Coupled Classical and Quantum Oscillators
Abstract
Some of the most enduring questions in physicsincluding the quantum measurement problem and the quantization of gravityinvolve 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 timedependent quantum squeezing which can be extreme.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 DOI:
 10.48550/arXiv.quantph/0403184
 arXiv:
 arXiv:quantph/0403184
 Bibcode:
 2004quant.ph..3184M
 Keywords:

 Quantum Physics
 EPrint:
 25 pages, no figures