Definition Of Coherent States Research Articles

Parastatistics and Uniquantization

A connection between the scheme of unitary quantization (uniquantization) and para-Fermi statistics of order 2 is considered. An appropriate generalization of the Green’s ansatz is suggested based on incorporation of the additional operator Ω which allows one to transform into the identity the bilinear and trilinear commutation relations of unitary quantization for the creation and annihilation operators of two different para-Fermi fields φа and φb. The way of incorporating para-Grassmann variables ξk into the general scheme of unitary quantization necessary for the definition of coherent states is suggested. For parastatistics of order 2, the new fact of existence of two alternative definitions of the coherent state for the para-Fermi oscillators is established.

Ladder operators and coherent states for continuous spectra

The notion of ladder operators is introduced for systems with continuous spectra. We identify two different kinds of annihilation operators allowing the definition of coherent states as modified ‘eigenvectors’ of these operators. Axioms of Gazeau–Klauder are maintained throughout the construction.

QUANTUM 1/f NOISE AND QUANTUM 1/f PHASE NOISE RELATED TO THE UNCERTAINTY RELATIONS

Quantum 1/f noise is the manifestation of the coherent and conventional quantum 1/f effects (Q1/fE). The conventional Q1/fE is a fundamental quantum fluctuation of physical cross sections σ and process rates Γ, caused by the bremsstrahlung (recoil) energy and momentum losses of charged particles, when they are scattered, or accelerated in any way. The closely related coherent Q1/fE is present in any current carried by many particles. It is caused by the energy spread characterizing any coherent state of the electromagnetic field oscillators. According to the Heisenberg's uncertainty principle, because an approximation of the phase or position variable is known, exact knowledge of the energy is precluded. This energy spread results in nonstationary energy values, or fluctuations in the energy of the oscillators. To find the spectral density of these inescapable basic fluctuations, which are known to characterize any quantum state, which is not an energy eigenstate, we use an elementary physical derivation based on Schrödinger's definition of coherent states, which can be supplemented by a rigorous derivation from a well-known quantum-electrodynamical branch-point propagator. The example of a simple harmonic oscillator is also useful for illustrating the uncertainty that arises due to Q 1/f Noise. Clearly illustrating the relation between the uncertainty principle and Q 1/f noise.

The correspondence of two definitions of coherent states in a particular system

Many generalizations of the harmonic oscillator coherent states are known in the literature. One such generalization by Nieto has been applied to a particular system known as the `harmonic oscillator with centripetal barrier'. In this paper, it is shown that Nieto's generalization in this system may be described in terms of a recent generalization due to Klauder. This is of considerable interest since the approaches to generalizing coherent states differ significantly.

Coherent and squeezed states on physical basis

A definition of coherent states is proposed as the minimum uncertainty states with equal variance in two hermitian non-commuting generators of the Lie algebra of the hamiltonian. That approach classifies the coherent states into distinct classes. The coherent states of a harmonic oscillator, according to the proposed approach, are shown to fall in two classes. One is the familiar class of Glauber states whereas the other is a new class. The coherent states of spin constitute only one class. The squeezed states are similarly defined on the physical basis as the states that give better precision than the coherent states in a process of measurement of a force coupled to the given system. The condition of squeezing based on that criterion is derived for a system of spins.

Coherent states in finite-dimensional Hilbert space and their Wigner representation

We consider two definitions of coherent states in a finite-dimensional Hilbert space based on (i) truncation of the usual coherent state expansion and (ii) generalization of the displacement operator acting on vacuum. The number-phase Wigner function is computed for such states. Analytical results and numerically computed graphs are presented. Special attention is paid to two-level states and to their Stokes parameter representations.

Multimode Coherent States

We define multimode (entangled) coherent states as properly chosen linear superpositions of suitable composition states. Our definition is equivalent to the definition of coherent states as eigenvectors of a corresponding generalized annihilation operator. In certain limit cases we discuss the statistical properties of the states defined.

Comments of the definitions of coherent states for the SUSY harmonic oscillator

We insist on the possibility of regarding coherent states for the supersymmetric harmonic oscillator equivalently in three different ways, just as in the usual bosonic case.

Uncertainty measures and uncertainty relations for angle observables

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {o} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed.