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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Minimum-uncertainty coherent states for certain time-dependent systems

John R. Ray

Published Jun 15, 1982• 38 citations
Publisher

Abstract

Nieto and Simmons have defined and studied coherent states for arbitrary potentials $V(q)$. We show how to extend their results to certain time-dependent potentials $V(q,t)$. For each $V(q)$ there is a $V(q,t)$, for which we can construct time-dependent coherent states.

DOI
10.1103/physrevd.25.3417

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Nieto and Simmons have defined and studied coherent states for arbitrary potentials V(q)V(q)V(q). We show how to extend their results to certain time-dependent potentials V(q,t)V(q,t)V(q,t). For each V(q)V(q)V(q) there is a V(q,t)V(q,t)V(q,t), for which we can construct time-dependent coherent states.
This chapter presents some basic aspects of coherent and squeezed states. Certain superpositions of energy Eigen functions of linear harmonic oscillators are called coherent states because they are of significance in optics for the representation of coherent light waves. The chapter obtains the Heisenberg uncertainty relation for the harmonic oscillator states and shows that it is a minimum for ground state. It defines coherent states and shows that they are the minimum uncertainty product states. Coherent states were constructed for many interesting potentials including infinite well and Poschl-Teller potentials and Morse potential. A particular quantum state of a spin system which most closely resembles a classical spin is termed as a spin coherent state. Use of squeezed states in quantum cryptography, quantum distribution of keys, extended coherence time, quantum engineering, teleportation, optics, detection of gravitational waves, quantum metrology and laser interferometers have been analyzed.