Alkaline-earth-metal atoms have a long-lived electronic excited state, and when atoms in this excited state are localized in the Fermi sea of ground-state atoms by an external potential, they serve as magnetic impurities, due to the spin-exchange interaction between the excited- and the ground-state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiments, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this paper we calculate the confinement-induced resonance (CIR) for the spin-exchanging interaction between the ground and the excited states of the alkaline-earth-metal atoms and propose that the spin-exchange interaction can be strongly enhanced by utilizing the CIR. We analyze this system by the renormalization-group approach and show that near a CIR, the Kondo temperature can be significantly enhanced.
The Kondo effect describes the spin-exchange interaction between localized impurities and 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 exchange interaction between clock state and ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiments, for which we have proposed to use transverse confinement to confine atoms into a one-dimensional tube and to use the confinement-induced resonance to enhance 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 can also act as an additional control knob to reach the confinement-induced resonance. We show that, in the presence of 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.
Motivated by recent theoretical and experimental advances in quantum simulations using alkaline earth (AE) atoms, we put forward a proposal to detect the Kondo physics in a cold atomic system. It has been demonstrated that the intrinsic spin-exchange interaction in AE atoms can be significantly enhanced near a confinement-induced resonance (CIR), which facilitates the simulation of Kondo physics. Since the Kondo effect appears only for antiferromagnetic coupling, we find that the conductivity of such system exhibits an asymmetry across a resonance of spin-exchange interaction. The asymmetric conductivity can serve as the smoking gun evidence for Kondo physics in the cold atom context. When an extra magnetic field ramps up, the spin-exchange process near Fermi surface is suppressed by Zee-man energy and the conductivity becomes more and more symmetric. Our results can be verified in the current experimental setup.
A recent experiment has observed Feshbach resonances between alkali and alkaline-earth-metal atoms. These Feshbach resonances are insensitive to the nuclear spin of alkaline-earth-metal atoms. Utilizing this feature, we propose to take this system as a candidate to perform quantum simulation of the Kondo effect. An alkali-metal atom can form a molecule with an alkaline-earth-metal atom with different nuclear spins, which plays the role of spin-exchange scattering responsible for the Kondo effect. Furthermore, we point out that the existence of three-body bound state and atom-molecule resonance due to the Efimov effect can enhance this spin-exchange scattering and therefore enhance the Kondo effect. We discuss this mechanism first with a three-body problem in free space and then demonstrate that the same mechanism still holds when the alkali-metal atom is localized by an external trap and becomes an impurity embedded in the alkaline-earth-metal atomic gases.
A nuclear-spin-exchange interaction exists between two ultracold fermionic alkali-earth-metal-like atoms in the electronic
1S0 state (
g state) and
3P0 state (
e state) and is an essential ingredient for the quantum simulation of the Kondo effect. We study the control of this spin-exchange interaction for two atoms simultaneously confined in a quasi-one-dimensional (quasi-1D) tube, where the
g atom is freely moving in the axial direction while the
e atom is further localized by an additional axial trap and behaves as a quasi-0D impurity. In this system, the two atoms experience effective 1D spin-exchange interactions in both even and odd partial-wave channels, whose intensities can be controlled by the characteristic lengths of the confinements via confinement-induced resonances (CIRs). In a previous work, we studied this problem with a simplified pure 1D model [Y. Cheng et al., Phys. Rev. A 96, 063605 (2017)]. In the present work, we go beyond that pure 1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths ${a}_{\ensuremath{\perp}}$ and
az, respectively, and exactly solve the quasi-1D--quasi-0D scattering problem between these two atoms. Using the solutions, we derive the effective 1D spin-exchange interaction and investigate the locations and widths of the even-odd wave CIRs for our system. It is found that when the ratio ${a}_{z}/{a}_{\ensuremath{\perp}}$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and a recent experiment by L. Riegger et al. [Phys. Rev. Lett. 120, 143601 (2018)] shows that the two experimentally observed resonance branches of the spin-exchange effect are due to an even-wave CIR and an odd-wave CIR, respectively. Our results are advantageous for the control and description of either the effective spin-exchange interaction or other types of interactions between ultracold atoms in quasi-(1+0)-dimensional systems.
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.