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Physical Review A

Theoretical analysis of a recent experiment on mesoscopic state superpositions in cavity QED

F. Abbate, ANTONINO MESSINA, Anna Napoli, Francesco Petruccione

Published Jul 11, 2005• 1 citation
Publisher

Abstract

Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative superoperators.

DOI
10.1103/physreva.72.013808

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Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative superoperators.
We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.
Cavity quantum electrodynamics (cavity QED) describes the interactions of single atoms and single photons in a resonator. In the laboratory, state-of-the-art experiments are able to observe the dynamics of these simple yet fundamental quantum systems. The recent development of quantum information science has also introduced a new role for cavity QED systems as quantum interfaces, in which information can be coherently mapped between photonic and atomic quantum bits. Groundbreaking optical cavity QED experiments in the past twenty years would not have been possible without the technological development of mirror coatings with extremely low scatter and absorption losses. Thermal noise has typically played a smaller role in cavity QED experiments but in certain instances is nevertheless important to consider. In this chapter, we begin with an overview of optical cavity QED experiments and some of the central questions that they address. It is hoped that this description, while by no means exhaustive, will provide a window for the nonspecialist into basic techniques and motivations in the field. We then turn to focus on the roles played by scattering and absorption loss and mechanical loss. We discuss how these losses have set limits on feasible experiments and the extent to which improvements may be possible. Experimental realizations of cavity QED systems An idealized cavity QED system consists of one atom placed between two highly reflective mirrors (Figure 17.1). In this model, a single atomic transition interacts with photons in a single cavity mode; the atom is often pictured at an antinode of the cavity standing wave, where it has a maximal dipole interaction with the cavity field.
A model is presented to describe the recently proposed experiment [J. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett 79, 1964 (1997)] in which a mesoscopic superposition of radiation states is prepared in a high-Q cavity that is coupled to a similar resonator. The dynamical coherence loss of such a state in the absence of dissipation is reversible and can be observed in principle. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that the phenomenon can still be observed provided the ratio between the damping constant and the intercavities coupling does not exceed about a few percent. This observation is favored for superpositions of states with a large overlap.
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 Ma\^{\i}tre [X. Ma\^{\i}tre et al., Phys. Rev. Lett. 79, 769 (1997)] and we obtain excellent agreement with the experimental results.
Using resonant interaction between atoms and the field in a high-quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasiprobability distributions and demonstrate the nonclassicality of the superposition in terms of the zeros of the QQQ function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by [Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.