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Physical Review A

Quantum-nondemolition measurement of atomic momentum

Tycho Sleator, Martin Wilkens

Published Oct 1, 1993• 41 citations
Publisher

Abstract

We present a quantum-nondemolition measurement scheme in which one component of the momentum of an atom traversing a propagating light wave is measured by monitoring a quandrature phase of the field. We show how a selective version of the measurement may be used to reduce the transverse momentum spread of an atomic beam and we suggest how this scheme could be used to transversely cool a beam of atoms in the absence of spontaneous emission.

DOI
10.1103/physreva.48.3286

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We present a quantum-nondemolition measurement scheme in which one component of the momentum of an atom traversing a propagating light wave is measured by monitoring a quandrature phase of the field. We show how a selective version of the measurement may be used to reduce the transverse momentum spread of an atomic beam and we suggest how this scheme could be used to transversely cool a beam of atoms in the absence of spontaneous emission.
In two recent papers,1,2 it was shown how the interaction of a two-level atom with a standing laser field allows for a QND measurement of the atomic position using a quadrature component of the laser field as a meter. Here we demonstrate a complementary scheme in which a quadrature component of a propagating laser wave acts as the meter for a QND measurement of the atomic momentum. The measurement is based on a detectable phase shift of the cavity mode that results from the atom-field interaction. The principal characteristics of the measurement scheme are presented. We demonstrate how a selective version of the measurement scheme may be used to tailor an atomic wave function and to turn the measurement scheme into a "virtual beam handler."
We present a theory for quantum nondemolition (QND) measurements of an atomic ensemble in the presence of spontaneous emission. We derive the master equation that governs the evolution of the ground state of the atoms and the quantum state of light. Solving the master equation exactly without invoking the Holstein-Primakoff approximation and projecting out the quantum state of light, we derive a positive operator-valued measure that describes the QND measurement. We show that, at high spontaneous emission conditions, the QND measurement has a unique dominant state to which the measurement collapses. We additionally investigate the behavior of the QND measurement in the limiting case of strong atom-light interactions, where we show that the positive operator valued measure becomes a projection operator. We further analyze the effect of spontaneous emission noise on atomic state preparation. We find that it limits the width of the eigenvalue spectrum available to a quantum state in a linear superposition. This effect leads to state collapse on the dominant state. We generate various nonclassical states of the atom by tuning the atom-light interaction strength. We find that nonclassical states such as the Schr\"odinger-cat state, whose coherence spans the entire eigenvalue spectrum of the total spin operator Jz{J}_{z}Jz​ for a given spin eigenvalue JJJ, lose their coherence because spontaneous emission limits the accessibility of states farther away from the dominant state.
We consider atoms traversing a cavity filled with an optical field. When the atoms are well detuned from the optical resonance the output momentum distribution of the atoms is found to be a sensitive probe of the photon statistics of the light field. Near resonance spontaneous emission smears the diffractive peaks. We obtain a good fit to the experimental data of Gould et at. (1991). As the atoms pass through the optical field they impart a position-dependent phase shift to the field. By making a quadrature phase measurement on the optical field a position measurement of the atom is achieved. We show that it is possible to prepare the atom in a 'contractive state' which beats the standard quantum limit for position measurements.
We present a detailed analysis of the quantum-nondemolition (QND) properties of a measurement scheme employing coherently driven three-level atoms in the \ensuremath{\Lambda} or cascade configuration inside an optical cavity. We propose to use a strong signal field to empty one of the transitions and dress the signal-transition levels. The atoms become transparent for the signal beam, which sees a ``ghost transition.'' When a probe is applied and tuned to the vicinity of one of the light-shifted levels, the probe phase is extremely sensitive to fluctuations of the signal intensity. This enhances the QND coupling and enables the system to operate at lower cooperativities.