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arXiv:1508.03016 · Physical Review A

Fully controllable Kondo system: Coupling a flux qubit and an ultracold Fermi gas

Kelly R. Patton

Published Feb 26, 2016• 1 citation
arXivHTMLPDF

Abstract

We show that a composite spin-\textonehalf{} Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature. We find that the Kondo temperature of this hybrid system is within current experimental limits. Furthermore, the momentum distribution of the trapped fermions is calculated, which clearly shows an experimental signature of the Kondo screening length. In addition to probing Kondo physics, the controllability of this system can be used to systematically explore the relaxation and equilibration of a strongly correlated system that has been initially prepared in a selected nonequilibrium state.

DOI
10.1103/physreva.93.023643

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We show that a composite spin-\textonehalf{} Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature. We find that the Kondo temperature of this hybrid system is within current experimental limits. Furthermore, the momentum distribution of the trapped fermions is calculated, which clearly shows an experimental signature of the Kondo screening length. In addition to probing Kondo physics, the controllability of this system can be used to systematically explore the relaxation and equilibration of a strongly correlated system that has been initially prepared in a selected nonequilibrium state.
We propose a novel realization of Kondo physics with ultracold atomic gases. It is based on a Fermi sea of two different hyperfine states of one atom species forming bound states with a different species, which is spatially confined in a trapping potential. We show that different situations displaying Kondo physics can be realized when Feshbach resonances between the species are tuned by a magnetic field and the trapping frequency is varied. We illustrate that a mixture of 40K and 23Na atoms can be used to generate a Kondo-correlated state and that momentum resolved radio frequency spectroscopy can provide unambiguous signatures of the formation of Kondo resonances at the Fermi energy. We discuss how tools of atomic physics can be used to investigate open questions for Kondo physics, such as the extension of the Kondo screening cloud.
The feasibility of realizing the overscreened Kondo effect in ultracold Fermi gas of atoms with spin $s\ensuremath{\ge}\frac{3}{2}$ in the presence of a localized magnetic impurity atom is proved realistic. Specifying (as a mere example) a system of ultracold 22Na^{22}\mathrm{Na}22Na Fermi gas and a trapped 6Li^{6}\mathrm{Li}6Li impurity, the mechanism of exchange interaction between the Na and Li atoms is elucidated and the exchange constant is found to be positive (antiferromagnetic). The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of 500 nK. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi-liquid fixed point. An observable displaying multichannel features even in the weak-coupling regime is the impurity magnetization that is negative for $T\ensuremath{\gg}{T}_{K}$ and becomes positive with decreasing temperature.
A hybrid quantum system is proposed by coupling the internal hyperfine transitions of a trapped atomic Bose-Einstein condensate (BEC) and a superconducting quantum interference device (SQUID) via the macroscopic quantum field of the flux qubit. The presence of the condensate leads to a bosonic enhancement of the Rabi frequency over the otherwise small single-particle magnetic-dipole transition matrix elements. This enhancement makes it possible to rapidly transfer and store qubit states in the BEC that were originally prepared in the SQUID. The fidelity of this transfer for different states is calculated, and a direct experimental protocol to determine the transfer fidelity by quantum tomography of the BEC qubit is presented.
We propose an experimental protocol to directly observe the Kondo effect by scattering ultracold atoms. We propose using an optical Feshbach resonance to engineer Kondo-type spin-dependent interactions in a system with ultracold 6Li^{6}\mathrm{Li}6Li and 87Rb^{87}\mathrm{Rb}87Rb gases. We calculate the momentum transferred from the 87Rb^{87}\mathrm{Rb}87Rb gas to the 6Li^{6}\mathrm{Li}6Li gas in a scattering experiment and show that it has a logarithmically enhanced temperature dependence, characteristic of the Kondo effect, and analogous to the resistivity of alloys with magnetic impurities. Experimentally detecting this enhancement will give a different perspective on the Kondo effect, and allow us to explore a rich variety of problems such as the Kondo lattice problem and heavy-fermion systems.
The Kondo effect in condensed-matter systems manifests itself most sharply in their transport measurements. Here we propose an analogous transport signature of the orbital Kondo effect realized with ultracold atoms. Our system consists of imbalanced Fermi seas of two components of fermions and an impurity atom of different species which is confined by an isotropic potential. We first apply a $\ensuremath{\pi}/2$ pulse to transform two components of fermions into two superposition states. Their interactions with the impurity atom then cause a ``transport'' of fermions from majority to minority superposition states, whose numbers can be measured after applying another $3\ensuremath{\pi}/2$ pulse. In particular, when the interaction of one component of fermions with the impurity atom is tuned close to a confinement-induced ppp-wave or higher partial-wave resonance, the resulting conductance is shown to exhibit the Kondo signature, i.e., universal logarithmic growth by lowering the temperature. The proposed transport measurement will thus provide a clear evidence of the orbital Kondo effect accessible in ultracold atom experiments and pave the way for developing new insights into Kondo physics.
We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid-state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the nonequilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multistep Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips.