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Decoherence of multimode thermal squeezed coherent states

Leehwa Yeh

Published Jan 1, 1992• 2 citations
OpenAlex

Abstract

It is well known that any multimode positive definite quadratic Hamiltonian can be transformed into a Hamiltonian of uncoupled harmonic oscillators. Based on this theorem, the multimode thermal squeezed coherent states are constructed in terms of density operators. Decoherence of multimode thermal squeezed coherent states is investigated via the characteristic function and it is shown that the decohered (reduced) states are still thermal squeezed coherent states in general.

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Journal of Physics A Mathematical and Theoretical•Mar 14, 2013•3 citations
It is well known that any multimode positive definite quadratic Hamiltonian can be transformed into a Hamiltonian of uncoupled harmonic oscillators. Based on this theorem, the multimode thermal squeezed coherent states are constructed in terms of density operators. Decoherence of multimode thermal squeezed coherent states is investigated via the characteristic function and it is shown that the decohered (reduced) states are still thermal squeezed coherent states in general.
The squeezed harmonic oscillator Hamiltonian H = ωa†a + αa2 + α*a†2 is analysed, where a† and a are harmonic oscillator creation and annihilation operators, ω is real, and α is a time independent constant. For the case that ω2 − 4|α|2 > 0 it is known that the Hamiltonian possesses real and positive eigenvalues. The exact eigenstates are constructed by using a Bogoliubov transformation to express them in terms of the algebra and states of the harmonic oscillator. Known properties of these states are reviewed and new results are derived. Modified coherent states are constructed from the exact eigenstates and shown to yield a unit projection operator for the original harmonic oscillator Hilbert space via generalized Gaussian integrals. Transition elements between harmonic oscillator coherent states are then evaluated exactly by using the properties of the modified coherent state projection operator.
By the complex multimode Bogoliubov transformation, we obtain the general forms of squeeze operators and squeezed states including squeezed vacuum states, squeezed coherent states, squeezed Fock states and squeezed coherent Fock states, for a general multimode boson system. We decompose the squeezed operator into disentangling form in normal ordering to simplify the expressions of the squeezed states. We also calculate the statistical properties of the SS. Furthermore we prove that if it is non-degenerate, a Bogoliubov transformation matrix can be decomposed into three basic matrix, by which we can not only check the criterion of the minimum uncertainty state (MUS) found by Milburn, but also prove that except the special cases, any multimode squeezed state is MUS after the original creation and annihilation operators rotate properly. We also discuss some special cases of the three basic matrices. Finally we give an analytical results of a two-mode system as an example.
We introduce the photon-subtracted squeezed coherent state (PSSCS), which is theoretically constructed by repeatedly subtracting photons from the squeezed coherent state (SCS) with squeezing parameter r and displacement amplitude α=|α|eiφ. Employing the normal ordering form of density operator of the SCS, we study the nonclassicality of the PSSCS by analyzing Mandel’s Q-parameter, quadratures squeezing, photon-number distribution (PND), and Wigner function (WF). We find that the PND in a PSSCS is a periodic function of φ with a period π and exhibits more remarkable oscillations than that of a SCS in the case of strong squeezing. The partial negative region of the WF is sensitive to r and |α|. The fidelity between PSSCS and SCS is analyzed, which manifests that larger photon subtraction number may result in lower fidelity. By virtue of the thermal entangled state representation the decoherence of the PSSCS in thermal environment is studied through the time evolution of the WF. The negative volume of the WF gradually diminishes with the increase of evolution time and thermal photon number, respectively. The study of the PSSCS shows that generating new photon-number-controllable nonclassical states from a weak coherent light may be realized by subtracting suitable photons from a SCS.
In this paper, photon-excited squeezed coherent states (PESCS) are studied theoretically by adding a photon to the squeezed coherent states repeatedly. By taking advantage of the normally ordered form of the density operator for PESCS, the analytical expressions of the normalization constant, Mandel Q -parameter, photon-number distribution, quadrature squeezing and Wigner function are derived and discussed in detail, and from these the sub-Poissonian photon statistics, photon-number oscillations, negative value of quadrature squeezing, and partial negativity and non-Gaussian distribution of a Wigner function are demonstrated, respectively. These criteria well exhibit the highly nonclassical properties and non-Gaussianity of PESCS. In addition, by deriving the normally ordered form of the density operator and Wigner function for PESCS in a thermal channel, the decoherence process of PESCS is analyzed both analytically and numerically.