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AIP conference proceedings

Manipulating quantum fields with a single atom in a cavity

S. Haroche

Published Jan 1, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.47571

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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.
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.
We present the experimental realisation of a cavity QED atom interferometer based on two consecutive resonant interactions of a circular Rydberg atom with the field mode of a high Q microwave resonator that is initially prepared in the vacuum state. The interferometer scheme is analogous to the Ramsey method with the classical field replaced by the quantum field stored in the cavity mode. We demonstrate the possibility to use this technique to probe, by dispersive interaction, the field stored in a second mode of the resonator.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
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.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
The coupling of atoms to high Q cavities results in strong modifications of the field and atomic frequencies. These effects are most conveniently analyzed in the ‘‘dressed atom’’ point of view. The vacuum Rabi splitting of the atom‐cavity resonance lines is now being observed in optical and microwave experiments where small samples of atoms resonantly interact with an empty cavity mode. Observation of this effect on a single atom coupled to a cavity vacuum is a realistic goal for experiments. Similar shifts are expected when the cavity mode is weakly excited. The detection of these shifts appears very promising for Quantum nondemolition measurements of very small photon numbers. We propose an experiment in which a microwave field stored in a high Q cavity is continuously monitored with the help of a non‐resonant beam of slow circular Rydberg atoms and we discuss possible applications of this method.