# Browsing by Author "Baranger, Harold U"

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Item Open Access Cavity-free photon blockade induced by many-body bound states.(Physical review letters, 2011-11) Zheng, Huaixiu; Gauthier, Daniel J; Baranger, Harold UThe manipulation of individual, mobile quanta is a key goal of quantum communication; to achieve this, nonlinear phenomena in open systems can play a critical role. We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an N-type four-level system. We focus on photon blockade and the creation of single-photon states in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, which can generate a sub-Poissonian single-photon source.Item Open Access Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point(Physical Review B, 2021-10-25) Zhang, Gu; Novais, E; Baranger, Harold UWe 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.Item Open Access Decoy-state quantum key distribution with nonclassical light generated in a one-dimensional waveguide.(Optics letters, 2013-03) Zheng, Huaixiu; Gauthier, Daniel J; Baranger, Harold UWe investigate a decoy-state quantum key distribution (QKD) scheme with a sub-Poissonian single-photon source, which is generated on demand by scattering a coherent state off a two-level system in a one-dimensional waveguide. We show that, compared to coherent state decoy-state QKD, there is a two-fold increase of the key generation rate. Furthermore, the performance is shown to be robust against both parameter variations and loss effects of the system.Item Open Access Driven-Dissipative Phase Transition in a Kerr Oscillator: From Semi-Classical PT Symmetry to Quantum Fluctuations.(Physical Review A, 2021-03-24) Zhang, Xin HH; Baranger, Harold UWe 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, Z2 symmetry breaking, 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.Item Open Access Dynamics of Open Quantum Systems: Measurement, Entanglement, and Criticality(2020) Zhang, Xin H. H.Open quantum systems refer to quantum systems that couple with their surrounding environment. They are ubiquitous, especially for quantum devices. Due to coupling with the external environment, the dynamics of open quantum systems becomes non-unitary, which leads to additional complexity and novel possibilities compared to the unitary dynamics of closed systems. The study of open quantum systems is therefore of both theoretical and practical interest.

In this dissertation, using paradigmatic models of (Markovian) open quantum systems, I study three aspects of open quantum systems: (i) measurement of emitted particles from an open quantum system, to probe its dynamics; (ii) quantum entanglement in open quantum systems, which demonstrates the significance of information gained from measurement; and (iii) quantum critical phenomena in an open quantum many-body system. The first part is of importance for probing dynamics of open quantum systems and for engineering quantum states of emitted particles using engineered open quantum systems. The second part is from the quantum information point of view, which clearly demonstrates the subtle relation between quantum entanglement of mixed states and measurement in open quantum systems. An entanglement generation protocol is provided, which can be useful for quantum information processing. The last part is concerned with open quantum many-body physics, which demonstrates the basic mechanism behind phase transitions in open quantum systems. The differences and similarities between Lindbladian and Hamiltonian phase transitions are shown from various perspectives.

Item Open Access Entropy production and equilibration in Yang-Mills quantum mechanics(2011) Tsai, Hung-MingEntropy production in relativistic heavy-ion collisions is an important physical quantity for studying the equilibration and thermalization of hot matters of quantumchromodynamics (QCD). To formulate a nontrivial definition of entropy for an isolated quantum system, a certain kind of coarse graining may be applied so that the entropy for this isolated quantum system depends on time explicitly. The Husimi distribution, which is a coarse grained distribution in the phase space, is a suitable candidate for this approach. We proposed a general and systematic method of solving the equation of motion of the Husimi distribution for an isolated quantum system. The Husimi distribution is positive (semi-)definite all over the phase space. In this method, we assume the Husimi distribution is composed of a large number of Gaussian test functions. The equation of motion of the Husimi distribution, formulated as a partial differential equation, can be transformed into a system of ordinary differential equations for the centers and the widths of these Gaussian test functions. We numerically solve the system of ordinary differential equations for the centers and the widths of these test functions to obtain the Husimi distribution asa function of time. To ensure the numerical solutions of the trajectories of the test particles preserve physical conservation laws, we obtain a constant of motion for the quantum system. We constructed a coarse grained Hamiltonian whose expectation value is exactly conserved. The conservation of the coarse grained energy confirms the validity of this method. Moreover, we calculated the time evolution of the coarse grained entropy for a model system (Yang-Mills quantum mechanics). Yang-Mills quantum mechanics is a quantum system whose classical correspondence possesses chaotic behaviors. The numerical results revealed that the coarse grained entropy for Yang-Mills quantum mechanics saturates to a value that coincides with the micro-canonical entropy corresponding to the energy of the system. Our results confirmed the validity of the framework of first-principle evaluation of the coarse grained entropy growth rate. We show that, in the energy regime under study, the relaxation time for the entropy production in Yang-Mills quantum mechanics is approximately the same as the characteristic time of the system, indicating fast equilibration of the system. Fast equilibration of Yang-Mills quantum mechanics is consistent to current understanding of fast equilibration of hot QCD matter in relativistic heavy-ion collisions.Item Open Access Exciting a Bound State in the Continuum through Multiphoton Scattering Plus Delayed Quantum Feedback.(Physical review letters, 2019-02) Calajó, Giuseppe; Fang, Yao-Lung L; Baranger, Harold U; Ciccarello, FrancescoExcitation 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 multiphoton 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 multiphoton 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 multiphoton scattering can occur without band edge effects or cavities, the essential resource being instead the delayed quantum feedback provided by a single mirror or the emitters themselves.Item Open Access Floquet Majorana fermions for topological qubits in superconducting devices and cold-atom systems.(Physical review letters, 2013-07) Liu, Dong E; Levchenko, Alex; Baranger, Harold UWe develop an approach to realizing a topological phase transition and non-Abelian braiding statistics with dynamically induced Floquet Majorana fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasienergy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasienergy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian braiding statistics and, thus, behave like their equilibrium counterparts.Item Open Access GaAsBi Synthesis: From Band Structure Modification to Nanostructure Formation(2017) Collar, Kristen N.Research and development bismides have proven bismides to be a promising field for material science with important applications in optoelectronics. However, the development of a complete description of the electrical and material properties of bismide ternaries is not comprehensive or straightforward. One of the main benefits of this ternary system is the opportunity for bandgap tuning, which opens doors to new applications. Tuning the bandgap is achieved by means of varying the composition; this allows access to a wider energy spectrum with particular applications in long wavelength emitters and detectors. In addition to bandgap tuning, Bi provides an opportunity to decrease lasing threshold currents, the temperature sensitivity and a major loss mechanism of today’s telecom lasers.

We propose to characterize the electronic and chemical structure of GaAsBi grown by molecular beam epitaxy. We probe the binding structure using x-ray photoelectron spectroscopy. This provides insights into the antisite incorporation of Bi and the reactivity of the surface. Furthermore, we use XPS to track the energy variation in the valence band with dilute Bi incorporation into GaAs. These insights provide valuable perspective into improving the predictability of bandgaps and of heterostructure band offsets for the realization of bismides in future electronics.

The stringent growth conditions required by GaAsBi and the surfactant properties of Bi provide a unique opportunity to study nanostructure formation and epitaxial growth control mechanisms. The GaAsBi epitaxial films under Ga-rich growth conditions self-catalyze Ga droplet seeds for Vapor-Liquid-Solid growth of embedded nanowires. We demonstrate a means to direct the nanowires unidirectionally along preferential crystallographic directions utilizing the step-flow growth mode. We mediated the step-flow growth by employing vicinal surfaces and Bi’s surfactant-like properties to enhance the properties of the step-flow growth mode. Semiconductor nanostructures are becoming a cornerstone of future optoelectronics and the work presented herein exploits the power of a bottom-up architecture to self-assemble aligned unidirectional planar nanowires.

Item Open Access Heralded Bell State of Dissipative Qubits Using Classical Light in a Waveguide.(Physical Review Letters, 2019-04-09) Zhang, Xin HH; Baranger, Harold UMaximally 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 that 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.Item Open Access Interacting Photons in Waveguide-QED and Applications in Quantum Information Processing(2013) Zheng, HuaixiuStrong coupling between light and matter has been demonstrated both in classical

cavity quantum electrodynamics (QED) systems and in more recent circuit-QED

experiments. This enables the generation of strong nonlinear photon-photon interactions

at the single-photon level, which is of great interest for the observation

of quantum nonlinear optical phenomena, the control of light quanta in quantum

information protocols such as quantum networking, as well as the study of

strongly correlated quantum many-body systems using light. Recently, strong

coupling has also been realized in a variety of one-dimensional (1D) waveguide-

QED experimental systems, which in turn makes them promising candidates for

quantum information processing. Compared to cavity-QED systems, there are

two new features in waveguide-QED: the existence of a continuum of states and

the restricted 1D phase space, which together bring in new physical effects, such

as the bound-state effects. This thesis consists of two parts: 1) understanding the

fundamental interaction between local quantum objects, such as two-level systems

and four-level systems, and photons confined in the waveguide; 2) exploring

its implications in quantum information processing, in particular photonic

quantum computation and quantum key distribution.

First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel

system to a 1D continuum, strongly-correlated photons can be generated

inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering

processes. As a result, photon bunching and antibunching can be observed

in the photon-photon correlation function, and nonclassical light source can be

generated on demand. In the case of an N-type four-level system, we show

that the effective photon-photon interaction mediated by the four-level system,

gives rise to a variety of nonlinear optical phenomena, including photon blockade,

photon-induced tunneling, and creation of single-photon states and photon

pairs with a high degree of spectral entanglement, all in the absence of a cavity.

However, to enable greater quantum networking potential using waveguide-

QED, it is important to study systems having more than just one TLS/qubit.

We develop a numerical Green function method to study cooperative effects in

a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in

photon-photon correlations, and persist to much longer time scales because of

non-Markovian processes. In addition, this system can be used to generate a

high-degree of long-distance entanglement when one of the two qubits is driven

by an on-resonance laser, further paving the way toward waveguide-QED-based

quantum networks.

Furthermore, based on our study of light-matter interactions in waveguide-

QED, we investigate its implications in quantum information processing. First,

we study quantum key distribution using the sub-Possonian single photon source

obtained by scattering a coherent state off a two-level system. The rate for key

generation is found to be twice as large as for other sources. Second, we propose

a new scheme for scalable quantum computation using flying qubits--propagating

photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton

interactions are mediated by the coupling to a three- or four-level system,

based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is

possible given recent dramatic experimental progress in superconducting circuits

and photonic-crystal waveguides. The proposed system can be an important

building block for future on-chip quantum networks.

Item Open Access Interference of chiral Andreev edge states(Nature Physics, 2020-08-01) Zhao, Lingfei; Arnault, Ethan G; Bondarev, Alexey; Seredinski, Andrew; Larson, Trevyn; Draelos, Anne W; Li, Hengming; Watanabe, Kenji; Taniguchi, Takashi; Amet, François; Baranger, Harold U; Finkelstein, Gleb© 2020, The Author(s), under exclusive licence to Springer Nature Limited. 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, which we refer to as chiral Andreev edge states (CAESs). These propagate along the interface in the direction determined by the magnetic field and their interference can turn an incoming electron into an outgoing electron or hole, depending on the phase accumulated by the CAESs along their path. Our results demonstrate that these excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation.Item Open Access Particle Production in Ultrastrong-Coupling Waveguide QED(Physical Review A, 2018-10-08) Gheeraert, Nicolas; Zhang, Xin HH; Sépulcre, Théo; Bera, Soumya; Roch, Nicolas; Baranger, Harold U; Florens, SergeUnderstanding 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 of multimode coherent states. This key idea is illustrated by the study of multiphoton emission from a single two-level artificial atom coupled to a high impedance waveguide, driven by a nearly monochromatic coherent tone. We find surprisingly that the off-resonant inelastic emission line shape 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.Item Open Access Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions.(Physical review letters, 2013-03) Zheng, Huaixiu; Baranger, Harold UWe study photon-photon correlations and entanglement generation in a one-dimensional waveguide coupled to two qubits with an arbitrary spatial separation. To treat the combination of nonlinear elements and 1D continuum, we develop a novel Green function method. The vacuum-mediated qubit-qubit interactions cause quantum beats to appear in the second-order correlation function. We go beyond the Markovian regime and observe that such quantum beats persist much longer than the qubit lifetime. A high degree of long-distance entanglement can be generated, increasing the potential of waveguide-QED systems for scalable quantum networking.Item Open Access Probing Exotic Boundary Quantum Phases with Tunable Nanostructure(2012) Liu, DongBoundary quantum phases ---a special type of quantum phenomena--- occur in the boundary part of the system. The boundary part can be a surface of a bulk material, an interface between two distinct system, and even it can be a single impurity or a impurity cluster embedded into a bulk system. The properties of the boundary degree of freedom can be affected by many strong electron correlation effects, mesoscopic effects, and topological effects, which, therefore, induce a vast variety of exotic boundary quantum phases. Many techniques for precise fabrication and measurement in nanostructures had been developed,

which can provide ways to prob, understand, and control those boundary quantum phases.

In this thesis, we focus on three types of the boundary quantum phases : Kondo effects, boundary quantum phase transitions, and Majorana fermions. Our motivation is to design and prob those effects by using a important type of nanostructures, i.e. quantum dots. A vast variety of models related to quantum dots (QDs) are studied theoretically, which includes a QD coupled to a mesoscopic bath, a quadruple QD system with metallic leads, a QD with dissipative environments, and a QD coupled to a Majorana fermion zero mode.

Quantum dots provide a way to study the interplay of Kondo effects and mesoscopic fuctuations. In chapter 5, we consider a model including an Anderson impurity (small QD) coupled to a mesoscopic bath (large QD). Both the weak and strong coupling Anderson impurity problems are characterized by Fermi-liquid theories with weakly interacting quasiparticles. We find that the fluctuations of single particle properties in the two limits are highly correlated and universal : The distributions of the spectrum within the Kondo temperature collapse to universal forms; and the strong coupling impurity changes the wave functions corresponding to the spectrum within the Kondo temperature.

Quantum dots also bring the possibility to study more complex quantum impurities (multi-QDs) and the competition among dierent interactions, which may induce exotic effects: boundary quantum phase transitions and novel Kondo effects. In chapter 7, we design a quadruple quantum dot system to study the competition among three types of interactions: Kondo, Heisenberg, and Ising. We find a rich phase diagram containing two sharp features : a Berezinsky-Kosterlitz-Thouless type quantum phase transition between a charge-ordered phase and a charge liquid phase and a U(1)XU(1) Kondo state with emergent symmetry from Z2 to U(1). In chapter 8, we study a dissipative resonant level model in which the coupling of a fermionc bath competes with a dissipation-induced bosonic bath. we establish an exact mapping from this dissipative resonant level model to a model of a quantum dot embedded into a Luttinger liquid wire, and we also find two kinds of boundary quantum phase transitions (a Berezinsky-Kosterlitz-Thouless type and a second order type).

Finally, in chapter 9, we propose an experimental system to detect Majorana fermion zero modes. This system consists of a spinless quantum do coupled to a Majorana fermion which exists in the end of a p-wave superconductor wire. The Majorana Fermion strongly infuence the transport properties of the quantum dot. The zero temperature conductance peak value (when the dot is on resonance and symmetrically coupled to the leads) is e^2/2h. In contrast, if the wire is in its topological trivial phase, the result is e^2/h; if the side-coupled mode is a regular fermionic zero mode, the result is zero. Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. This result can be used to detect the existence of Majorana fermions.

Item Open Access Quantum phase transition in a resonant level coupled to interacting leads.(Nature, 2012-08) Mebrahtu, Henok T; Borzenets, Ivan V; Liu, Dong E; Zheng, Huaixiu; Bomze, Yuriy V; Smirnov, Alex I; Baranger, Harold U; Finkelstein, GlebA Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.Item Open Access Rescuing a Quantum Phase Transition with Quantum Noise.(Physical review letters, 2017-02) Zhang, Gu; Novais, E; Baranger, Harold UWe 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.Item Open Access Stabilization of a Majorana Zero Mode through Quantum Frustration.(Physical Review B, 2020-07-01) Zhang, Gu; Baranger, Harold UWe analyze a system in which a topological Majorana zero mode (MZM) combines with a MZM produced by quantum frustration. At the boundary between the topological and non-topological states, a MZM does not appear. The system that we study combines two parts, a grounded topological superconducting wire that hosts two MZM 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 MZM at the dot. We find that coupling the dot to one of the wire Majoranas stabilizes the MZM at the other end of the wire. 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 Majorana.Item Open Access Studies on the effect of noise in boundary quantum phase transitions(2018) Zhang, GuBoundary quantum phase transitions are abrupt ground state transitions triggered by the change of the boundary conditions at single or multiple (but finite) points.

When boundary effects dominate, understanding boundary quantum phase transitions requires a deeper knowledge of strongly correlated electron systems that is beyond the widely applied mean field treatment.

Meanwhile, with strong boundary effect, most systems with boundary quantum phase transition can generally be considered as effectively zero-dimensional, with reservoir details ignored. Consequently, the critical features of boundary quantum phase transitions only involve long-time correlations instead of long-range ones.

On the other hand, different from the geometrical confinement of boundaries, dissipation or quantum noise widely exists along the entire system.

In bulk quantum phase transitions, dissipation decreases system coherence by reducing the long-range correlations.

This fact makes it plausible that dissipation destroys the critical behavior of the quantum critical points.

The effect of dissipation, however, remains unclear in boundary quantum phase transition systems due to their lack of long-range correlations.

In this thesis I thus focus on the effect of dissipation in boundary quantum phase transitions.

These studies are motivated and encouraged by recent experimental triumphs where dissipation is realized and precisely measured in mesoscopic systems, which provide experimental evidences to check theoretical researches.

This thesis involves multiple dissipative mesoscopic systems, including the dissipative two impurity Kondo, two channel Kondo, resonant level, and Anderson models.

To begin with, the effect of dissipation in two impurity Kondo model has been explored and we find that the presence of dissipation restores the quantum phase transition by reducing the unwanted charge tunneling process. We further provide the phase diagram for the system that has an exotic double-quantum-critical-point feature.

After that, the non-equilibrium $I$-$V$ feature of a dissipative resonant level model is studied.

This model has been experimentally proven to host a boundary quantum phase transition.

With different tuning parameters, we calculate the $I$-$V$ feature at both the quantum critical point and in the crossover regime analytically. The theoretical calculation agrees remarkably with the experimental data.

As the spinful version of the resonant level model, the dissipative Anderson model has multiple unique features, including the experimentally observed peak position shifting and dissipation dependent saturated peak conductance. Through renormalization group studies and mapping the model to the quantum Brownian motion model, we understand these features qualitatively.

As an example of the application of above research achievements, we study the stabilization of a Majorana zero mode with the quantum frustration in a dissipative resonant level model. The Majorana zero mode is known to be unstable against the coupling to its partner at the other end of the Majorana hosted nanowire.

We prove that the Majorana zero mode can be stabilized by coupling its partner to the quantum dot of a frustrated dissipative resonant level model, where an isolated impurity Majorana fermion is produced.

Finally, we study the relation between boundary quantum phase transitions and geometric phases. The calculation is carried out at the Toulouse point of a dissipative resonant level model.

Although it satisfies the criteria of bulk quantum phase transitions to host a non-trivial geometric phase, the dissipative resonant level model has zero geometric phase due to the identical zero geometric curvature. This phenomenon is generally explained by studying the geometric tensor of boundary quantum phase transition-hosted systems.

Item Open Access Waveguide QED: Multiple Qubits, Inelastic Scattering, and Non-Markovianity(2017) Fang, Yao-Lung LeoWaveguide quantum electrodynamics (QED) studies multi-level systems (or qubits) strongly interacting with one-dimensional (1D) light fields confined in a waveguide. This rapidly growing research field attracts much attention because it provides a fascinating platform for many-body physics, quantum nonlinear optics, as well as open quantum systems (OQS). On this platform, researchers are able to control single qubit using single photons and vice versa, based on which many potential applications in quantum information processing and quantum computing are proposed. Due to the reduced dimensionality, the coupling between light and matter is greatly enhanced and so is the light interference. This, together with the strong nonlinearity provided by the qubits, results in striking quantum-optical effects at the few-photon level, which have been demonstrated experimentally in the past few years on various systems such as superconducting circuits thanks to the explosive experimental progress.

While much has been known with regard to a single qubit in an infinite waveguide, it is less understood how multiple qubits would reshape the properties of 1D light. For instance, there can be effective interaction between a pair of qubits in a waveguide even in the absence of dipole-dipole interaction, which in turn causes a splitting in the power spectra and interesting bunching and anti-bunching effects for the photons. Moreover, from the OQS point of view, the systems (qubits) and its environment (photons) are highly correlated, so it is natural to question and test the validity of Markovian dynamics in a waveguide-QED setup.

In this thesis, I consider two or more distant qubits present in a waveguide under weak driving. The role of inelastic scattering and its connection to dark states and photon correlations are emphasized. I report two-photon scattering wavefunction for multiple qubits (N>2) in an infinite or semi-infinite waveguide. The latter has a perfect mirror at the end that reflects all of the incident photons. I find that by tuning the separation between each qubit it is possible to have stronger (anti-)correlations compared to the single-qubit case, and that the correlation can last over hundreds of the lifetime of a single qubit. The inelastic scattering is highly sensitive to the qubit-qubit (or qubit-mirror) separation and the incident frequency due to the narrow widths caused by the dark states. I also investigate the differences in scattering due to the level structure of the qubits, including two-level systems (2LS), three-level systems (3LS), and their mixture. For example, I find that a "2-3-2" setup --- two distant 2LS sandwiching a 3LS --- can either rectify photons or induce correlation among elastically transmitted photons.

I further propose a simple waveguide-QED system as a model system for OQS studies owing to its complex yet exactly solvable nature. To this end, a time-dependent scattering is considered, from which a dynamical map describing the system evolution can be obtained. In combination with OQS tools, I present detailed analysis for the non-Markovian properties of the system, and point out that the scattering setup generally gives rise to a different class of dynamical maps that are largely unexplored in conventional OQS studies. The parameters considered throughout this thesis are fully accessible with existing experimental technology, so realistic tests of my work are within reach.