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arXiv:0901.4832 · Physical Review Letters

Angular Momentum of Supersymmetric Cold Rydberg Atoms

Jian-zu Zhang A B

Published Jul 1, 1996• 28 citations
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Abstract

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 $3\ensuremath{\Elzxh}/2$. A possible experimental verification is suggested.

DOI
10.1103/physrevlett.77.44

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Superpartner systems and semiunitary transformations in supersymmetric quantum mechanics

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Physical Review A•Dec 1, 1996•1 citation
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 3\ensuremath\Elzxh/23\ensuremath{\Elzxh}/23\ensuremath\Elzxh/2. A possible experimental verification is suggested.
The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic di-pole 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 variant Planck's over h/2. Furthermore, in the limit of eliminating the magnetic field, the dominate value of the lowest canonical angular momentum changes from variant Planck's over h/2 to variant Planck's over h/4. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.
The angular momentum spectrum of an atomic dipole in constant electric and magnetic fields is calculated. The arrangement of the fields are such that the motion of the dipole is planar and rotationally symmetric, with the result that the R\"ontgen term of the Lagrangian takes on the appearance of a Chern-Simons interaction. On eliminating the kinetic energy term of the Lagrangian, the angular momentum spectrum changes from one consisting of integers to one consisting of positive half integers. The possibility of physically achieving such an elimination is discussed in the context of cold Rydberg atoms.
Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. Optical excitation on the discrete Rydberg resonances reveals long-lasting electron emission from the Rydberg gas ( >20 ms). Our observations are explained by lm-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities.
In this dissertation I investigate cold Rydberg atoms and molecules in which the angular-momentum character of the quantum states involved strongly influences their properties and dynamics. In the first part I focus on long-range diatomic Rydberg molecules formed by a rubidium D-state Rydberg atom and a second rubidium atom in its ground state. Spectroscopic measurements of molecular binding energies are presented showing the effect of the Rydberg atom size and fine-structure coupling on the molecular potentials. A theoretical model is introduced that takes into account all relevant angular-momentum couplings between the molecular constituents, successfully reproducing experimental observations. Calculations of adiabatic potentials and binding energies, molecular-state lifetimes, electric and magnetic dipole moments are also presented. In the second part, I describe the production and magnetic trapping of cold circular Rydberg atoms. The circular Rydberg atoms are generated out of a cold gas of rubidium using the crossed-fields method and magnetically trapped. The trapping force is employed to induce center-of-mass oscillations of the trapped atom sample. Trap parameters and observed oscillation frequencies are used to measure the magnetic moments of the circular Rydberg atoms. Trap losses and the atomic internal-state evolution in the 300 Kelvin thermal background are also investigated.
It is shown that in supersymmetric quantum mechanics the superpartner Hamiltonian H+{\mathit{H}}_{+}H+​ is related to the Hamiltonian ${\mathit{H}}_{\mathrm{\ensuremath{-}}}$ by a semiunitary transformation. The properties of the semiunitary transformation are discussed. \textcopyright{} 1996 The American Physical Society.