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Physical Review Letters

Quantum nondemolition measurement of small photon numbers by Rydberg-atom phase-sensitive detection

M. Brune, S. Haroche, V. Lefèvre-Seguin, J. M. Raimond, Nicim Zagury

Published Aug 20, 1990• 507 citations
Publisher

Abstract

We describe a new quantum nondemolition method to monitor the number N of photons in a microwave cavity. We propose coupling the field to a quasiresonant beam of Rydberg atoms and measuring the resulting phase shift of the atom wave function by the Ramsey separated-oscillatory-fields technique. The detection of a sequence of atoms reduces the field into a Fock state. With realistic Rydberg atom-cavity systems, small-photon-number states down to N=0 could be prepared and continuously monitored.

DOI
10.1103/physrevlett.65.976

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We describe a new quantum nondemolition method to monitor the number N of photons in a microwave cavity. We propose coupling the field to a quasiresonant beam of Rydberg atoms and measuring the resulting phase shift of the atom wave function by the Ramsey separated-oscillatory-fields technique. The detection of a sequence of atoms reduces the field into a Fock state. With realistic Rydberg atom-cavity systems, small-photon-number states down to N=0 could be prepared and continuously monitored.
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.
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.
A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.
We propose a scheme for realizing a quantum nondemolition (QND) measurement of a small number of optical photons. Our scheme has two stages: First, we couple a propagating light pulse with fixed photon number to a trapped cold atomic gas within a cavity, such that the pulse is stored within a collective polariton mode. Second, a small-photon-number measurement is engineered by monitoring the cavity-transmission spectrum. Since the polariton mode profile is preserved during the process of detecting the spectrum, photon-number QND measurements could be achieved by retrieving the light pulse from the polariton mode. We also discuss a method which uses QND measurements to generate small-photon Fock states.