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Physical Review A

Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser

Martin Wilkens, Pierre Meystre

Published Apr 1, 1991• 105 citations
Publisher

Abstract

We propose a measurement scheme to detect the multiphoton coherences inherent in the macroscopic quantum superpositions that can be generated in a superconducting micromaser cavity. The scheme is a nonlinear version of a single-atom homodyne detector. It is shown that the ionization probability of a single test atom is given in terms of the Wigner characteristic function of the field.

DOI
10.1103/physreva.43.3832

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We propose a measurement scheme to detect the multiphoton coherences inherent in the macroscopic quantum superpositions that can be generated in a superconducting micromaser cavity. The scheme is a nonlinear version of a single-atom homodyne detector. It is shown that the ionization probability of a single test atom is given in terms of the Wigner characteristic function of the field.
Part I. We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given. Part II. We evaluate a nonlinear atomic homodyne detection scheme for measuring the Wigner characteristic function of a microwave cavity field. We find numerically that the semiclassical approximation, on which this scheme is based, does not give results consistent with a full quantum calculation. We analyze the back-action of the measurements on steady-state 'macroscopic superpositions' that can be generated in high-Q microwave cavities. We show that the measurements required for a full characterization of the state destroys the macroscopic superposition such that it cannot be reconstructed by using the scheme that was used to generate it in the first place.
We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector atom that is simultaneously coupled to the resonator via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the ground state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the back-action effect of this destructive measurement on the state of the resonator.
We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector atom that is simultaneously coupled to the resonator via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the ground state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the back-action effect of this destructive measurement on the state of the resonator.
We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, ``probe,'' atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed.
We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector-atom that is simultaneously coupled to the cantilever via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the excited state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the backaction effect of this destructive measurement on the state of the cantilever.
Homodyne detection is a typical continuous-variable measurement scheme, ubiquitously used in quantum optics and quantum information. A conventional homodyne detector performs a projective measurement onto a quadrature of the electromagnetic field mode, thus yielding a continuously distributed measurement outcome. The outcome distribution is the marginal of the Wigner function of the state. Homodyne detection also forms the basis of heterodyne, or “dual homodyne” detection, which corresponds to measuring the Q function of the state.