Abstract In a previous paper [Phys. Rev. A 95, 060 701(R) (2017)], we demonstrated that a new type of two-body interaction, which depends on the center of mass (CoM) momentum, can be realized for ultracold atoms via laser-modulated magnetic Feshbach resonance (MFR). Further studies (e.g. L He et al, Phys. Rev. Lett. 120, 045 302 (2018)) show that various interesting phenomena, such as Fulde–Ferrell superfluids, can be induced by scattering between ultracold atoms with this interaction. In this work we investigate the shallow bound states of two ultracold atoms with this type of interaction. We show that when the magnetic field B is below the MFR point B 0, two shallow bound states can appear in this system. Namely, a ‘two-component dimer’ or a dimer with pseudo-spin 1/2 can be formed by two atoms. Furthermore, the dispersion curve of the dimer may have either single or double minimums in the CoM momentum space. The latter case can be explained as a result from significant pseudo-spin-orbital coupling (SOC) effects. Our results show that the ultracold gases with CoM momentum dependent interaction may be a candidate for quantum simulations with ultracold two-component molecules, especially the molecule gases with SOC.
In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], it has been shown that center-of-mass-momentum-dependent two-body interactions can be generated and tuned by Raman coupling the closed-channel bound states in a magnetic Feshbach resonance. Here we investigate the universal relations in a three-dimensional Fermi gas near such a laser modulated
s-wave Feshbach resonance. Using the operator-product expansion approach, we find that to fully describe the high-momentum tail of the density distribution up to ${q}^{\ensuremath{-}6}$ (
q is the relative momentum), four center-of-mass-momentum-dependent parameters are required, which we identify as contacts. These contacts appear in various universal relations connecting microscopic and thermodynamic properties. One contact is related to the variation of energy with respect to the inverse scattering length and determines the leading ${q}^{\ensuremath{-}4}$ tail of the high-momentum distribution. Another vector contact appears in the subleading ${q}^{\ensuremath{-}5}$ tail, which is related to the velocity of closed-channel molecules. The other two contacts emerge in the ${q}^{\ensuremath{-}6}$ tail and are respectively related to the variation of energy with respect to the range parameter and to the kinetic energy of closed-channel molecules. Particularly, we find that the ${q}^{\ensuremath{-}5}$ tail and part of the ${q}^{\ensuremath{-}6}$ tail of the momentum distribution show anisotropic features. We derive the universal relations and, as a concrete example, estimate the contacts for the zero-temperature superfluid ground state of the system using a mean-field approach.
Ultracold gases of fermionic alkaline-earth(-like) atoms are hopeful candidates for the quantum simulation of many-body physics induced by magnetic impurities (e.g., the Kondo physics), because there are spin-exchange interactions (SEIs) between two atoms in the electronic ground (
1S0) and metastable (
3P) state, respectively. Nevertheless, this SEI cannot be tuned via magnetic Feshbach resonance. In this paper, we propose three methods to control the SEI between one atom in the
1S0 state and another atom in the
3P2 states or $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ dressed states, with one or two laser beams. These methods are based on the spin-dependent ac-Stark shifts of the
3P2 states or the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling. We show that due to the structure of alkaline-earth (like) atoms, the heating effects induced by the laser beams of our methods are very weak. For instance, for ultracold Yb atoms, ac-Stark-shift difference of variant spin states of the
3P2(F=3/2) level, or the strength of the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling, could be of the order of $(2\ensuremath{\pi})\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, while the heating rate (photon scattering rate) is only of the order of Hz. As a result, the Feshbach resonances, with which one can efficiently control the SEI by changing the laser intensity, may be induced by the laser beams with a low-enough heating rate, even if the scattering lengths of the bare interatomic interaction are so small that they are comparable with the length scale associated with the van der Waals interaction.
A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these inelastic confinement-induced resonances are of interest since they can lead to coherent molecule formation, losses, and heating in ultracold atomic gases. A perturbative model is introduced to describe the resonance positions and the coupling strengths. The validity of the model and the behavior of the resonances for different confinement geometries are analyzed in comparison with exact numerical ab initio calculations. While such resonances have so far only been detected for large positive values of the
s-wave scattering length, it is found that they are present also for negative
s-wave scattering lengths, i.e., for attractive interactions. The possibility to coherently tune the resonances by a variation of the external confinement geometry might pave the way for coherent molecule association where magnetic Feshbach resonances are inaccessible.
Most of the current theories on the
p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low-energy
p-wave scattering amplitude
f1(k) is given by ${f}_{1}(k)=\ensuremath{-}1/[\mathit{ik}+1/(\mathcal{V}{k}^{2})+1/\mathcal{R}]$. Here
k is the incident momentum,
V and
R are the
k-independent scattering volume and effective range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the
p-wave scattering amplitude of the two atoms is not described by the effective-range theory [J. Math. Phys. 4, 54 (1963); Phys. Rev. A 58, 4222 (1998)]. In this paper we provide an explicit calculation for the
p-wave scattering of two ultracold atoms near the
p-wave magnetic Feshbach resonance. We show that in this case the low-energy
p-wave scattering amplitude ${f}_{1}(k)=\ensuremath{-}1/[\mathit{ik}+1/({\mathcal{V}}^{\mathrm{eff}}{k}^{2})+1/({\mathcal{S}}^{\mathrm{eff}}k)+1/{\mathcal{R}}^{\mathrm{eff}}]$ where
Veff, Seff, and
Reff are
k-dependent parameters. Based on this result, we identify sufficient conditions for the effective-range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the
p-wave scattering in the ultracold gases of
6Li and
40K when the scattering volume is enhanced by the resonance.