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International Journal of Quantum Chemistry

Amplitude squared squeezed states in the Fock–Bargmann space

Manuel Martín, L. Sandoval, Juan Francisco Rivas-Silva, Alberto José Palma

Published Jan 1, 1993• 1 citation
Publisher

Abstract

Abstract Squeezed states are normally studied in configuration space or using the Glauber formalism for the coherent states. Here we show that the use of the Fock–Bargmann space can lead to more general solutions, especially in the case of squeezed states associated with the square of field amplitude. The relations that we obtain are completely general and several well‐known, approximate results can be obtained as the limit cases of our approach.© 1993 John Wiley & Sons, Inc.

DOI
10.1002/qua.560460402

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We examine the generalized squeezed states defined as eigenstates of a linear combination of the lowering and raising operators a2{\mathrm{a}}^{2}a2 and (${\mathrm{a}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$)2{)}^{2})2, respectively. This approach is entirely equivalent to the minimum-uncertainty method applied to the amplitude-squared operators. We solve the eigenvalue equation in Glauber's coherent-state representation and find two independent solutions. Their Fock-state expansions, one containing only even and the other only odd number states, reveal a strong nonclassical character. We show that the calculation of the mean photon number is sufficient to obtain the expectation values of interest. Consequently, photon statistics is investigated in both cases by using the generating function of the photon-number distribution. We find the conditions under which the second-order squeezed states display photon antibunching and quadrature squeezing. Also discussed is the preservation of their amplitude-squared squeezing by linear amplification at gains exceeding 2. Analytically, our results are simple formulas in terms of Kummer and Gauss hypergeometric functions that allow straightforward numerical calculations.
General solutions to the eigenvalue equation for amplitude-squared squeezed minimum uncertainty states have been found and investigated. An expression for the average photon number in these states is derived. The Q-function as well as the photocount distribution of these states has been investigated. Plots of Q-functions indicate that the 'manner' of amplitude-squared squeezing is different from that of normal squeezing. It is shown that twofold and fourfold symmetry of Q-function in phase space is related to the suppression of certain terms of the photocount probability for a quantum state. Finally, oscillation of the photocount probability in highly squeezed minimum uncertainty states for amplitude-squared squeezing has been found and interpreted in terms of 'interference in phase space'.
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