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arXiv:1509.06141 · Physical review. B./Physical review. B

Kondo induced π -phase shift of microwave photons in a circuit quantum electrodynamics architecture

Guangwei Deng, Loïc Henriet, Da Wei, Shuxiao Li, Hai-Ou Li, Gang Cao, Ming Xiao, Guang‐Can Guo, Marco Schirò, Karyn Le Hur, Guo‐Ping Guo

Published Sep 3, 2021• 7 citations
arXivHTMLPDF

Abstract

The Kondo effect refers to the screening of a spin-1/2 impurity by a cloud of conduction electrons, then forming a many-body Fermi liquid ground state. Theoretical calculations suggest that the Kondo resonance can interact with light and should give rise to a $\ensuremath{\pi}$-phase shift of the photon signal in the case where the ground state is a Fermi liquid. This $\ensuremath{\pi}$-phase shift of light is driven from the Korringa-Shiba relation of quantum impurity Fermi-liquid ground states. We report the first observation of such a $\ensuremath{\pi}$-phase shift in a graphene double quantum dot within a circuit quantum electrodynamics architecture where the microwave photons couple to the pseudospin or charge degrees of freedom. We study the evolution of the $\ensuremath{\pi}$-phase shift as a function of temperature and bias voltage. The observed Kondo temperature ${T}_{K}\ensuremath{\sim}550\phantom{\rule{0.16em}{0ex}}\text{mK}$ is in agreement with dc conductance measurements. All our results support the formation of a Kondo resonance located above the Fermi level of the electronic reservoirs with the occurrence of an $SU(4)$ Fermi-liquid ground state. We finally study how the Kondo-photon interaction can be tuned by inter-dot electron tunnel coupling strengths. Our findings may contribute to a better understanding of many-body physics in hybrid circuit systems, and open up applications in atomic thin materials from the light-matter interaction.

DOI
10.1103/physrevb.104.125407

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The Kondo effect refers to the screening of a spin-1/2 impurity by a cloud of conduction electrons, then forming a many-body Fermi liquid ground state. Theoretical calculations suggest that the Kondo resonance can interact with light and should give rise to a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift of the photon signal in the case where the ground state is a Fermi liquid. This \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift of light is driven from the Korringa-Shiba relation of quantum impurity Fermi-liquid ground states. We report the first observation of such a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift in a graphene double quantum dot within a circuit quantum electrodynamics architecture where the microwave photons couple to the pseudospin or charge degrees of freedom. We study the evolution of the \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift as a function of temperature and bias voltage. The observed Kondo temperature TK\ensuremath∼550mK{T}_{K}\ensuremath{\sim}550\phantom{\rule{0.16em}{0ex}}\text{mK}TK​\ensuremath∼550mK is in agreement with dc conductance measurements. All our results support the formation of a Kondo resonance located above the Fermi level of the electronic reservoirs with the occurrence of an SU(4)SU(4)SU(4) Fermi-liquid ground state. We finally study how the Kondo-photon interaction can be tuned by inter-dot electron tunnel coupling strengths. Our findings may contribute to a better understanding of many-body physics in hybrid circuit systems, and open up applications in atomic thin materials from the light-matter interaction.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime.The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy.We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase.A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy.In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD).While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state.By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs.Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.
We present a study of the correlated transport regimes of a double quantum impurity system with mutual capacitive interactions. Such system can be implemented by a double quantum dot arrangement or by a quantum dot and nearby quantum point contact, with independently connected sets of metallic terminals. Many-body spin correlations arising within each dot-lead subsystem give rise to the Kondo effect under appropriate conditions. The otherwise independent Kondo ground states may be modified by the capacitive coupling, decisively modifying the ground state of the double quantum impurity system. We analyze this coupled system through variational methods and the numerical renormalization group technique. Our results reveal a strong dependence of the coupled system ground state on the electron-hole asymmetries of the individual subsystems, as well as on their hybridization strengths to the respective reservoirs. The electrostatic repulsion produced by the capacitive coupling produces an effective shift of the individual energy levels toward higher energies, with a stronger effect on the ``shallower'' subsystem (that closer to resonance with the Fermi level), potentially pushing it out of the Kondo regime and dramatically changing the transport properties of the system. The effective remote gating that this entails is found to depend nonlinearly on the capacitive coupling strength, as well as on the independent subsystem levels. The analysis we present here of this mutual interaction should be important to fully characterize transport through such coupled systems.
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.
We study the three-body Fermi liquid effects in the SU(NNN) Anderson impurity model within the strong interaction limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, where the occupation number Nd{N}_{d}^{}Nd​ of the impurity levels varies over the range of 0<Nd<10<{N}_{d}^{}<10<Nd​<1. The three-body correlations arise among the impurity electrons when the electron-hole symmetry, the time-reversal symmetry, or both are broken by external fields or potentials. They play a key role in low-energy transport, particularly in the next-to-leading-order terms of power expansion with respect to temperature TTT and bias voltage eVeVeV. Using the numerical renormalization group approach, we calculate the differential conductance and nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases, demonstrating how the three-body correlations evolve in the strong interaction limit across the 1/N1/N1/N-filling Kondo regime at ${N}_{d}^{}\ensuremath{\simeq}1.0$ and the valence fluctuation regime where the occupation number Nd{N}_{d}^{}Nd​ varies rapidly with the position ${\ensuremath{\epsilon}}_{d}^{}$ of the impurity levels. We also show that the three-body correlations strongly couple with asymmetries in the tunnel couplings between quantum dots and reservoirs. For N=4N=4N=4, this coupling significantly affects the order (eV)3{(eV)}^{3}(eV)3 nonlinear current through the quarter-filling Kondo state, where the electron-hole symmetry is broken. In particular, in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, the expansion coefficients exhibit clear plateau structures associated with the Kondo effect at ${N}_{d}^{}\ensuremath{\simeq}1.0$. Our formulation and analysis pave the way for deducing the three-body correlations from the low-energy experiments on the next-to-leading-order transport.
We investigate Kondo physics in a quantum dot side coupled to a Majorana zero mode, where the Majorana coupling induces both spin and charge fluctuations that determine low-energy behavior. Using a wave-function-based Schrieffer-Wolff transformation combined with numerical renormalization group calculations, we discover an SUL(2)S{U}_{L}(2)SUL​(2) spin-charge-entangled Kondo state, in which conduction electrons screen the spin-charge-entangled degrees of freedom of the Majorana-quantum dot subsystem. We show that the parity degeneracy of this state gives rise to spin-resolved Andreev-normal boundary conditions, resulting in non-Fermi-liquid behavior. Density matrix renormalization group simulations directly resolve a hallmark of these boundary conditions---a subleading even-odd effect in the screening cloud. Our framework bridges strongly correlated and topological phenomena, and naturally extends to ZN{\mathbb{Z}}_{N}ZN​ parafermions and SU(N)SU(N)SU(N) Kondo systems.