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Fortschritte der Physik

Fully Quantized Treatment of Molecular Beam Resonance

David A. Kokorowski, Al-Amin Dhirani, Troy D. Hammond, Bernd Rohwedder, Richard A. Rubenstein, Edward T. Smith, David E. Pritchard

Published Nov 1, 1998• 1 citation
Publisher

Abstract

We present a fully quantal treatment of a beam of two state particles interacting with temporally oscillating potentials. A single oscillatory potential, in resonantly coupling the two internal states, generally entangles each with a different longitudinal momentum. Two successive oscillatory fields, if differentially detuned (DSOF), can couple an initially monochromatic state to a coherent momentum superposition, or alternatively may be used to detect a pre-existing momentum superposition.

DOI
10.1002/(sici)1521-3978(199811)46:6/8<849::aid-prop849>3.0.co;2-e

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We present a fully quantal treatment of a beam of two state particles interacting with temporally oscillating potentials. A single oscillatory potential, in resonantly coupling the two internal states, generally entangles each with a different longitudinal momentum. Two successive oscillatory fields, if differentially detuned (DSOF), can couple an initially monochromatic state to a coherent momentum superposition, or alternatively may be used to detect a pre-existing momentum superposition.
We provide a fully quantal treatment of a beam of two-state particles interacting with temporally oscillating potentials, and propose a number of longitudinal atom optics devices. A single oscillatory potential, in coupling the two internal states, generally entangles each with a different longitudinal momentum. An oscillatory potential can also act as an amplitude modulator, creating momentum coherences within a single internal state. Two successive oscillatory fields (DSOF's), if differentially detuned, can couple an initially monochromatic state to a coherent momentum superposition, or alternatively may be used to detect a pre-existing momentum superposition. DSOF's can create amplitude modulation which, despite the presence of a broad velocity distribution, rephases at a selected distance downstream of the device. Phase modulation generates coherent momentum sidebands which can evolve into amplitude modulation at a particular location downstream.
Coherence in an atom interferometer - longitudinal and transverse, D. Pritchard a fully quantum treatment of molecular beam resonance - creation and detection of longitudinal momentum coherences, R.A. Rubenstein coherence of Bose-condensates in atomic gases, M.R. Andrews neutrino oscillations - a two-level system example, E. Sassaroli coherence and fluctuations in particle-field interactions, B.L. Hu time crystals, Y. Srivastava Greenberger-Horne-Zellinger experiment on mixed states, S. Lloyd Einstein acausality with application to laboratory systems, A. Widom. (Part contents).
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators provide a simple, exactly soluble model for exploring such interaction. Even the ground state of a pair of identical oscillators exhibits effects on the quantum nature of one oscillator, e.g., a diminution of position uncertainty, and an increase in momentum uncertainty and uncertainty product, from their unperturbed values. Interaction between quantum and classical oscillators is simulated by constructing a quantum state with one oscillator initially in its ground state, the other in a coherent or Glauber state. The subsequent wave function for this state is calculated exactly, both for identical and distinct oscillators. The reduced probability distribution for the quantum oscillator, and its position and momentum expectation values and uncertainties, are obtained from this wave function. The oscillator acquires an oscillation amplitude corresponding to a beating between the normal modes of the system; the behavior of the position and momentum uncertainties can become quite complicated. For oscillators with equal unperturbed frequencies, i.e., at resonance, the uncertainties exhibit a time-dependent quantum squeezing which can be extreme.