Publisher Correction: Classical analogue to driven quantum bits based on macroscopic pendula (Scientific Reports, (2023), 13, 1, (18386), 10.1038/s41598-023-45118-y)
Lorenz H., Kohler S., Parafilo A., Correction to: Scientific Reports, published online 26 October 2023 The original version of this Article contained errors in Figure 2 where the gray data curves were incorrectly captured in panels (a) and (b). The original Figure 2 and accompanying legend appear below. (Figure presented.) Near resonance Rabi oscillations between the two pendula with mean frequency (Formula presented.) mHz, frequency difference (Formula presented.) mHz and modulation frequency (Formula presented.) mHz. At (Formula presented.) pendulum 1 was deflected at maximally attracting lower and no upper magnets. Individual oscillations are not visible owing to the time axis covering 45 minutes. (a, b) Deflections (Formula presented.) and (Formula presented.) of the two pendula for the pivot distances (Formula presented.) mm and (Formula presented.) mm resulting in Rabi frequencies of (Formula presented.) mHz versus (Formula presented.) mHz. (c, d) Effective frequency (Formula presented.) and visibility (Formula presented.) of the Rabi oscillations for (Formula presented.) mm. The solid lines represent model predictions. The original Article has been corrected.
Classical analogue to driven quantum bits based on macroscopic pendula
Lorenz H., Kohler S., Parafilo A., Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle, classical mechanics is often seen as a theory for large systems where quantum coherence is completely averaged out. Surprisingly, it is still possible to reconstruct the coherent dynamics of a quantum bit (qubit) by using a classical model system. This classical-to-quantum analogue is based on wave mechanics, which applies to both, the classical and the quantum world. In this spirit we investigate the dynamics of macroscopic physical pendula with a modulated coupling. As a proof of principle, we demonstrate full control of our one-to-one analogue to a qubit by realizing Rabi oscillations, Landau-Zener transitions and Landau-Zener-Stückelberg-Majorana interferometry. Our classical qubit demonstrator can help comprehending and developing useful quantum technologies.
Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe
We show that the transport integrals of the two-site charge Kondo circuits connecting various multichannel Kondo simulators satisfy the generalized Wiedemann-Franz law with the universal Lorenz ratios all greater than 1. The magic Lorenz ratios are directly related to the Anderson's orthogonality catastrophe in quantum simulators providing some additional universal measure for the strong electron-electron correlations. We present a fullly fledged theory for the magic Lorenz ratios and discuss possible routes for the experimental verifications of the theory.
Charge Kondo circuit as a detector for electron-electron interactions in a Luttinger liquid
Nguyen T.K.T., Parafilo A.V., Nguyen H.Q., We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area L in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot a. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.
Thermoelectrics of a two-channel charge Kondo circuit: Role of electron-electron interactions in a quantum point contact
Parafilo A.V., Nguyen T.K.T., In this Letter we investigate the properties of a quantum impurity model in the presence of additional many-body interactions between mobile carriers. The fundamental question which is addressed here is how the interactions in the charge and spin sectors of an itinerant system affect the quantum impurity physics in the vicinity of the intermediate coupling fixed point. To illustrate the general answer to this question we discuss a two-channel charge Kondo circuit model. We show that the electron-electron interactions resulting in the formation of a massive spin mode in an itinerant electron subset drive the system away from the unstable non-Fermi-liquid (NFL) fixed point to the stable Fermi-liquid (FL) regime. We discuss the thermoelectric response as a benchmark for the NFL-FL crossover.
Multistage Kondo effect in a multiterminal geometry: A modular quantum interferometer
Karki D.B., Pavlov A.I., Quantum systems characterized by an interplay between several resonance scattering channels demonstrate very rich physics. To illustrate it we consider a multistage Kondo effect in nanodevices as a paradigmatic model for a multimode resonance scattering. We show that the channel crosstalk results in a destructive interference between the modes. This interplay can be controlled by manipulating the tunneling junctions in the multilevel and multiterminal geometry. We present a full-fledged theory of the multistage Kondo effect at the strong-coupling Fermi-liquid fixed point and discuss the influence of quantum interference effects to the quantum transport observables.
Seven Études on dynamical Keldysh model
Efremov D.V., We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green’s functions, self-energy, vertex part and T-matrix. These results are based on a closed form solution of the Dyson equation combined with the Ward identity. Analytical properties of the solution are discussed. Further we describe the combinatorics of the Feynman diagrams for the Green’s function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. Asymptotically exact equations for the number of skeleton diagrams in the limit of large N are derived. Finally, we consider possible realizations of a multicomponent Gaussian random potential in quantum transport via complex quantum dot experiments.
Overscreened Kondo problem with large spin and large number of orbital channels: Two distinct semiclassical limits in quantum transport observables
Karki D.B., We investigate quantum transport through the Kondo impurity assuming both a large number of orbital channels K≫1 for the itinerant electrons and a semiclassical spin S≫1 for the impurity. The non-Fermi-liquid regime of the Kondo problem is achieved in the overscreened sector K>2S. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: (i) K≫S≫1, differential conductance vanishes, and (ii) S/K=C with 0
Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade
Pavlov A.I., We present a microscopic theory for quantum thermoelectric and heat transport in the Schwarzian regime of the Sachdev-Ye-Kitaev (SYK) model. As a charged fermion realization of the SYK model in nanostructures, we assume a setup based on a quantum dot connected to the charge reservoirs through weak tunnel barriers. We analyze particle-hole symmetry breaking effects crucial for both Seebeck and Peltier coefficients. We show that the quantum charge and heat transport at low temperatures are defined by the interplay between elastic and inelastic processes such that the inelastic processes provide a leading contribution to the transport coefficients at the temperatures that are smaller compared to the charging energy. We demonstrate that both electric and thermal conductance obey a power law in temperature behavior, while thermoelectric, Seebeck, and Peltier coefficients are exponentially suppressed. This represents selective suppression of only nondiagonal transport coefficients. We discuss the validity of the Kelvin formula in the presence of a strong Coulomb blockade.
Quantum thermoelectric and heat transport in the overscreened Kondo regime: Exact conformal field theory results
Karki D.B., We develop a conformal field theory approach for investigation of the quantum charge, heat, and thermoelectric transport through a quantum impurity fine-tuned to a non-Fermi liquid regime. The non-Fermi-liquid operational mode is associated with the overscreened spin Kondo effect and controlled by the number of orbital channels. The universal low-temperature scaling and critical exponents for Seebeck and Peltier coefficients are investigated for the multichannel geometry. We discuss the universality of Lorenz ratio and power factor beyond the Fermi-liquid paradigm. Different methods of verifying our findings based on the recent experiments are proposed.
Thermoelectric Transport in a Three-Channel Charge Kondo Circuit
Nguyen T.K.T., We theoretically investigate the thermoelectric transport through a circuit implementation of the three-channel charge Kondo model quantum simulator [Z. Iftikhar et al., Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592]. The universal temperature scaling law of the Seebeck coefficient is computed perturbatively approaching the non-Fermi liquid strong coupling fixed point using the Abelian bosonization technique. The predicted T1/3logT scaling behavior of the thermoelectric power sheds light on the properties of Z3 emerging parafermions and gives access to exploring prefractionalized zero modes in the quantum transport experiments. We discuss a generalization of approach for investigating a multichannel Kondo problem with emergent ZN→ZM crossovers between "weak"non-Fermi liquid regimes corresponding to different low-temperature fixed points.
Kondo effect in a Aharonov-Casher interferometer
Parafilo A.V., Gorelik L.Y., We consider a model describing a spin field-effect transistor based on a quantum nanowire with a tunable spin-orbit interaction embedded between two ferromagnetic leads with anticollinear magnetization. We investigate a regime of a strong interplay between resonance Kondo scattering and interference associated with the Aharonov-Casher effect. Using the Keldysh technique at a weak-coupling regime we calculate perturbatively the charge current. It is predicted that the effects of the spin-orbit interaction result in a nonvanishing current for any spin polarization of the leads including the case of fully polarized anticollinear contacts. We analyze the influence of the Aharonov-Casher phase and degree of spin polarization in the leads onto a Kondo temperature.
Effects of strong electron interactions and resonant scattering on power output of nano-devices
Karki D., We develop a Fermi-liquid based approach to investigate the power output of nano-devices in the presence of strong interactions and resonance scattering. The developed scheme is then employed to study the power output of a SU(N) Kondo impurity at the strong-coupling regime. The interplay between Kondo resonance and the filling factors in the SU(N) quantum systems is found to be a key to enhance output power. Such enhancement results in an output power corresponding to ∼50% of the quantum upper bound. We demonstrate that given a proper tuning of the electron occupancy, the investigated power grows linearly with degeneracy of Kondo state (N). This relation can hence be exploited to obtain output power that is larger than the one in existing noninteracting setups.
Nonlinear Seebeck effect of SU(N) Kondo impurity
Karki D., We develop a theoretical framework to study the influence of coupling asymmetry on the thermoelectrics of a strongly coupled SU(N) Kondo impurity based on a local Fermi liquid theory. Applying a nonequilibrium Keldysh formalism, we investigate a charge current driven by the voltage bias and temperature gradient in the strong coupling regime of an asymmetrically coupled SU(N) quantum impurity. The thermoelectric characterizations are made via nonlinear Seebeck effects. We demonstrate that the beyond particle-hole (PH) symmetric SU(N) Kondo variants are highly desirable with respect to the corresponding PH-symmetric setups in order to have significantly improved thermoelectric performance. The greatly enhanced Seebeck coefficients by tailoring the coupling asymmetry of beyond PH-symmetric SU(N) Kondo effects are explored. Apart from presenting the analytical expressions of asymmetry-dependent transport coefficients for general SU(N) Kondo effects, we make a close connection of our findings with the experimentally studied SU(2) and SU(4) Kondo effects in quantum dot nanostructures. Seebeck effects associated with the theoretically proposed SU(3) Kondo effects are discussed in detail.
Landau-Zener transitions and Rabi oscillations in a Cooper-pair box: Beyond two-level models
Parafilo A.V., We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step"- and "beats"-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by the change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between a pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.
Landau-Zener transitions and Rabi oscillations in a Cooper-pair box: Beyond two-level models
Parafilo A., We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: “step”- and “beats”-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.
Full counting statistics of the two-stage Kondo effect
Karki D., We developed a theoretical framework which extends the method of full counting statistics (FCS) from conventional single-channel Kondo screening schemes to a multichannel Kondo paradigm. The developed idea of FCS has been demonstrated considering an example of a two-stage Kondo (2SK) model. We analyzed the charge-transferred statistics in the strong-coupling regime of a 2SK model using a nonequilibrium Keldysh formulation. A bounded value of the Fano factor, 1≤F≤5/3, confirmed the crossover regimes of charge-transferred statistics in the 2SK effect, from Poissonian to super-Poissonian. An innovative way of measuring the transport properties of the 2SK effect, by the independent measurements of charge current and noise, has been proposed.
Phase diagram of the Hubbard-Kondo lattice model from the variational cluster approximation
Faye J.P.L., The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction J between the localized spins and the conduction electrons, this model also contains the local repulsion U between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Néel antiferromagnetic phase dominates from small to moderate J and UJ, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.
Two-color Fermi-liquid theory for transport through a multilevel Kondo impurity
Karki D.B., Mora C., Von Delft J., We consider a quantum dot with K≥2 orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multilevel Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel S=1 Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi liquid. Using nonequilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field, and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.
Seebeck effect on a weak link between Fermi and non-Fermi liquids
Nguyen T., We propose a model describing Seebeck effect on a weak link between two quantum systems with fine-tunable ground states of Fermi and non-Fermi liquid origin. The experimental realization of the model can be achieved by utilizing the quantum devices operating in the integer quantum Hall regime [Z. Iftikhar et al., Nature (London) 526, 233 (2015)NATUAS0028-083610.1038/nature15384] designed for detection of macroscopic quantum charged states in multichannel Kondo systems. We present a theory of thermoelectric transport through hybrid quantum devices constructed from quantum-dot-quantum-point-contact building blocks. We discuss pronounced effects in the temperature and gate voltage dependence of thermoelectric power associated with a competition between Fermi and non-Fermi liquid behaviors. High controllability of the device allows to fine tune the system to different regimes described by multichannel and multi-impurity Kondo models.