Abstract
Abstract The generalization of squeezing is realized in terms of the Virasoro algebra. The higher-order squeezing can be introduced through the higher-order time-dependent potential, in which the standard squeezing operator is generalized to higher-order Virasoro operators. We give a formula that describes the number of particles generated by the higher-order squeezing when a parameter specifying the degree of squeezing is small. Formula (18) shows that the higher the order of squeezing, the larger the number of generated particles.
Highlights
Squeezing has received great attention in various fields such as quantum optics [1], cosmology [2] and quantum information [3].In particular, particle generation is an important issue; in the time-dependent oscillator, the number of produced particles is increased by repeated application of squeezing.it is expected that a generalization of squeezing can increase the number of the generated particles more effectively.Braunstein and McLachlan [5] generalized the parametric amplification by producing k-photon correlation, and numerically showed the structure of phase space
We investigate the generalized squeezing from the viewpoint of the Virasoro algebra
As the beyond squeezing effect, we have proposed the N-th order squeezing based on the Virasoro algebra, in which the N-th order squeezing is induced by the N-th order time-dependent potential
Summary
Squeezing has received great attention in various fields such as quantum optics [1], cosmology [2] and quantum information [3]. The statistics of heterodyne and homodyne detection in cubic and quartic interactions were examined by Braunstein and Caves [6] These studies have shown that the features of higherorder interactions are well reflected in the structure of the phase space. We investigate the generalized squeezing from the viewpoint of the Virasoro algebra. The symmetries of parallel translation and scale transformation make up SL(2, C) as a subalgebra of the Virasoro algebra. Squeezing can be considered as a kind of scale transformation combined with parallel translation to form subalgebra of Virasoro algebra. This is the standpoint from which we construct a theory in this study.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
