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arXiv:quant-ph/0611138 · Physical Review A

Atomic detection in microwave cavity experiments: A dynamical model

R. Rossi, Maria Carolina Nemes, J. G. Peixoto de Faria

Published Jun 20, 2007• 1 citation
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Abstract

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.

DOI
10.1103/physreva.75.063819

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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.
Starting with early experiments about lifetimes of excited atoms near metallic boundaries, I review the evolution of Cavity Quantum Electrodynamics in the microwave and in the optical domains. The coherent coupling of single atoms with photons in high-Q cavities has led to the demonstration of fundamental quantum effects in light-matter interaction processes and to the generation of micromasers and microlasers emitting radiation with non-classical properties. It has made possible the development of single photon light sources and efficient detectors of single atoms as well as the implementation of quantum information and communication procedures in which atoms and photons play the roles of quantum bits. Mesoscopic superpositions of field states have been generated by entangling single atoms to fields made of many photons and the decoherence of these states has been studied, shedding new light on the quantum to classical boundary. Cavity Quantum Electrodynamics has also led recently to the quantum non-demolition counting of photons in a cavity, opening new perspectives for studying non-classical states of radiation. These atomic physics experiments are now extended - with promising applications in perspective - to the study of solid-state devices with microcavities built on substrates and coupled to artificial atoms such as quantum dots or superconducting junctions.
A common experimental setup in cavity quantum electrodynamics consists of a single two-level atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.
We study the stochastic dynamics of the electromagnetic field in a lossless cavity interacting with a beam of two-level atoms, given that the atomic states are measured after they have crossed the cavity. The atoms first interact at the exit of the cavity with a classical laser field ℰ and then enter into a detector which measures their states. Each measurement disentangles the field and the atoms and changes in a random way the state |ψ(t)〉 of the cavity field. For weak atom-field coupling, the evolution of |ψ(t)〉 when many atoms cross the cavity and the detector is characterized by a succession of quantum jumps occurring at random times, separated by quasi-Hamiltonian evolutions, both of which depend on the laser field ℰ. For ℰ=0, the dynamics is the same as in the Monte Carlo wave function model of Dalibard et al. [Phys. Rev. Lett. 68, 580 (1992)] and Carmichael, An Open System Approach to Quantum Optics, Lecture Notes in Physics Vol. 18 (Springer, Berlin, 1991)]. The density matrix of the quantum field, obtained by averaging the projector |ψ(t)〉〈ψ(t)| over all results of the measurements, is independent of ℰ and follows the master equation of the damped harmonic oscillator at finite temperature. We provide numerical evidence showing that for large ℰ, an arbitrary initial field state |ψ(0)〉 evolves under the monitoring of the atoms and the measurements toward squeezed states |α,re2iφ〉, moving in the α-complex plane but with almost constant squeezing parameters r and φ. The values of r and φ are determined analytically. On the other hand, for ℰ=0, the dynamics transforms the initial state into Fock states |n〉 with fluctuating numbers of photons n, as shown in Kist et al. [J. Opt. B: Quantum Semiclassical Opt. 1, 251 (1999)]. In the last part, we derive the quantum jump dynamics from the linear quantum jump model proposed in Spehner and Bellissard [J. Stat. Phys. 104, 525 (2001)], for arbitrary open quantum systems having a Lindblad-type evolution. A careful derivation of the infinite jump rates limit, where the dynamics can be approximated by a diffusion process of the quantum state, is also presented.
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We propose an experiment for the observation of the quantum Zeno effect (QZE) in a bipartite system. The setup involves two microwave cavities and a ``tunneling'' photon, which is observed by the passage of Rydberg atoms. Our proposal allows for the consideration of two types of measurements, namely, sequential observations of the atomic state and its inclusive measurement. In the present system the two processes are shown to lead to the same result in the ideal case. We consider realistic atom-field interaction times, cavity dissipation, and limited detection efficiency. Analytical expressions for the ``tunneling'' probability are obtained exhibiting a competition between the environment induced exponential decay and the characteristic t2{t}^{2}t2 (for short times) dependence of the QZE. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.
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.