The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic fields, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads the canonical angular momentum to possess fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes h=2. Furthermore, in the limit of eliminating the magnetic field, the dominate value of the lowest canonical angular momentum changes from h=2 to h=4. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.

Semiunitary transformation is applied to discuss upersymmetrization of cold Rydberg atoms. In the limit of vanishing kinetic energy the lowest angular momentum of the supersymmetric cold Rydberg atom is 3

Recent studies on nonperturbation 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 Letter 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 noncommunicative 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.

In noncommutative spaces to maintain Bose–Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space–space non-commutativity and momentum–momentum non-commutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.

The non-perturbation and perturbation structures of the q-deformed probability currents are studied. According to two ways of realizing the q-deformed Heisenberg algebra by the undeformed operators, the perturbation structures of two q-deformed probability currents are explored in detail. Locally the structures of two perturbation q-deformed probability currents are different, one is explicitly potential dependent; the other is not. But their total contributions to the whole space are the same.