arXiv subjects

Harold U. Baranger

Publications and source records attributed to Harold U. Baranger.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Hall Andreev Conversion in Graphene Nanostructures

We study Andreev conversion in clean nanostructures containing an interface between graphene in the quantum Hall (QH) state and a superconductor, focusing on the lowest Landau level. First, several graphene nanostructures formed from zigzag edges with sharp corners are considered using a tight-binding model. We find the scattering state for an electron impinging on the interface from the upstream QH edge state, together with the probability of it exiting as a hole in the downstream QH edge state (Andreev conversion). From these results, we deduce the behavior for edges at an arbitrary angle and for rounded corners. A key issue is whether the graphene-superconductor interface is fully transparent or only partially transparent. For full transparency, we recover previous results. In contrast, interfaces with partial but substantial transparency (well away from the tunneling limit) behave very differently: (i) the hybrid electron-hole interfacial modes are not valley degenerate and (ii) intervalley scattering can occur at the corners, even when rounded. As a result, interference between the two hybrid modes can occur, even in the absence of disorder. Finally, we compare the sensitivity of Andreev conversion to interface transparency in the QH regime to that in the absence of a magnetic field. While the zero-field result closely follows the classic Blonder-Tinkham-Klapwijk relation, Andreev conversion in the QH regime is more robust.

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arXiv2026

Same-spin Andreev reflections in the quantum Hall regime: the role of loss

The interfaces of superconductors and topological materials hold promise for realizing exotic states and excitations. An important example is provided by the chiral Andreev edge states (CAES), which are formed at interfaces between quantum Hall (QH) states and superconductors (SC). CAES combine electron and hole amplitudes which are hybridized via Andreev reflections. This study explores the spin properties of the CAES through selective spin filtering of the QH edge channels. We find robust evidence of spin-flips accompanying the Andreev processes: electrons can be reflected from the superconductor as holes in the same spin channel. We demonstrate that the distribution of the reflection probabilities is exponential and then use random matrix theory to account for this observation. Finally, we observe Andreev reflections in the spin-polarized ν = 1 case, which is enabled by particle loss. Our findings shed light on the mechanism underlying Andreev reflections of spin-polarized chiral states. They also demonstrate the importance of considering non-Hermiticity when constructing topological superconductors in hybrid materials.

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arXiv2025

Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes

We study clean, edge-contacted graphene/superconductor interfaces in both the quantum Hall (QH) and zero field regimes. We find that Andreev reflection is substantially stronger than at an interface with a semiconductor two-dimensional electron gas: the large velocity at graphene's conical Dirac points makes the requirement of current continuity to a metal much less restrictive. In both our tight-binding and continuum models, we find a wide range of parameters for which Andreev reflection is strong. For a transparent interface, we demonstrate the following for graphene in the lowest Landau level QH state: (i) Excellent electron-hole hybridization occurs: the electron and hole components in graphene are simply related by an exchange of sublattice. The spatial profile for the electron component is predominantly gaussian on one sublattice and peaked at the interface, and so very different from the QH edge state of a terminated lattice. (ii) The degree of hybridization is independent of the graphene filling: no fine-tuning is needed. (iii) The spectrum is valley degenerate: the dispersion of each chiral Andreev edge mode (CAEM) self-aligns to be antisymmetric about the center of each valley, independent of filling. Achieving a transparent interface requires the absence of any barrier as well as a superconductor that is suitably matched to graphene; we argue that the latter condition is not very stringent. We further consider the effect of reduced transparency and Zeeman splitting on both the wavefunctions of the CAEM and their dispersion.

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arXiv2023

Interference of chiral Andreev edge states

The search for topological excitations such as Majorana fermions has spurred interest in the boundaries between distinct quantum states. Here, we explore an interface between two prototypical phases of electrons with conceptually different ground states: the integer quantum Hall insulator and the s-wave superconductor. We find clear signatures of hybridized electron and hole states similar to chiral Majorana fermions, to which we refer as chiral Andreev edge states (CAES). They propagate along the interface in the direction determined by magnetic field and their interference can turn an incoming electron into an outgoing electron or a hole, depending on the phase accumulated by the CAES along their path. Our results demonstrate that these excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation.

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arXiv2022

Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point

We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature -- we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.

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arXiv2021

Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{PT}$ symmetry to quantum fluctuations

We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z_{2}$ symmetry breaking, $\mathcal{PT}$ symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.

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arXiv2020

Stabilization of a Majorana Zero Mode through Quantum Frustration

We analyze a system in which a topological Majorana zero mode (tMZM) combines with a Majorana produced by quantum frustration (fMZM) to produce a novel ground state. The system that we study combines two parts, a grounded topological superconducting wire that hosts two tMZMs at its ends, and an on-resonant quantum dot connected to two dissipative leads. The quantum dot with dissipative leads creates an effective two-channel Kondo (2CK) state in which quantum frustration yields an isolated fMZM at the dot. We find that coupling the dot to one end of the topological wire stabilizes the tMZM at the other end. Three routes are used to obtain these results: (i) calculation of the conductance through an auxiliary detector quantum dot, (ii) renormalization group (RG) arguments and the g-theorem, and (iii) a fully non-equilibrium calculation of the I(V ) curve and shot noise S(V ) through the detector dot. In addition to providing a route to achieving an unpaired Majorana zero mode, this scheme provides a clear signature of the presence of the 2CK frustration-induced Majorana.

cond-mat.str-el↗

arXiv2019

Heralded Bell State of Dissipative Qubits Using Classical Light in a Waveguide

Maximally entangled two-qubit states (Bell states) are of central importance in quantum technologies. We show that heralded generation of a maximally entangled state of two intrinsically open qubits can be realized in a one-dimensional (1d) system through strong coherent driving and continuous monitoring. In contrast to the natural idea that dissipation leads to decoherence and so destroys quantum effects, continuous measurement and strong interference in our 1d system generate a pure state with perfect quantum correlation between the two open qubits. Though the steady state is a trivial product state which has zero coherence or concurrence, we show that, with carefully tuned parameters, a Bell state can be generated in the system's quantum jump trajectories, heralded by a reflected photon. Surprisingly, this maximally entangled state survives the strong coherent state input---a classical state that overwhelms the system. This simple method to generate maximally entangled states using classical coherent light and photon detection may, since our qubits are in a 1d continuum, find application as a building block of quantum networks.

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arXiv2019

Exciting a Bound State in the Continuum through Multi-Photon Scattering plus Delayed Quantum Feedback

Excitation of a bound state in the continuum (BIC) through scattering is problematic since it is by definition uncoupled. Here, we consider a type of dressed BIC and show that it can be excited in a nonlinear system through multi-photon scattering and delayed quantum feedback. The system is a semi-infinite waveguide with linear dispersion coupled to a qubit, in which a single-photon, dressed BIC is known to exist. We show that this BIC can be populated via multi-photon scattering in the non-Markovian regime, where the photon delay time (due to the qubit-mirror distance) is comparable with the qubit's decay. A similar process excites the BIC existing in an infinite waveguide coupled to two distant qubits, thus yielding stationary entanglement between the qubits. This shows, in particular, that single-photon trapping via multi-photon scattering can occur without band-edge effects or cavities, the essential resource being instead the {\it delayed} quantum feedback provided by a single mirror or the emitters themselves.

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arXiv2018

Particle Production in Ultra-Strong Coupling Waveguide QED

Understanding large-scale interacting quantum matter requires dealing with the huge number of quanta that are produced by scattering even a few particles against a complex quantum object. Prominent examples are found from high energy cosmic ray showers to the optical or electrical driving of degenerate Fermi gases. We tackle this challenge in the context of many-body quantum optics, as motivated by the recent developments of circuit quantum electrodynamics at ultrastrong coupling. The issue of particle production is addressed quantitatively with a simple yet powerful concept rooted in the quantum superposition principle. This key idea is illustrated by the study of multi-photon emission from a single two-level artificial atom coupled to a high impedance waveguide. We find surprisingly that the off-resonant inelastic emission lineshape is dominated by broadband particle production, due to the large phase space associated with contributions that do not conserve the number of excitations. Such frequency conversion processes produce striking signatures in time correlation measurements, which can be tested experimentally in quantum waveguides. These ideas open new directions for the simulation of a variety of physical systems, from polaron dynamics in solids to complex superconducting quantum architectures.

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arXiv2018

Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to discuss the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.

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arXiv2017

Multiple Emitters in a Waveguide: Non-Reciprocity and Correlated Photons at Perfect Elastic Transmission

We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven Λ-type three-level system (3LS) in both the single- and two- photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted photons completely uncorrelated. Slightly away from this separation, we find that the inelastic scattering (fluorescence) is large, leading to nonlinear effects such as non-reciprocity (rectification). We connect this non-reciprocity to inelastic scattering caused by driving a dark pole and so derive a condition for maximum rectification. Finally, by placing a true 3LS midway between the two 2LS, we show that elastic scattering produces only transmission, but inelastic scattering nevertheless occurs (the fluorescence is not quenched) causing substantial photon correlations.

quant-ph↗

arXiv2017

Rescuing a Quantum Phase Transition with Quantum Noise

We show that placing a quantum system in contact with an environment can enhance non-Fermi-liquid correlations, rather than destroy quantum effects as is typical. The system consists of two quantum dots in series with two leads; the highly resistive leads couple charge flow through the dots to the electromagnetic environment, the source of quantum noise. While the charge transport inhibits a quantum phase transition, the quantum noise reduces charge transport and restores the transition. We find a non-Fermi-liquid intermediate fixed point for all strengths of the noise. For strong noise, it is similar to the intermediate fixed point of the two-impurity Kondo model.

cond-mat.str-el↗

arXiv2016

Dynamics of a Qubit in a High-Impedance Transmission Line from a Bath Perspective

We investigate quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the emitted photonic states, in the framework of the spin-boson model Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using NRG calculations. NRG provides a benchmark for any linear response property throughout the ultra-strong coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide QED. Finally, the scattering results using the coherent state wavefunction approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.

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arXiv2015

Photon Correlations Generated by Inelastic Scattering in a One-Dimensional Waveguide Coupled to Three-Level Systems

We study photon correlations generated by scattering from three-level systems (3LS) in one dimension. The two systems studied are a 3LS in a semi-infinite waveguide (3LS plus a mirror) and two 3LS in an infinite waveguide (double 3LS). Our two-photon scattering approach naturally connects photon correlation effects with inelastically scattered photons; it corresponds to input-output theory in the weak-probe limit. At the resonance where electromagnetically induced transparency (EIT) occurs, we find that no photons are scattered inelastically and hence there are no induced correlations. Slightly away from EIT, the total inelastically scattered flux is large, being substantially enhanced due to the additional interference paths. This enhancement carries over to the two-photon correlation function, which exhibits non-classical behavior such as strong bunching with a very long time-scale. The long time scale originates from the slow-light effect associated with EIT.

quant-ph↗

arXiv2015

Waveguide QED: Power Spectra and Correlations of Two Photons Scattered Off Multiple Distant Qubits and a Mirror

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.

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arXiv2015

Detecting Photon-Photon Interactions in a Superconducting Circuit

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required high impedance transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\hbarω_s$, where $ω_s$ is the plasma frequency of the superconducting circuit. The features at $n\ge 2$ are a direct signature of the photon-photon interaction in the system.

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arXiv2014

Tunable Quantum Phase Transitions in a Resonant Level Coupled to Two Dissipative Baths

We study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect.

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