An Effective Field Theory for Feshbach Resonance in a Two-Body System

Strongly confining an ultracold atomic gas in one direction to create a quasi-two-dimensional system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, is computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a two-dimensional model system, suited for the study of resonant superfluidity and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.Strongly confining an ultracold atomic gas in one direction to create a quasi-two-dimensional system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, is computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a two-dimensional model system, suited for the study of resonant superfluidity and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.

arXiv:cond-mat/0305235Physical Review ANov 3, 200321 citations

Three-Body System with Two-Channel Zero-Range Interaction Model of Feshbach Resonance

Peder K. Sørensen, D. V. Fedorov, A. S. Jensen

Few-Body SystemsDec 2, 20104 citations

Quantum defect theory for the orbital Feshbach resonance

Yanting Cheng, Ren Zhang, Peng Zhang

In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.

arXiv:1607.07513Physical Review AJan 23, 201712 citations

The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length

Ji, C., Daniel R. Phillips, Lucas Platter

We analyze how corrections linear in the effective range, r(0), affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using a perturbative expansion in powers of r(0). In particular, we show that two linear-in-r(0) counterterms are needed for renormalization at this order if scattering-length-dependent observables are considered. We exemplify the implications of this result using various three-body observables. Analytical results for the running of the next-to-leading-order portion of the three-body force in this effective field theory are provided. Expressions which incorporate O(r(0)) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented.We analyze how corrections linear in the effective range, r(0), affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using a perturbative expansion in powers of r(0). In particular, we show that two linear-in-r(0) counterterms are needed for renormalization at this order if scattering-length-dependent observables are considered. We exemplify the implications of this result using various three-body observables. Analytical results for the running of the next-to-leading-order portion of the three-body force in this effective field theory are provided. Expressions which incorporate O(r(0)) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented.

Jan 1, 201247 citations

Effective Field Theory Approach to Two- and Many-Body Forces

R. Machleidt

Bulletin of the American Physical SocietyMay 14, 20050 citations

In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold

^{173}\mathrm{Yb}

atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the

^{173}\mathrm{Yb}

atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.