A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled-channel calculations. Using $R$ -matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled-channel calculations. Using $R$-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.

arXiv:cond-mat/0601542Physical Review AApr 12, 200639 citations

A Quantum Model of Feshbach Resonances

Raffaele Carlone, M. Correggi, D. Finco +1 more

arXiv:1901.08282Annales Henri PoincaréJun 4, 20193 citations

Shifts and widths of p-wave confinement induced resonances in atomic waveguides

Shahpoor Saeidian, Vladimir S. Melezhik, Peter Schmelcher

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 $^{40}$ 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 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.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 $^{40}$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 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.

arXiv:1503.02469Mar 9, 20151 citation

Shifts and widths of p -wave confinement induced resonances in atomic waveguides

Shahpoor Saeidian, Vladimir S. Melezhik, Peter Schmelcher

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.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.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 26, 20159 citations

R

-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.

^{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 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.