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Journal of Experimental and Theoretical Physics Letters

Field states upon micromaser dispersive quantum nondemolition measurement of the number of photons

A. V. Kozlovskiĭ

Published Dec 1, 2005• 1 citation
Publisher

Abstract

Dispersive quantum nondemolition measurement of the number of photons is analyzed in the micromaser scheme. It has been shown that the stationary Fock state of the field in a cavity that is considered as the result of quantum nondemolition measurement is realized only in a particular case for strictly determined parameters of the system, and small variation in one of the parameters of the system results in a qualitative change in the field state. In the general case, the field state is characterized by large fluctuations of the number of photons and the mean number of photons, which are very sensitive to the parameters of the system. It has been shown that the detection of the Ramsey interference pattern is possible only when the sequence of atoms passing through the cavity is highly monokinetic.

DOI
10.1134/1.2171720

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Dispersive quantum nondemolition measurement of the number of photons is analyzed in the micromaser scheme. It has been shown that the stationary Fock state of the field in a cavity that is considered as the result of quantum nondemolition measurement is realized only in a particular case for strictly determined parameters of the system, and small variation in one of the parameters of the system results in a qualitative change in the field state. In the general case, the field state is characterized by large fluctuations of the number of photons and the mean number of photons, which are very sensitive to the parameters of the system. It has been shown that the detection of the Ramsey interference pattern is possible only when the sequence of atoms passing through the cavity is highly monokinetic.
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.
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.
It is shown that the theoretical analysis of a micromaser experiment with the selective measurement of atomic states is impossible without consideration of the spatial structure of the field and of the statistical spread of the atomic velocities in the cavity. An approximate theory, ignoring the dynamic effects associated with the mentioned factors, yields not only quantitatively, but also qualitatively different theoretical predictions. The dynamics of the field and the mean number of photons in the trapping states realized in this case differ significantly from the predictions of the idealized standard theory used at present. Along with the process of establishment of the stationary Fock state of the field, under certain conditions, it appears possible to form the quasistationary quantum state of the field with large fluctuations of the number of photons, accompanied by the exit of the field from the cavity (“quasi-dissipation”), and the following stepwise transition into the state of the electromagnetic vacuum. It is shown that, under the conditions of the micromaser experiment, the information about the states of atoms, passed through the cavity, in the case considered, does not allow one to draw an unambiguous conclusion about the state of the field in the cavity.
We propose a quantum nondemolition measurement of the photon-number distribution for a two-mode cavity field. In the scheme two sequences of two-level atoms interact dispersively with the respective cavity modes and resonantly with two classical fields, and then are detected continually. The field finally reduces to a two-mode Fock state. The probability of collapsing to a given Fock state is determined by the initial photon-number distribution. The scheme can be easily generalized to a field with N modes.
We describe the optimum detection procedure to follow in order to measure by atomic interferometry the number of photons present in a cavity by using a Quantum nondemolition scheme. The method we discuss is the one recently introduced by Brune et al. [1, 2], in which the field intensity is detected by recording atomic interferences in a Ramsey type set up. A succession of two-level atoms interacts with the cavity field which is the analog of a birefringent retarding plate for the atomic wave function. The information is acquired in the form of binary digits (atoms detected in one level or the other). We discuss an optimal strategy which yields the value of the photon number with a number of atoms of the order of the base 2 logarithm of the field photon number dispersion. The procedure described here is the one we intend to use in an experiment in preparation.