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arXiv:quant-ph/0603191 · Physical Review A

Entanglement and decoherence of N atoms and a mesoscopic field in a cavity

Tristan Meunier, Arnaud Le Diffon, Clément Ruef, Pascal Degiovanni, J. M. Raimond

Published Sep 6, 2006• 24 citations
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Abstract

We investigate the behavior of $N$ atoms resonantly coupled to a single electromagnetic field mode sustained by a high quality cavity, containing a mesoscopic coherent field. We show with a simple effective Hamiltonian model that the strong coupling between the cavity and the atoms produces an atom-field entangled state, involving $N+1$ nearly coherent components slowly rotating at different paces in the phase plane. The periodic overlap of these components results in a complex collapse and revival pattern for the Rabi oscillation. We study the influence of decoherence due to the finite cavity quality factor. We propose a simple analytical model, based on the Monte Carlo approach to relaxation. We compare its predictions with exact calculations and show that these interesting effects could realistically be observed on a two or three atoms sample in a 15 photon field with circular Rydberg atoms and superconducting cavities.

DOI
10.1103/physreva.74.033802

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We investigate the behavior of NNN atoms resonantly coupled to a single electromagnetic field mode sustained by a high quality cavity, containing a mesoscopic coherent field. We show with a simple effective Hamiltonian model that the strong coupling between the cavity and the atoms produces an atom-field entangled state, involving N+1N+1N+1 nearly coherent components slowly rotating at different paces in the phase plane. The periodic overlap of these components results in a complex collapse and revival pattern for the Rabi oscillation. We study the influence of decoherence due to the finite cavity quality factor. We propose a simple analytical model, based on the Monte Carlo approach to relaxation. We compare its predictions with exact calculations and show that these interesting effects could realistically be observed on a two or three atoms sample in a 15 photon field with circular Rydberg atoms and superconducting cavities.
Summary form only given. We have prepared a single-photon entangled state involving two field modes of a high finesse microwave superconducting cavity, and we have probed its coherence after storing it for a variable time in the cavity. We use the resonant interaction between circular Rydberg atoms and the field. This coupling is stronger than any dissipation rate so that the energy exchange between the atoms and the cavity is periodic (Rabi oscillation). A first atom prepares the entangled field state (writer atom) and a second one probes its coherence (reader atom).
Quantum Rabi oscillation in cavity quantum electrodynamics is at the very heart of the interaction of an atomic system with a single electromagnetic field in a resonator. It has proved a powerful tool to entangle the atom with the field in the case of an empty cavity (vacuum Rabi oscillation). On the other side, as soon as the field is macroscopic, its state seems unaffected and one observes the well-known phenomenon of classical Rabi oscillation which only affects the atomic populations. We propose to experimentally investigate the frontier between those two behaviours, when one has to take into account the fluctations of the photon number. In order to do so, we let interact circular Rydberg atoms with a microwave resonator in which a mesocopic field is injected (a few tens of photons). We observe a strong correlation between specific atomic states and the phase of the injected field, which is measured by a homodyne technique. Those correlations explain in an easy way all the standard features of quantum Rabi oscillations (especially the collapses and revivals). Moreover they allow for the preparation of atom-field entangled state as well as non classical Schroedinger cat like states for the field.
We perform experiments with Rydberg atoms crossing one at a time a superconducting cavity containing a few microwave photons. The coupling between the atoms and the cavity field is either resonant or dispersive. In the resonant case, quantum Rabi oscillations induced by the vacuum or by a small coherent field are observed. These signals reveals in a striking way the quantization of the field. Quantum Rabi oscillations are also used to prepare Fock states of radiation, to transfer information or to produce entanglement between two successive atoms crossing the cavity. Dispersive atom–field coupling is used to prepare and probe coherent superpositions of field states with different phases (Schrödinger's cat states). The progressive decoherence of these states is observed. These experiments constitute fundamental tests of quantum theory and shed light on the transition from quantum to classical in mesoscopic systems.
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.
Experiments on the interaction of a single atom with a single mode of a resonant electromagnetic field in a cavity are reviewed. The atoms used in these experiments were Rydberg atoms with a very large principal quantum number. Another important ingredient is a superconductivity cavity, the quality factor of which is high enough for a periodic energy exchange between atom and cavity field to be observed. The dynamics of the atom-field interaction predicted by theory was measured. Some of the features are explicitly a consequence of the quantum nature of the electromagnetic field: The statistical and discrete nature of the photon field leads to new dynamic characteristics such as collapse and revivals in the Rabi nutation.