Engineering the Kondo impurity problem with alkaline-earth atom arrays

TL;DR

The paper proposes quantum simulation of the Kondo impurity problem using alkaline-earth-like atoms in a state-dependent optical lattice combined with optical tweezers. It derives an atomic two-orbital Hubbard model that reduces to a Kondo-like Hamiltonian with tunable $J$ and $U$, and shows that parasitic spin-independent terms can suppress Kondo screening unless compensated by a local impurity potential; a local tweezer can restore the KE at experimentally accessible temperatures. The authors identify optimal parameter regimes (e.g., $|J| oughly t$, $U\approx 0$) for observing Kondo physics and characterize multiple KE signatures (transport, spin, and thermodynamics) in small arrays, including a set of markers $T_K^{(\rho)}, T_K^{(\chi)}, T_K^{(C)}, T_K^{(S)}$. They further show that impurity tunneling can induce emergent Kondo lattice behavior with heavy-fermion features, and they provide concrete preparation and readout protocols for ${}^{171}$Yb systems, paving the way for exploring unconventional KE regimes and fermion-mediated interactions in cold-atom quantum simulators.

Abstract

We propose quantum simulation experiments of the Kondo impurity problem using cold alkaline-earth(-like) atoms (AEAs) in a combination of optical lattice and optical tweezer potentials. Within an ab initio model for atomic interactions in the optical potentials, we analyze hallmark signatures of the Kondo effect in a variety of observables accessible in cold-atom quantum simulators. We identify additional terms not part of the textbook Kondo problem, mostly ignored in previous works and giving rise to a direct competition between spin and charge correlations - strongly suppressing Kondo physics. We show that the Kondo effect can be restored by locally adjusting the chemical potential on the impurity site, and we identify realistic parameter regimes and preparation protocols suited to current experiments with AEA arrays. Our work paves the way for novel quantum simulations of the Kondo problem and offers new insights into Kondo physics in unconventional regimes.

Figures (7)

• Figure 1: Exploring Kondo physics in AEA arrays. (a) Illustration of the cold-atomic Kondo impurity problem studied in this work. Mobile fermionic atoms in two spin states (blue circles with arrows) hop with amplitude $t$ on a chain with periodic boundary conditions. At the impurity site ($i=0$), a pinned impurity atom serves as localized moment (red circle with arrow). The spin-exchange coupling $J$ with the mobile fermions and the potential $U$ are set by the atomic singlet and triplet interaction strengths $U_{eg}^\pm$ (see main text). (b) Kondo temperature ${T_K^{(\rho)}}$ for variable $J/t$ and $U/|J|$ (colored lines). Termination of lines indicates that the resistivity minimum ceases to exist for the corresponding parameters.
• Figure 2: Emergence of the Kondo effect in a small-scale system. (a) Estimated Kondo temperature scales in comparison with the perturbative exponential behavior (gray line). See main text for the definitions of the different symbols. Inset: Impurity-fermion spin correlations ${\mathcal{C}^{(S)}_{\delta}}$ at $T=0$ for different values of $|J|$ indicated in the labels. (b,c) Charge and spin physics of the KE as a function of the exchange coupling $J$ and temperature $T$. The dark areas delimit the regions of Kondo crossover regime. The colors scales correspond to the normalized temperature derivative of (b) the resistivity and (c) spin susceptibility. Red lines denote ${T_K^{(\rho)}}$ and ${T_K^{(\chi)}}$ obtained for Eq. \ref{['eq:ham']} with $U=0$. (d) Spin correlations ${\mathcal{C}^{(\alpha)}_{\delta}}$ for $|J|/t=1$ at variable $T$ and distances $\delta$ from the impurity (inset). The shaded yellow region denotes ${T_K^{(\rho)} < T < T_K^{(S)}}$.
• Figure 3: Adiabatic ground-state preparation of a small-scale atomic Kondo problem. (a) Illustration of AEA atoms trapped in a combined optical potential featuring a state-selective lattice for $g$-state particles and a state-dependent tweezer at site $i=0$, enabling to pin the impurity and precisely adjust the local onsite potential $\mu$. (b) Illustration of the staggered magnetic field $B$ and ground states for the high-$B$ (left) and low-$B$ (right) limits. The state $|{\kappa}\rangle$ sketched on the left can be prepared experimentally with high fidelity. (c) Energies of the lowest $M=20$ excitations with respect to the ground state, as a function of a variable staggering field strength $B$. The energy $\Delta E_1$ of the lowest excitation (red line) remains $\Delta E_1\sim t$ from $|B|/t \gg 1$ to $|B|/t \ll 1$. (d) Bath-spin correlators ${\mathcal{C}^{(s)}_{\delta}}$ for $\delta = 1, 2, 3$, showing the build-up of nonlocal fermion correlations mediated by the impurity while the staggered field is lowered.
• Figure 4: Kondo lattice effects in a single-impurity system with finite impurity tunneling. Specific heat $C_v$ as a function of the temperature for $J=-t$, $U=2.75\,t$ and various values of $\tilde{t}$. The Schottky anomaly of the standard Kondo model (solid gray line) is shown for reference. The sketch illustrates the mobile-impurity Kondo problem in Eq. \ref{['eq:ham2']}, as implemented with AEAs in a state-dependent 1D optical lattice.
• Figure 5: The effects of weak and strong coupling $J$ in the Kondo problem. (a) Temperature behavior of the normalized resistivity $\rho(T)/\rho(T\to 0)$, showing the formation of a marked minimum due to the Kondo effect for $|J|=0.2\,t$. (b) Local spin susceptibility $\chi_{zz}(T)$ as a function of the temperature $T$. Results for $|J|=0.2\,t$ display a crossover from a Curie-Weiss $\tfrac{1}{4k_BT}$ (gray solid line) to a Pauli-like constant behavior at low temperature. (c) Temperature-dependence of the specific heat $C_v(T)$. All data are for $|J|=0.2\,t$ (black solid) and $|J|=1.5\,t$ (red dashed).