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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Experiments with single atoms in a cabity: entanglement, Schrödinger's cats and decoherence

S. Haroche, M. Brune, J. M. Raimond

Published Dec 15, 1997• 44 citations
Publisher

Abstract

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.

DOI
10.1098/rsta.1997.0133

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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.
Experiments involving Rydberg atoms crossing one at a time a superconducting cavity lead to new tests of quantum theory, such as the generation of entangled pairs of atoms of the Einstein-Podolsky-Rosen type, the preparation of mesoscopic superpositions of field states in the cavity ("Schrödinger cats") and the observation of the progressive decoherence of these states. These experiments illustrate basic aspects of the quantum-classical boundary and demonstrate steps of quantum logic operations essential for quantum information processing.
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.
In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.
The dynamics of quantum decoherence have been experimentally studied for the first time. A single circular Rydberg atom prepares in a high-quality superconducting cavity a ‚Schrödinger cat‘ state of the radiation field. This highly non-classical state is a quantum superposition of two coherent components with different classical phases. A second atom probes the cavity state after a tunable delay. The decay of the quantum correlations between the two atoms reveals the evolution of the initial quantum superposition into a mere statistical mixture. The time scale of this process decreases when the separation beween the two components increases. A simple theoretical model of the experiment is presented. The excellent agreement with the experimental signals confirms in a striking way the decoherence approach.
Various experiments on entangled atomcavity states in cavity QED will be presented. Rydberg atoms can be coupled to a superconducting cavity either resonantly by emitting and absorbing photons, or nonresonantly, by producing a macroscopic phase shift on a coherent field injected in the cavity (single atom dispersive index effect). By sending atoms one at a time across the cavity, it is possible to use these resonant and dispersive effects to entangle atoms with each other or with the cavity field.
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.