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International Journal of Modern Physics B

TIME EVOLUTION OF VARIANCES OF QUADRATURE OPERATORS IN A TWO-MODE BOSON SYSTEM

Alexei Vladimirovich Chizhov, R. G. Nazmitdinov

Published Dec 1, 1990• 6 citations
Publisher

Abstract

A two-mode boson system described by a Hamiltonian containing a nonlinear interaction of a general enough form is investigated. Nontrivial effects concerning a transition of a coherent state to a squeezed state and vice versa in the process of evolution of that system are revealed.
DOI
10.1142/s0217979290001091

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We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases are formally equivalent, leading to the same differential equations encoding the full time evolution. These differential equations can be easily employed in any application. We analytically predict a dramatic transition in the population of the modes when the coupling takes a specific critical value, leading to exponential growth of the excitation population. We discuss the validity, scope and generality of our results.
Three identical, interacting with each other nonlinear oscillators are considered. In addition, they are also externally driven by a coherent field of constant amplitude. The possibility of generating two-mode squeezed states is analyzed in this system. The two-mode principal squeeze variance is used to study the properties of the squeezed states of the system. The time evolution of this variance is analyzed, as well as the effect of the strength of the interaction between the oscillators and the damping strength on the generation of squeezed states.
We study the full time evolution of a system of two modes of a bosonic quantum field that interact through quadratic hamiltonians. We specialise to a time dependent two-mode squeezing Hamiltonian where the coupling is switched on and off smoothly. We find the analytical solutions to the time evolution after the interaction is turned off, which apply to arbitrary coupling functions. We investigate the final state of the system and compute all physically relevant quantities, such as average particle number, entanglement and change in energy. Our techniques can be applied to a wide range of scenarios, which include implementations of time dependent two-mode squeezing, coupled harmonic oscillators, harmonic oscillators coupled to light. Furthermore, these techniques can be extended to more complicated time-dependent quadratic Hamiltonians. We briefly discuss possible applications within the area of relativistic and quantum information.
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