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arXiv:2312.07247

Unlocking Novel Quantum States: Virasoro-Bogoliubov Transformations in Two Modes

So Katagiri

Published Dec 12, 2023• 0 citations
arXivHTMLPDF

Abstract

This paper explores the Bogoliubov transformation's extension to two-mode squeezed states, building on our previous work with Virasoro-squeezing. We establish the Virasoro-Bogoliubov transformation as a non-linear extension of the traditional Bogoliubov transformation, creating non-linear two-mode squeezed states. This research unveils novel quantum states with the potential for innovative insights in various fields of quantum physics.

DOI
10.48550/arxiv.2312.07247

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This paper explores the Bogoliubov transformation's extension to two-mode squeezed states, building on our previous work with Virasoro-squeezing. We establish the Virasoro-Bogoliubov transformation as a non-linear extension of the traditional Bogoliubov transformation, creating non-linear two-mode squeezed states. This research unveils novel quantum states with the potential for innovative insights in various fields of quantum physics.
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We present analytical results for the multiphoton squeezed states defined through nonlinear quadrature-dependent Bogoliubov transformations. These analytical results turn a nonlinear problem into an essentially linear one and they can be utilized to express explicitly the mean walues and deviations of the quadrature operators and the photon variables under the multiphoton states in terms of those quantities averaged over the standard squeezed states which only involves the quadrature-independent Bogoliubov transformation.
We present analytical results for the multiphoton squeezed states defined through nonlinear quadrature-dependent Bogoliubov transformations. These analytical results turn a nonlinear problem into an essentially linear one and they can be utilized to express explicitly the mean values and deviations of the quadrature operators and the photon variables under the multiphoton states in terms of those quantities averaged over the standard squeezed states which only involves the quadrature-independent Bogoliubov transformation.
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