# Browsing by Author "Baranger, HU"

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Item Open Access Bound on quantum computation time: Quantum error correction in a critical environment(Physical Review A - Atomic, Molecular, and Optical Physics, 2010-08-31) Novais, E; Mucciolo, ER; Baranger, HUWe obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.Item Open Access Conductance of quantum impurity models from quantum monte carlo(Physical Review B - Condensed Matter and Materials Physics, 2010-10-28) Liu, D; Chandrasekharan, S; Baranger, HUThe conductance of two Anderson impurity models, one with twofold and another with fourfold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the imaginary time QMC data to zero frequency yields the linear conductance, which is then compared to numerical renormalization-group results in order to assess its accuracy. We find that the method gives excellent results at low temperature (T TK) throughout the mixed-valence and Kondo regimes but it is unreliable for higher temperature. © 2010 The American Physical Society.Item Open Access Detecting a Majorana-fermion zero mode using a quantum dot(Physical Review B - Condensed Matter and Materials Physics, 2011-11-16) Liu, DE; Baranger, HUWe propose an experimental setup for detecting a Majorana zero mode consisting of a spinless quantum dot coupled to the end of a p-wave superconducting nanowire. The Majorana bound state at the end of the wire strongly influences the conductance through the quantum dot: Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. In the topological phase, the zero-temperature peak value of the dot conductance (i.e., when the dot is on resonance and symmetrically coupled to the leads) is e2/2h. In contrast, if the wire is in its trivial phase, the conductance peak value is e2/h, or if a regular fermionic zero mode occurs on the end of the wire, the conductance is 0. The system can also be used to tune Flensberg's qubit system to the required degeneracy point. © 2011 American Physical Society.Item Open Access Detecting photon-photon interactions in a superconducting circuit(Physical Review B - Condensed Matter and Materials Physics, 2015-10-06) Jin, LJ; Houzet, M; Meyer, JS; Baranger, HU; Hekking, FWJA local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required 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 ωs, where ωs is the plasma frequency of the superconducting circuit. The features at n≥2 are a direct signature of the photon-photon interaction in the system.Item Open Access Dynamics of a qubit in a high-impedance transmission line from a bath perspective(Physical Review A, 2016-03-28) Bera, S; Baranger, HU; Florens, SWe investigate the quantum dynamics of a generic model of light-matter interaction in the context of high-impedance waveguides, focusing on the behavior of the photonic states generated in the waveguide. The model treated consists simply of a two-level system coupled to a bosonic bath (the Ohmic 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 wave function; formally, this approach combines in a single framework 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 numerical renormalization group (NRG) calculations. NRG provides a benchmark for any linear response property throughout the ultrastrong-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 quantum electrodynamics. Finally, the scattering results using the coherent state wave-function 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.Item Open Access From weak- to strong-coupling mesoscopic Fermi liquids(EPL, 2012-01-01) Liu, DE; Burdin, S; Baranger, HU; Ullmo, DWe study mesoscopic fluctuations in a system in which there is a continuous connection between two distinct Fermi liquids, asking whether the mesoscopic variation in the two limits is correlated. The particular system studied is an Anderson impurity coupled to a finite mesoscopic reservoir described by the random matrix theory, a structure which can be realized using quantum dots. We use the slave boson mean-field approach to connect the levels of the uncoupled system to those of the strong-coupling Nozières' Fermi liquid. We find strong but not complete correlation between the mesoscopic properties in the two limits and several universal features. © 2012 Europhysics Letters Association.Item Open Access Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system(Physical Review B - Condensed Matter and Materials Physics, 2014-08-07) Bera, S; Nazir, A; Chin, AW; Baranger, HU; Florens, SWe develop a systematic variational coherent-state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counterdisplacements due to quantum tunneling effects). We present a comprehensive study of the ground-state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double-well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization-group calculations and to the exact Bethe ansatz solution of the model demonstrate the rapid convergence of our variationally optimized multipolaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry. © 2014 American Physical Society.Item Open Access Kondo effect and mesoscopic fluctuations(Pramana - Journal of Physics, 2011-11-01) Ullmo, D; Burdin, S; Liu, DE; Baranger, HUTwo important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature TK which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/TK. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling. © Indian Academy of Sciences.Item Open Access Mesoscopic Anderson box: Connecting weak to strong coupling(Physical Review B - Condensed Matter and Materials Physics, 2012-04-27) Liu, DE; Burdin, S; Baranger, HU; Ullmo, DWe study the Anderson impurity problem in a mesoscopic setting, namely the "Anderson box," in which the impurity is coupled to finite reservoir having a discrete spectrum and large sample-to-sample mesoscopic fluctuations. Note that both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. We study how the statistical fluctuations in these two problems are connected, using random matrix theory and the slave boson mean-field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise-type toy model. Third, we study the fluctuations of the mean-field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements. We find that the introduction of the strongly coupled impurity considerably changes the wave function but that a substantial correlation remains. © 2012 American Physical Society.Item Open Access Mesoscopic fluctuations in the Fermi-liquid regime of the Kondo problem(European Physical Journal B, 2013-08-01) Ullmo, D; Liu, DE; Burdin, S; Baranger, HUWe consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Mesoscopic fluctuations of both the quasiparticle energy levels and the corresponding wavefunctions are large in this case. These mesoscopic fluctuations make the traditional approach to Fermi-liquids impracticable, as it assumes the existence of a limited number of relevant parameters. We show here how this difficulty can be overcome and discuss the relationship between the resulting Fermi-liquid description "à la Nozières" and the mean field slave fermion approximation. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.Item Open Access Multiple emitters in a waveguide: Nonreciprocity and correlated photons at perfect elastic transmission(Physical Review A, 2017-07-21) Fang, YLL; Baranger, HUWe 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 nonreciprocity (rectification). We connect this nonreciprocity 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.Item Open Access Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide(New Journal of Physics, 2018-04-16) Fang, Y-LL; Ciccarello, F; Baranger, HUWe 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 qubitʼs dynamical map. Tools of open quantum systems theory allow us then to show 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.Item Open Access Observation of majorana quantum critical behaviour in a resonant level coupled to a dissipative environment(Nature Physics, 2013-01-01) Mebrahtu, HT; Borzenets, IV; Zheng, H; Bomze, YV; Smirnov, AI; Florens, S; Baranger, HU; Finkelstein, GA quantum phase transition is an abrupt change between two distinct ground states of a many-body system, driven by an external parameter. In the vicinity of the quantum critical point (QCP) where the transition occurs, a new phase may emerge that is determined by quantum fluctuations and is very different from either phase. In particular, a conducting system may exhibit non-Fermi-liquid behaviour. Although this scenario is well established theoretically, controllable experimental realizations are rare. Here, we experimentally investigate the nature of the QCP in a simple nanoscale system - a spin-polarized resonant level coupled to dissipative contacts. We fine-tune the system to the QCP, realized exactly on-resonance and when the coupling between the level and the two contacts is symmetric. Several anomalous transport scaling laws are demonstrated, including a striking non-Fermi-liquid scattering rate at the QCP, indicating fractionalization of the resonant level into two Majorana quasiparticles. © 2013 Macmillan Publishers Limited.Item Open Access Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment(Nature Physics, 2013) Mebrahtu, HT; Borzenets, IV; Zheng, H; Bomze, YV; Smirnov, AI; Florens, S; Baranger, HU; Finkelstein, GA quantum phase transition is an abrupt change between two distinct ground states of a many-body system, driven by an external parameter. In the vicinity of the quantum critical point (QCP) where the transition occurs, a new phase may emerge that is determined by quantum fluctuations and is very different from either phase. In particular, a conducting system may exhibit non-Fermi-liquid behaviour. Although this scenario is well established theoretically, controllable experimental realizations are rare. Here, we experimentally investigate the nature of the QCP in a simple nanoscale system-a spin-polarized resonant level coupled to dissipative contacts. We fine-tune the system to the QCP, realized exactly on-resonance and when the coupling between the level and the two contacts is symmetric. Several anomalous transport scaling laws are demonstrated, including a striking non-Fermi-liquid scattering rate at the QCP, indicating fractionalization of the resonant level into two Majorana quasiparticles.Item Open Access One-dimensional waveguide coupled to multiple qubits: Photon-photon correlations(EPJ Quantum Technology, 2014-12-01) Fang, YLL; Zheng, H; Baranger, HUFor a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation L. We study the correlations by calculating the second-order correlation function g 2 (t) in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function g2(t) including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation L could be readily explored with our approach.Item Open Access Photon correlations generated by inelastic scattering in a one-dimensional waveguide coupled to three-level systems(Physica E: Low-Dimensional Systems and Nanostructures, 2016-04-01) Fang, YLL; Baranger, HU© 2015 Elsevier B.V. All rights reserved.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.Item Open Access Quantum interference and complex photon statistics in waveguide QED(Physical Review A, 2018-02-07) Zhang, XHH; Baranger, HUWe obtain photon statistics by using a quantum jump approach tailored to a system in which one or two qubits are coupled to a one-dimensional waveguide. Photons confined in the waveguide have strong interference effects, which are shown to play a vital role in quantum jumps and photon statistics. For a single qubit, for instance, the bunching of transmitted photons is heralded by a jump that increases the qubit population. We show that the distribution and correlations of waiting times offer a clearer and more precise characterization of photon bunching and antibunching. Further, the waiting times can be used to characterize complex correlations of photons which are hidden in g(2)(τ), such as a mixture of bunching and antibunching.Item Open Access Stabilizing spin coherence through environmental entanglement in strongly dissipative quantum systems(Physical Review B - Condensed Matter and Materials Physics, 2014-03-18) Bera, S; Florens, S; Baranger, HU; Roch, N; Nazir, A; Chin, AWThe key feature of a quantum spin coupled to a harmonic bath - a model dissipative quantum system - is competition between oscillator potential energy and spin tunneling rate. We show that these opposing tendencies cause environmental entanglement through superpositions of adiabatic and antiadiabatic oscillator states, which then stabilizes the spin coherence against strong dissipation. This insight motivates a fast-converging variational coherent-state expansion for the many-body ground state of the spin-boson model, which we substantiate via numerical quantum tomography. © 2014 American Physical Society.Item Open Access Strongly correlated photons generated by coupling a three- or four-level system to a waveguide(Physical Review A - Atomic, Molecular, and Optical Physics, 2012-04-19) Zheng, H; Gauthier, DJ; Baranger, HUWe study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on demand by sending coherent states into the proposed system. We calculate the second-order correlation function of the transmitted field and observe bunching and antibunching caused by the bound states. Furthermore, we demonstrate that the proposed system can produce photon pairs with a high degree of spectral entanglement, which have a large capacity for carrying information and are important for large-alphabet quantum communication. © 2012 American Physical Society.Item Open Access Time-dependent transport through molecular junctions.(J Chem Phys, 2010-06-21) Ke, SH; Liu, R; Yang, W; Baranger, HUWe investigate transport properties of molecular junctions under two types of bias--a short time pulse or an ac bias--by combining a solution for Green's functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency ac bias, the electron flow either tracks or leads the bias signal (resistive or capacitive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.