Spectra and generalized eigenfunctions of the one- and two-mode squeezing operators in quantum optics
Bengt Nagel
Abstract
The spectra and generalized eigenfunctions of the hyperbolic and parabolic generators of the standard representation of SU(1,1) in the one-mode boson Hilbert space are derived. The eigenfunctions are given in three different forms, corresponding to the coordinate, photon number, and Fock-Bargmann representations of the state vectors. The possible spectra of general second degree Hamiltonians are determined. Some corresponding results in the two-mode case are also given. - In the Appendix we prove completeness and orthonormality relations for the polynomials giving the number representation expansion coefficients of the generalized eigenfunctions of the hyperbolic generator (= squeezing generator). These polynomials are special cases of Pollaczek polynomials.
Create a lesson
Related papers
Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups
Junyang Liu, Hang Wang, Houjin Wang et al.
An example of universal braiding in Links--Gould topological quantum computation
Matthew Harper, Ben-Michael Kohli
Reasoning about Shared-Qubit Concurrency in Quantum Computing
Mingsheng Ying
Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems
Newshaw Bahreyni, Paul M. Alsing
Initialization-controlled fault sensitivity and force-balance plateaus in noisy variational quantum optimization
Longhui Shen, Fangzhou Jin, Bin Guo
Quantum identity authentication protocol via perturbed probability amplitudes
Xiangqun Fu, Zheng Han, Hongwei Li et al.