Deformed Two-Photon Squeezed States in Noncommutative Space

Recent studies on non-perturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This paper devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in NC space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator.Comment: 11 pages. Physics Letters B (accepted

Induced fractional zero-point angular momentum for charged particles of the Bohm–Aharonov system by means of a “spectator” magnetic field

AbstractAn induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment

Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes

The possibility of testing spatial noncommutativity in the case of both position-position and momentum-momentum noncommuting via a Chern-Simons' process is explored. A Chern-Simons process can be realized by an interaction of a charged particle in special crossed electric and magnetic fields, in which the Chern-Simons term leads to non-trivial dynamics in the limit of vanishing kinetic energy. Spatial noncommutativity leads to the spectrum of the orbital angular momentum possessing fractional values. Furthermore, in both limits of vanishing kinetic energy and subsequent vanishing magnetic field, the Chern-Simons term leads to this system having non-trivial dynamics again, and the dominant value of the lowest orbital angular momentum being $\hbar/4$, which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.Comment: 18 page