Angular Momentum of Supersymmetric Cold Rydberg Atoms.

Semiunitary transformation is applied to discuss supersymmetrization of cold Rydberg atoms. In the limit of vanishing kinetic energy the lowest angular momentum of the supersymmetric cold Rydberg atom is 3h̄/2. A possible experimental verification is suggested. [S0031-9007(96)00109-3] PACS numbers: 32.80.Rm, 11.30.Pb Recently Baxter [1] showed that cold Rydberg atoms can play an interesting role of realizable analogs of ChernSimons theory [2, 3]. By choosing an atomic dipole of a cold Rydberg atom in electric and magnetic field, and by an appropriate experimental arrangement the motion of the dipole is constrained to be planar and rotationally symmetric, the Rötgen interaction takes on the form of a Chern-Simons term [3]. By placing the dipole in a strong magnetic field and in an appropriate optical trapping field, the elimination of the kinetic energy term in the Lagrangian could be achieved physically and Baxter [1] showed that the canonical angular momentum spectrum changes from one consisting of integers to one consisting of positive half integers; thus in principle an experimental verification of the Chern-Simons feature of fractional angular momentum is allowed. Reference [4] showed evidence for a phenomenological supersymmetry in atomic physics. In SS QM the term supersymmetry has nothing to do with spins at all, its meaning is just as that SS QM is represented by a pair of bosonic Hamiltonians H− and H+ which are superpartners of the SS Hamiltonian Hs = H− +H+, and SS charge Qs, Q † s, and Hs satisfy SS algebra [5]. In SS QM the form of the problem must be truly one dimensional. For the onedimensional system there is no room to define the angular momentum; one cannot discuss the relation of spectra of angular momenta between the system and its superpartner. For the case of two-dimensional Rydberg atoms angular momentum can be defined as an exterior product. This system can be reduced into two uncoupled one-dimensional systems, thus the supersymmetrization of its Hamiltonian and angular momentum can be simultaneously performed by a semiunitary transformation (SUT ) which will be defined later. This for the first time allows in principle a verification of the relation of spectra of angular momentum between a system and its superpartner. The results show that in the limit of vanishing kinetic energy the angular momentum spectrum of the SS cold Rydberg atom changes from one consisting of integers to one consisting of positive half integers, with the lowest angular momentum 3h̄/2; SUT destroys the lowest angular momentum state with h̄/2 of the cold Rydberg atom. Cold Rydberg atom.—The Lagrangian of the cold Rydberg atom with an atomic dipole