Coherent state quantization and phase operator

Pedro Lenin García de León, Jean‐Pierre Gazeau

M. C. Ashworth

Duan Lu-ming, Guo Guang-Can

By introducing a series of mathematical symbols and phase quantization condition, we give a new approach to the phase operator, which is defined directly in the conventionally-used infinite-dimensional state spaces. Properties of the phase operator and its expressions in some widely-used representations are given. As an example, phase properties of coherent states are analyzed based on this definition.

Mark A. Hennings, T B Smith, Daniel A. Dubin

In a previous paper, we considered Weyl quantization of functions of the angle in phase space, in particular a phase operator Delta ( phi ) and the quantized exponentials Delta (e +or-1 phi ). In this paper we consider the first and second moments of these operators with respect to the harmonic oscillator Hermite states h n and the coherent states Phi alpha . Taking asymptotic limits we find, for example, that var[ Delta ( phi ); h n ]= pi 2 /3+O(log n/n) (n to infinity ) for the variance of Delta ( phi ) in the Hermite states. For the second moment of the phase operator in ||[ Delta ( phi )- theta ] Phi alpha || 2 =O(1/| alpha |) as | alpha | tends to infinity, amongst other results.

S. Twareque Ali

Sándor Varró

A new solution is proposed to the longstanding 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 phase operator' are SU(1,1) coherent states associated to the Holstein–Primakoff realization. In terms of these eigenstates the diagonal representation of phase densities and a generalized spectral resolution of the regular phase operator are derived, which are very well suited to our intuitive pictures of classical phase-related quantities.