Narrow Results

In lattice Schrödinger picture, the wave functionals of the squeezed vacuum states of a free real scalar field in de Sitter space are constructed explicitly in momentum space by using the method of instantaneous Hamiltonian diagonalization. The modified power spectrum and particle production in the general mixed, squeezed initial states are also presented. For the massless minimally coupled scalar field which is relevant to slow roll inflationary models, we recover the power spectrum of scalar fluctuations for the squeezed vacuum states, and show that the evolution of the squeezed vacuum states exhibits an attractor behavior. The case of a massless conformally coupled scalar field is also discussed.

Time evolution of quantum fluctuations is investigated for an over-damped mesoscopic circuit with the help of the quantum characteristic function. It is found that, for an initial squeezed state, the quantum fluctuations of charge and current evolve with time by hyperbolic functions, and relate not only with the circuit parameters, but also the squeezing parameter. It is also found that with other conditions invariant to reducing the quantum fluctuations of charge and current, we should reduce the squeezing amplitude parameter. The research will be helpful in miniaturizing integrated circuits and electric components. It will also be significant for the further study of quantum information.

The Wigner distribution function (WDF) for the time-dependent quadratic Hamiltonian system is investigated in the squeezed Schrödinger cat states with the use of Lewis–Riesenfeld theory of invariants. The nonclassical aspects of the system produced by superposition of two distinct squeezed states are analyzed with emphasis on their application into special systems beyond simple harmonic oscillator. An application of our development to the measurement of quantum state by reconstructing the WDF via Autler–Townes spectroscopy is addressed. In addition, we considered particular models such as Cadirola–Kanai oscillator, frequency stable damped harmonic oscillator, and harmonic oscillator with time-variable frequency as practical applications with the object of promoting the understanding of nonclassical effects associated with the WDF.

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

We study particle production of coherently oscillating inflaton in semiclassical theory of gravity by representing inflaton in coherent and squeezed state formalisms. A comparative study of the inflaton in classical gravity with coherent state inflaton in semiclassical gravity is also presented.

In the preceding paper (arXiv: 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.

We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.