Fermi liquid approach to the quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:math>circuit: Renormalization group analysis of the Anderson and Coulomb blockade models

Filippone, Michele; Mora, Christophe

doi:10.1103/physrevb.86.125311

Cited by 28 publications

(42 citation statements)

References 106 publications

(203 reference statements)

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“…universality of the charge relaxation resistance R q was shown to have its roots in a Korringa-Shiba relation [39]. Deviations from universality arise in non-Fermi liquid regimes [40][41][42][43], or for the low-temperature limit of an Anderson impurity, upon breaking the Kondo singlet by an applied magnetic field [44][45][46].…”

Section: Deg Cavitymentioning

confidence: 99%

Interacting mesoscopic capacitor out of equilibrium

2017

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We consider the full nonequilibrium response of a mesoscopic capacitor in the large transparency limit, exactly solving a model with electron-electron interactions appropriate for a cavity in the quantum Hall regime. For a cavity coupled to the electron reservoir via an ideal point contact, we show that the response to any time-dependent gate voltage V g (t) is strictly linear in V g . We analyze the charge and current response to a sudden gate voltage shift and find that this response is not captured by a simple circuit analogy. In particular, in the limit of strong interactions a sudden change in the gate voltage leads to the emission of a sequence of multiple charge pulses, the width and separation of which are controlled by the charge-relaxation time τ c = hC g /e 2 and the time of flight τ f . We also consider the effect of a finite reflection amplitude in the point contact, which leads to nonlinear-in-gate-voltage corrections to the charge and current response.

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Section: Deg Cavitymentioning

confidence: 99%

Interacting mesoscopic capacitor out of equilibrium

2017

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“…[7][8][9][10][11] Here, we show that the Korringa-Shiba law Eq. (19) is equivalent to the instantaneous Joule law Eq.…”

Section: Interacting Electrons a Exact Resultsmentioning

confidence: 99%

“…In the interacting case, it is a nontrivial result, which was originally proved by Shiba in the Anderson model 26 and later generalized by Fillipone et al when a magnetic field is also considered. 10,11 It reads…”

Section: Interacting Electrons a Exact Resultsmentioning

confidence: 99%

“…As mentioned before, in linear response, it is usual to represent this setup in terms of a resistance in series with a capacitor, as sketched at the top of Fig.1. [1][2][3][4][5][6][7][8][9][10][11] In this paper, we show that this representation with R = R q is also sound to describe the adiabatic dynamics of the interacting system without magnetic field beyond linear response. In the case of a magnetic field applied at the quantum dot, we analyze the setup in the context of the circuit sketched in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The universality of this resistance remains robust in the low frequency regime upon adding electronelectron interactions in the quantum dot provided that the system behaves as a Fermi liquid (FL). [7][8][9][10][11] While in some experiments the driving amplitudes were within the range of linear response theory, 1 further experimental 2,3 and theoretical [12][13][14][15] contributions focused on quantum capacitors as single-electron sources, implying large amplitudes. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear charge and energy dynamics of an adiabatically driven interacting quantum dot

et al. 2017

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We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven interacting quantum dot in contact to a reservoir for arbitrary amplitudes of the driving potential. We study within this framework the Anderson impurity model with a local ac gate voltage. We show that the exact adiabatic quantum dynamics of this system is fully determined by the behavior of the charge susceptibility of the frozen problem. At T = 0, we evaluate the dynamic response functions with the numerical renormalization group (NRG). The time-resolved heat production exhibits a pronounced feature described by an instantaneous Joule law characterized by an universal resistance quantum R 0 = h/(2e 2 ) for each spin channel. We show that this law holds in non-interacting as well as in the interacting system and also when the system is spin-polarized. In addition, in the presence of a static magnetic field, the interplay between many-body interactions and spin polarization leads to a non-trivial energy exchange between electrons with different spin components.

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Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

Hur

Henriet

Petrescu

et al. 2016

Comptes Rendus. Physique

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We review recent developments regarding non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled to an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing to engineer the Jaynes-Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott-superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin-orbit couplings have been successfully implemented with ultra-cold atoms in optical lattices -using time-dependent Floquet perturbations periodic in time, for exampleas well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries. The Bose-Hubbard model is related to the Jaynes-Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase. arXiv:1505.00167v2 [cond-mat.mes-hall] 15 Jan 2016 be either Rydberg atoms (cold atoms) or trapped ions [3, 4] for example. A step towards the realization of manybody physics has also been made through the realization of model Hamiltonians such as the Dicke Hamiltonian [5], where the associated super-radiant quantum phase transition has been observed in non-equilibrium conditions [6]. A solid-state version of cavity quantum electrodynamics, related to circuit quantum electrodynamics, built with superconducting quantum circuits [7,8], is also a very active field both from experimental and theoretical points of view. Theorists have predicted novel emergent quantum phenomena either in relation with strong light-matter coupling [9] or non-equilibrium quantum physics [10,11].The goal here is to review developments, both theoretical and experimental, towards realizing many-body physics and quantum simulation in circuit QED starting from small networks to larger ensembles of superconducting elements in the microwave limit. An experimental endeavor has been accomplished towards the realization of larger arrays in circuit QED [12,13,14,15] and towards controlling trajectories in small systems [16,17]. This research is c...

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Fermi liquid approach to the quantumRCcircuit: Renormalization group analysis of the Anderson and Coulomb blockade models

Cited by 28 publications

References 106 publications

Interacting mesoscopic capacitor out of equilibrium

Interacting mesoscopic capacitor out of equilibrium

Nonlinear charge and energy dynamics of an adiabatically driven interacting quantum dot

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

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