[Paper Review] Optical Control of Exchange Interaction and Kondo Temperature in cold Atom Gas

Igor Kuzmenko, Tanya Kuzmenko+1 more|arXiv (Cornell University)|Jan 1, 2018

Cold Atom Physics and Bose-Einstein Condensates4 references3 citations

TL;DR

This paper demonstrates optical control of the exchange interaction and Kondo temperature in a cold-atom system using 173Yb atoms, where laser intensity tunes the sign and strength of the exchange coupling between itinerant 1S0 and localized 3P0 atoms. As light intensity increases, the interaction switches from ferromagnetic to antiferromagnetic, enabling the Kondo effect with a sharp rise in Kondo temperature near a singlet Feshbach resonance, confirmed by analytical and numerical calculations of scattering lengths and T_K.

ABSTRACT

The relevance of magnetic impurity problems in cold atom systems depends crucially on the nature of exchange interaction between itinerant fermionic atoms and a localized impurity atom. In particular, Kondo physics occurs only if the exchange interaction is anti-ferromagnetic, and strong enough to yield high enough Kondo temperature ($T_K/T_F \ge 0.1$). Focusing, as an example, on the experimentally accessible system of ultra-cold $^{173}$Yb atoms, it is shown that the sign and strength of an exchange interaction between an itinerant Yb($^{1}$S$_{0}$) atom and a trapped Yb($^{3}$P$_{0}$) atom can be optically controlled. Explicitly, as the light intensity increases (from zero), the exchange interaction changes from ferromagnetic to anti-ferromagnetic. When the light intensity is just below a singlet Feshbach resonance, the singlet scattering length $a_S$ is large and negative, and the Kondo temperature increases sharply.

Motivation & Objective

• To enable optical tuning of the exchange interaction in quantum impurity systems using ultracold 173Yb atoms.
• To identify conditions under which the exchange interaction becomes antiferromagnetic, a prerequisite for the Kondo effect.
• To calculate and analyze the dependence of the Kondo temperature T_K on laser intensity via scattering length control.
• To correct a prior error in the literature regarding the existence of antiferromagnetic exchange in the absence of laser fields.
• To establish a feasible platform for studying Kondo physics and related exotic phenomena in cold-atom systems using optical control.

Proposed method

• The system uses 173Yb atoms in the 1S0 (itinerant) and 3P0 (localized) states, with both having spin F=5/2, enabling SU(6) symmetric Kondo physics.
• Laser beams induce a state-dependent optical potential that traps 3P0 atoms, while the 1S0 atoms form a degenerate Fermi gas in a shallow square well.
• The exchange interaction is derived from the scattering matrix using the effective Hamiltonian formalism, with couplings expressed in terms of singlet (a_S) and triplet (a_T) scattering lengths.
• The sign and magnitude of the exchange interaction are controlled by tuning the laser intensity, which modifies the potential depth V_0 and thus a_S and a_T via the optical Feshbach resonance mechanism.
• The Kondo temperature T_K is calculated using the standard Kondo model: T_K = D_0 exp(-1/(6 g_exch ρ(ε_F))), with D_0 = 2ħΩ_e / k_B and ρ(ε_F) the density of states at the Fermi energy.
• Numerical results are obtained by computing a_S(V_0) and a_T(V_0) from the coupled-channel Schrödinger equation, and T_K is evaluated in regions where a_T > a_S.

Experimental results

Research questions

• RQ1 Can the sign of the exchange interaction between itinerant and localized fermionic atoms in a cold-atom system be optically tuned?
• RQ2 How does the Kondo temperature T_K depend on the laser intensity in a system with tunable scattering lengths?
• RQ3 At what laser intensity does the exchange interaction transition from ferromagnetic to antiferromagnetic, enabling the Kondo effect?
• RQ4 What is the quantitative behavior of the Kondo temperature near an optical Feshbach resonance, particularly as the singlet scattering length approaches -∞?
• RQ5 Does the optical control mechanism allow for a robust and experimentally feasible route to realize SU(6) symmetric Kondo physics in ultracold 173Yb gases?

Key findings

• The exchange interaction between 1S0 and 3P0 173Yb atoms switches from ferromagnetic to antiferromagnetic as the laser intensity (proportional to V_0) increases from zero.
• The transition occurs when the singlet scattering length a_S becomes less than the triplet scattering length a_T, which occurs near a singlet Feshbach resonance.
• The Kondo temperature T_K increases sharply as the system approaches the Feshbach resonance, where a_S → -∞, due to the divergence in the effective exchange coupling.
• For ε_F / k_B = 100 nK, T_K reaches values significantly above the threshold T_K / T_F ≥ 0.1 required for observable Kondo physics, confirming the feasibility of the effect.
• The critical potential V_c separates the regime where the Kondo effect is absent (a_S > a_T, red region in Fig. 3) from the regime where it is present (a_S < a_T, blue region).
• The study corrects a prior claim in Ref. [IK-TK-YA-GBJ-PRB-16] that antiferromagnetic exchange exists without laser fields, showing instead that such exchange is only induced by optical control.