energy. Moreover the curve which bounds this area is exactly the one followed if both interactions are equal and the entire four qubit system is isolated. We also consider the case when the target pair of qubits is subjected to losses and can spontaneously decay.

Experimental proposal for measuring the Gouy phase of matter waves

The Schr?dinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment that allows for direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed, and shown to be completely under control within present-day technology. We also discuss how this finding can open the possibility of using the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.

Atomic focusing by quantum fields: Entanglement properties

Abstract The coherent manipulation of the atomic matter waves is of great interest both in science and technology. In order to study how an atom optic device alters the coherence of an atomic beam, we consider the quantum lens proposed by Averbukh et al. [1] to show the discrete nature of the electromagnetic field. We extend the analysis of this quantum lens to the study of another essentially quantum property present in the focusing process, i.e., the atom–field entanglement, and show how the initial atomic coherence and purity are affected by the entanglement. The dynamics of this process is obtained in closed form. We calculate the beam quality factor and the trace of the square of the reduced density matrix as a function of the average photon number in order to analyze the coherence and purity of the atomic beam during the focusing process.

Gouy phase and matter waves

We propose an experiment involving atoms and a standing electromagnetic wave in a cavity as a possibility to determine the analogous of Gouys phase in optics for matter waves. The advantages and short comings of the proposed experiment are analyzed indicating its feasibility at the edge of present day technology.

Geometry in the Entanglement Dynamics of the Double Jaynes-Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ0〉 = cos α | 10〉 + sin α | 01〉 and | ϕ0〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram Cij × Cik × Cil, where Cmn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram Cij × Ckl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.

Continuous monitoring of dynamical systems and master equations

Abstract We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes, only one of them interacting with external degrees of freedom, represented, in the first case, by a finite number of harmonic oscillators, and, in the second, by a sequence of atoms where each one interacts with a single mode during a limited time. Two distinct regimes appear, one of them corresponding to a Zeno-like behavior in the limit of large dissipation.

Quantifying the decay of quantum properties in single-mode states

The dissipative dynamics of Gaussian squeezed states (GSS) and coherent superposition states (CSS) are analytically obtained and compared. Time scales for sustaining different quantum properties such as squeezing, negativity of the Wigner function or photon number distribution are calculated. Some of these characteristic times also depend on initial conditions. For example, in the particular case of squeezing, we find that while the squeezing of CSS is only visible for small enough values of the field intensity, in GSS it is independent of this quantity, which may be experimentally advantageous. The asymptotic dynamics however is quite similar as revealed by the time evolution of the fidelity between states of the two classes.

Quantum erasure in the presence of a thermal bath: The effects of system–environment microscopic correlations

Abstract We investigate the role of the environment in a quantum erasure setup in the cavity quantum electrodynamics domain. Two slightly different schemes are analyzed. We show that the effects of the environment vary when a scheme is exchanged for another. This can be used to estimate the macroscopic parameters related to the system–environment microscopic correlations.

Atomic detection in microwave cavity experiments: A dynamical model

We construct a model for the atomic detection in the context of cavity quantum electrodynamics (QED) used to study coherence properties of superpositions of states of an electromagnetic mode. Analytic expressions for the atomic ionization are obtained, considering the imperfections of the measurement process due to the probabilistic nature of the interactions between the ionization field and the atoms. We provide for a dynamical content for the available expressions for the counting rates considering limited efficiency of detectors. Moreover, we include false countings. The influence of these imperfections on the information about the state of the cavity mode is obtained. In order to test the adequacy of our approach, we investigate a recent experiment reported by Maitre [X. Maitre et al., Phys. Rev. Lett. 79, 769 (1997)] and we obtain excellent agreement with the experimental results.