Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System

Abstract

As an aid to understanding the {\it displacement operator} definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the {\it ladder-operator or minimum-uncertainty} definitions of squeezed states are equivalent to an extent displacement-operator definition. We exemplify this in a setting where there are operators satisfying $[A,A^{†}]=1$, but the $A$'s are not necessarily the Fock space $a$'s; the multiboson system. It has been previously observed that the ground state of a system often can be shown to to be a coherent state. We demonstrate why this must be so. We close with a discussion of an alternative, effective definition of displacement-operator squeezed states.

Two sections added and new title. LaTeX, 18 pages. Accepted by Forschritte der Physik

References in corpus (5)

• Squeezed States for General Systems
• ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES
• Analytic Description of the Motion of a Trapped Ion in an Even or Odd Squeezed State
• Functional Forms for the Squeeze and the Time-Displacement Operators
• Rydberg Wave Packets are Squeezed States

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