Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

Abstract

A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the oscillator, a regular phase operator is constructed in the Hilbert-Fock space as a strongly convergent power series. It is shown that the eigenstates of the new 'exponential operators are SU(1,1) coherent states in the Holstein-Primakoff realization. In terms of these eigenstates, the diagonal representation of phase densities and a generalized spectal resolution of the regular phase operator are derived, which suit very well to our intuitive pictures on classical phase-related quantities

arXiv comment34 pages, 3 Figures

References in corpus (14)

• f-Oscillators and Nonlinear Coherent States
• Quantization of the canonically conjugate pair angle and orbital angular momentum
• Quantum Phase and Quantum Phase Operators: Some Physics and Some History
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Are Number and Phase Complementary Observables?
• Photon states associated with Holstein-Primakoff realization of SU(1,1) Lie algebra
• Number operator-annihilation operator uncertainty as an alternative of the number-phase uncertainty relation
• Entangled Photon-Electron States and the Number-Phase Minimum Uncertainty States of the Photon Field
• The canonical phase measurement is pure
• A New Look at the Quantum Mechanics of the Harmonic Oscillator
• Entangled States and Entropy Remnants of a Photon-Electron System
• Einstein's fluctuation formula. A historical overview
• On the structure of covariant phase observables
• Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

Cited by in corpus (5)

• The Pegg-Barnett phase operator and the discrete Fourier transform
• Regular phase operator and SU(1,1) coherent states of the harmonic oscillator
• Nuclear and Quark Matter at High Temperature
• Coherent phase states in the coordinate and Wigner representations
• Coherent and incoherent superposition of transition matrix elements of the squeezing operator