Enhancing Kondo coupling in alkaline-earth-metal atomic gases with confinement-induced resonances in mixed dimensions

Abstract

The Kondo effect describes the spin-exchanging interaction between localized impurity and the itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchanging interaction between the clock state and the ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiment, for which we have proposed using a transverse confinement to confine atoms into a one-dimensional tube and to utilize the confinement-induced resonance to enhance the Kondo coupling. In this work, we further consider the 1 + 0 dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock state atoms not only plays a role for localizing them, but also can act as an additional control knob to reach the confinement-induced resonance. We show that by combining both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system. I. MOTIVATION AND BACKGROUNDIn the past decades, experiments in cold atom systems have successfully explored many intriguing quantum many-body phenomena of different paradigms, including fermion pairing and the BCS-BEC crossover, the Bose and the Fermi Hubbard models [1], the KosterlizeThouless transition [1], one-dimensional integrable models [2], spin-orbit coupling [3] and topological models [4]. Exploring these phenomena with cold atom systems have a list of advantages, for instance, one can access physical quantities that have not been measured before in their condensed matter realizations, and one can also study non-equilibrium dynamics in a highly controllable way. However, until now there is still one important category that has not been experimentally realized with cold atom systems yet, despite of quite a few existing proposals [5][6][7][8][9][10][11][12][13][14], and that is the Kondo physics.The Kondo model describes the spin-exchanging interaction between localized impurities and the itinerant fermions [15]. The alkaline-earth atomic gases have natural advantages for performing quantum simulation of the Kondo model. The schematic energy level of single alkaline-earth atoms is shown in Fig. 1. First of all, there is a long-lived electronic excited state known as the clock state, usually denoted by |e . Atoms in this clock state generically has a different ac polarization comparing to atoms in their electronic ground state, usually denoted by |g , except for lasers with a magic wavelength [16,17]. Therefore, it is easy to realize a situation that lasers cre- * Electronic address: rine.zhang@gmail.com † Electronic address: pengzhang@ruc.edu.cn |e, "i |e, #i |g, #i |g, "i ate a deep lattice for |e -atoms and make them localized as impurities, while |g -atoms experience a quite shallow lattice and remain itinerant, as shown in...

Controlling the interaction of ultracold alkaline-earth atoms

“…3(b), experimentally this situation is realized by the Munich group and a resonant enhanced spin-exchanging scattering amplitude has been observed [45]. Theoretically, this problem can be treated with different degrees of approximations [43,44,[55][56][57], and quantitative results can be systematically improved [56]. The most accurate results are shown in Fig.…”

Confinement-induced resonance with weak background interaction

“…It is clearly shown that in each case multiple CIRs can appear for either a s > 0 or a s < 0. As pointed out in our previous work, that is due to the coupling between the relative and center-of-mass of the two atoms in the z-direction [12,20,21,34,35].…”

“…For instance, this CIR can occur at zero magnetic field (B = 0), for which different atomic hyperfine states are degenerate, and thus the inelastic scattering processes between hyperfine spin channels are energetically permitted [14,15]. Using this CIR one can control these processes and then realize systems with strong inter-atomic spin-spin interaction, e.g., the spinexchange interaction, which are important for the quantum simulation of the Kondo effect or other magnetic effects [16][17][18][19][20][21][22][23]. Notice that these spin-spin interactions cannot be controlled via an usual MFR because the inelastic scattering processes are energetically suppressed by the Zeeman-energy gap between different hyperfine channels, which is induced by the magnetic field applied to induce the MFR [24].…”

Tight-binding Kondo model and spin-exchange collision rate of alkaline-earth-metal atoms in a mixed-dimensional optical lattice

“…The parameters t, u It is easy to prove that when there is only one gatom, the Hamiltonians H (2,12).…”

“…Our results show that this effect is very significant, and the quasi-momentum of the g-atoms in this experiment may be already in the second Brillouin zone of the optical lattice. * renzhang@xjtu.edu.cn † pengzhang@ruc.edu.cn Furthermore, with the help of confinement-induced resonance (CIR) [12][13][14], one can control the spin-exchange interaction by tuning the trapping potentials [1][2][3][4]. This technique has already been realized in the recent experiment of ultracold 173 Yb atoms [4].In our previous works [1-3] we studied the control of spin-exchange interaction for alkaline-earth-(like) atoms in a mixed-dimensional system via the CIRs.…”