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AIP conference proceedings

Measuring and Manipulating Quantum Fields in a Cavity by Atom Interferometry

J. M. Raimond, M. Brune, S. Haroche, Ferdinand Schmidt‐Kaler, L. Davidovich, Nicim Zagury, D. J. Wineland, Carl Wieman, Stuart James Smith

Published Jan 1, 1994• 0 citations
Publisher

Abstract

Long lived circular Rydberg atoms interacting with high finesse superconducting cavities offer unique opportunities to perform tests on fundamental quantum mechanics. “Schrödinger cats”, multiparticle nonlocal correlations, “quantum teleportation” offer striking illustrations of the less intuitive aspects of quantum mechanics. At the heart of these experiments is the dispersive atom‐cavity interaction. We present its experimental manifestations, with the measurement of single photons light shifts and of Lamb shifts due to a single, empty, cavity mode. We then describe some possible extensions of this experiment, some of which being under way in our laboratory.

DOI
10.1063/1.2946012

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Long lived circular Rydberg atoms interacting with high finesse superconducting cavities offer unique opportunities to perform tests on fundamental quantum mechanics. “Schrödinger cats”, multiparticle nonlocal correlations, “quantum teleportation” offer striking illustrations of the less intuitive aspects of quantum mechanics. At the heart of these experiments is the dispersive atom‐cavity interaction. We present its experimental manifestations, with the measurement of single photons light shifts and of Lamb shifts due to a single, empty, cavity mode. We then describe some possible extensions of this experiment, some of which being under way in our laboratory.
Circular Rydberg atoms, detected by the very sensitive and state selective field ionization method, can be used to measure and manipulate quantum fields stored in a cavity. The method is based on an interferometric detection of the dispersive energy shifts experienced by these atoms when they interact with a slightly off‐resonant field mode sustained by a cavity which the atoms cross one at a time. These shifts give rise to a translation of the Ramsey fringe pattern observed in the field ionization signal of the atoms. The method consitutes a non‐destructive way of photon counting. In this experiment, non local correlations between the atom and the cavity field are created, which could be used to perform new types of Einstein‐Podolsky‐Rosen experiments. Non classical fields could also be generated, which would display some of the properties discussed by Schrödinger in his famous ‘‘cat paradox.’’ We present the theory of these experiments which until very recently would have been considered as mere ‘‘gedanken’’ ones and we describe the operation of a Rydberg atom interferometer which has already enabled us to detect subphoton fields and to measure vacuum field effects in a cavity.
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.
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.
A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ``Schr\"odinger cat states.'' Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ``manipulation'' through nonresonant atom-field interactions opens a domain in cavity QED studies.
A single circular Rydberg atom is used to prepare in a high quality superconducting cavity a “Schrödinger cat” state, quantum superposition of two coherent fields 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 field state from an initial quantum superposition into a mere statistical mixture. The time scale of this decay decreases when the separation between the two components increases. This is the first experimental observation of the dynamics of decoherence, lying at the heart of the quantum measurement process.
We review recent experiments in which Rydberg atoms interacting with microwave photons in a superconducting cavity are used to perform quantum information manipulations. We describe quantum phase gates using atoms and photons as "qubits", various engineered entanglement experiments involving up to three particles at a time and ideal non-destructive measurements of single photons. We also analyse an atomic interferometry experiment which illustrates the link between the notions of complementarity and entanglement. We finally recall previous experiments performed with the same set-up, in which we had generated and studied quantum superpositions of coherent fields with different phases, the so called "Schrödinger cat states" of the field. The decoherence of these states was experimentally studied. We conclude by discussing some of the perspectives opened by this line of research.