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arXiv:0801.0636 · Physical Review A

Energy levels of two identical fermions in a harmonic trap near a p -wave Feshbach resonance

Sungkit Yip

Published Jul 9, 2008• 16 citations
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Abstract

We investigate theoretically the energy levels of two identical fermions in a harmonic potential trap under a $p$-wave Feshbach resonance. The magnetic fields needed to affect the energy levels differ strongly among the levels, and they can be at values far from the free-space resonant field.

DOI
10.1103/physreva.78.013612

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We investigate theoretically the energy levels of two identical fermions in a harmonic potential trap under a ppp-wave Feshbach resonance. The magnetic fields needed to affect the energy levels differ strongly among the levels, and they can be at values far from the free-space resonant field.
We develop and analyze a theoretical model to study p-wave Feshbach resonances of identical fermions in atomic waveguides by extending the two-channel model of A.D. Lange et. al. [Phys. Rev. A 79, 013622 (2009)] and S. Saeidian et. al. [Phys. Rev. A 86, 062713 (2012)]. The experimentally known parameters of Feshbach resonances in free space are used as input of the model. We calculate the shifts and widths of p-wave magnetic Feshbach resonance of 40^{40}40K atoms emerging in harmonic waveguides as p-wave confinement induced resonance (CIR). Particularly, we show a possibility to control the width and shift of the p-wave confinement induced resonance by the trap frequency and the applied magnetic field which could be used in corresponding experiments. Our analysis also demonstrates the importance of the inclusion of the effective radius in the computational schemes for the description of the p-wave CIRs contrary to the case of s-wave CIRs where the influence of this term is negligible.
Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal l=2l=2l=2 energy spectrum for such a system, with a caveat, is presented in this paper and checked with the spectrum obtained by direct numerical integration of the Schr\"odinger equation. The results reported here extend those of Yip for ppp-wave resonance [S.-K. Yip, Phys. Rev. A 78, 013612 (2008)], while exploring the limitations of a universal expression for the spectrum for the higher partial waves.
Abstract We develop and analyze a theoretical model to study p -wave Feshbach resonances of identical fermions in atomic waveguides by extending the two-channel model of Lange et al (2009 Phys. Rev. A 79 013622 ) and Saeidian et al (2012 Phys. Rev. A 86 062713 ). The experimentally known parameters of Feshbach resonances in free space are used as input of the model. We calculate the shifts and widths of p -wave magnetic Feshbach resonance of 40 K atoms emerging in harmonic waveguides as p -wave confinement induced resonance (CIR). Particularly, we show a possibility to control the width and shift of the p -wave CIR by the trap frequency and the applied magnetic field which could be used in corresponding experiments. Our analysis also demonstrates the importance of the inclusion of the effective range in the computational schemes for the description of the p -wave CIRs contrary to the case of s -wave CIRs where the influence of this term is negligible.
We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in ppp wave and confined in an axially symmetric harmonic trap. To this end we utilize ppp-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a ppp-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the ppp-wave Feshbach resonance.