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Communications in Theoretical Physics

Two-component dimers of ultracold atoms with center-of-mass-momentum dependent interactions

Yaru Liu, Shu Sheng Yang, Peng Zhang

Published Feb 26, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1572-9494/ad2d52

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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.
We show that a type of two-body interaction, which depends on the momentum of the center of mass (COM) of these two particles, can be realized in ultracold atom gases with a laser-modulated magnetic Feshbach resonance (MFR). Here the MFR is modulated by two laser beams propagating along different directions, which can induce Raman transition between two-body bound states. The Doppler effect causes the two-atom scattering length to be strongly dependent on the COM momentum of these two atoms. As a result, the effective two-atom interaction is COM-momentum dependent, while the one-atom free Hamiltonian is still the simple kinetic energy p2/(2m){\mathbf{p}}^{2}/(2m)p2/(2m).
In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge fields using cold atoms. In the experiment it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range interatomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, paving the way for future characterizations of topological superfluid states in the experimentally relevant systems.
At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment (M. W. Zwierlein et al, Phys. Rev. Lett. 92, 120403 (2004)). The dimeric gas can be also used to interpret the frequency of the radial breathing mode observed in the experiment by J. Kinast et al (Phys. Rev. Lett. 92, 150402 (2004)).
We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few fermionic impurities are immersed in a noninteracting two-component Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Because of the interplay of SOC and the spin-selective interaction, the molecular state intrinsically acquires a nonzero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular states with different center-of-mass momenta, which corresponds to a first-order transition between FF phases in the thermodynamic limit. As the interaction strength is tuned, a polaron-molecule transition occurs in the highly imbalanced system, where the boundary varies nonmonotonically with SOC parameters and gives rise to the reentrance of polaron states. The rich physics in this system can be probed using existing experimental techniques.
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 sss-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 ${q}^{\ensuremath{-}6}$ (qqq 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.