# Browsing by Subject "Condensed matter physics"

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Item Open Access AC Measurements of Graphene-Superconductor Devices(2022) Larson, TrevynThe field of quantum transport studies electron motion at low temperatures in nanos-tructures. Exciting electron phenomenon can be engineered by combining device designs like quantum dots, Josephson junctions, and interferometers with materials which host physics such as various quantum Hall effects and superconductivity. Com- binations of these ingredients can be mixed to design a device which is then cooled down and has its I ́ V curves measured while tuning key physical parameters, such as magnetic field, temperature, and gate electrode voltages. These time independent (DC) measurements can provide a wealth of information, but ultimately they can only access highly averaged physical properties. Fortunately, this is not a fundamental constraint. By measuring the emission of and response to higher frequency signals, we are able to access additional properties of our devices. This dissertation explores two projects related to time oscillating (AC) measure- ments of graphene devices with superconducting contacts. The first project is related to the measurement of “Shapiro steps” in graphene based Josephson junctions. By applying a gigahertz drive to the junction, it becomes possible to probe the dynamics of the phase difference of the junction. The work presented here explores the effects of the RF environment on the Shapiro step pattern, and on a bistability observed in this system. The second project addresses the noise measured downstream of a superconduct- ing contact for a device in the quantum Hall regime. Recent work has observed the coupling of superconductivity to a quantum Hall edge, a promising test-bed for mix- ing superconductivity with topological physics. However, the signal in real devices remains fairly small compared to the ideal limit. Noise measurements should allow us to probe the microscopics in these devices, but we find indications that signals seemingly related to contact heating obscure the desired signal. Additional devices which should show a tunable signal amplitude show only very small signal variation, opening questions about what physical phenomena may be suppressing this noise.

Item Open Access An experimental study of the jamming phase diagram for two-dimensional granular materials.(2020) Zhao, YiqiuWhat affects the transition of a collection of grains from flowing to a rigid packing? Previous efforts towards answering this important question have led to various versions of ``jamming’’ phase diagrams, which specify conditions under which a granular material behaves like solid, i.e., in a jammed phase. In this dissertation, we report two sets of experiments to study the influence of particle shape and of the form of the applied shear strain on the jamming phase diagram of slowly deformed frictional granular materials. We use 2d photoelastic particles to measure the overall pressure of the system and various physical quantities that characterize the contact network such as the averaged number of contacts per particle.

In the first set of experiments, we systematically compare the mechanical and geometrical properties of uniaxially compressed granular materials consisting of particles with shapes of either regular pentagon or disk. The compression is applied quasi-statically and induces a density-driven jamming transition. We find that pentagons and disks jam at similar packing fraction. At the onset of jamming, disks have contact numbers consistent with predictions from an ideal constraint counting argument. However, this argument fails to predict the right contact number for pentagons. We also find that both jammed pentagons and disks show the Gamma distribution of the Voronoi cell area with the same parameters. Moreover, jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. Finally, we report observations that for jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.

In the second set of experiments, we use a novel multi-ring Couette shear apparatus that we developed to eliminate shear banding which unavoidably appears in conventional Couette shear experiments. A shear band is a narrow region where a lot of rearrangements of particles occur. The shear band usually has a much smaller packing fraction than the rest of the system. We map out a jamming phase diagram experimentally, and for the first time perform a systematic direct test of the mechanical responses of the jammed states created by shearing under reverse shear. We find a clear distinction between fragile states and shear-jammed states: the latter do not collapse under reverse shear. The yield stress curve is also mapped out, which marks the stress needed for the shear-jammed states to enter a steady regime where many plastic rearrangements of particles happen and the overall stress fluctuates around a constant. Interestingly, for large packing fraction, a shear band still develops when the system remains strongly jammed in the steady regime. We find that the cooperative motion of particles in this regime is highly heterogeneous and can be quantified by a dynamical susceptibility, which keeps growing as the packing fraction increases.

Our observations not only serve as important data to construct theories to explain the origin of rigidity in density-driven jamming and shear-induced jamming but also are relevant to many other key problems in the physics of granular matter from the stability of a jammed packing to the complex dynamics of dense granular flows.

Item Open Access Andreev conversion in the quantum Hall regime(2022) Zhao, LingfeiHigh quality type-II superconducting contacts have recently been developed for a variety of 2D systems, allowing one to explore superconducting proximity in the quantum Hall (QH) regime, which is one of the routes for creating exotic topological states and excitations. Here, we experimentally 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 (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 paths. However, the observed signals are small in comparison to theoretical predictions which calls for a better understanding of the limitations imposed by the physics of real materials. We then perform a systematic study of Andreev conversion in the QH regime. We find that the probability of Andreev conversion of electrons to holes follows an unexpected but clear trend: the dependencies on temperature and magnetic field are nearly decoupled. These trends unveil the loss and decoherence mechanisms of CAES. To complement our understanding of a QH-superconductor interface, we also study the thermal response under tens of nA current bias. We find that the superconductor is significantly overheated at low field in comparison to a similar-sized normal metal and the temperature distribution is not uniform. Our results demonstrate the existence of chiral edge states propagating along a QH-superconductor interface and interfering over a significant length. The study of the loss, decoherence and overheating of these states further paves the way for engineering topological superconductivity in exotic quantum circuits.

Item Open Access Crystal Symmetry Algorithms in a High-Throughput Framework for Materials Research(2013) Taylor, Richard HansenThe high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.

Item Embargo Driven-dissipative Phase Transitions for Markovian Open Quantum Systems(2024) Zhang, YikangDue to recent experimental progress on highly controllable quantum systems, increasing attention has been paid to open quantum systems, where driving and dissipation can lead to undesirable decoherence but may also stabilize interesting states and lead to new physics. Theoretically speaking, the generator of the dynamics (called the Liouvillian) for open quantum systems is non-Hermitian, giving rise to phenomena not allowed in closed systems.This dissertation mainly studies dissipative phase transitions in open systems where the steady state undergoes a non-analytic change at the transition point. We apply various analytic methods to investigate different open many-body models. (i) We study open systems where the Liouvillian can be brought into a block-triangular form. This allows us to bound the spectral gap from below, showing that, in a large class of systems, dissipative phase transitions are impossible. (ii) We perform perturbative treatment to spin-1/2 systems with a large dephasing channel and study the non-Hermitian skin effect in such systems. (iii) We establish the solvability of quadratic open systems using the third-quantization technique. With this, we further investigate quadratic fermionic and bosonic systems respectively. We find that criticality is not allowed for quadratic fermionic systems while we find examples of bosonic criticality for d>=2 dimensional quadratic systems. We also establish a proposition stating that without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase. (iv) We employ Keldysh field theory to study dissipative Bose-Einstein condensation. With the one-loop renormalization group calculation, we elucidate the universality class to which this phase transition belongs. (v) We study the mathematical structure of the Liouvillian and establish an algebraic condition for the irreducibility of the Liouvillian. Irreducibility will lead to the uniqueness and faithfulness of the steady state.

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 Eigenstate Entanglement Scaling and Quantum Simulation of Many-body Systems by Entanglement Renormalization(2022) Miao, QiangQuantum entanglement lies at the heart of modern physics and pervades various research fields. In the field of quantum many-body physics, celebrated area and log-area laws have been established for the entanglement entropy of ground states. However, there exists a long-standing question regarding the transition of eigenstate entanglement entropy from the ground state to the highly excited states. Our study fills this gap and elucidates a crossover behavior with universal scaling properties. In the study of quantum matters, knowledge about the entanglement structure can be used to guide the design of tensor network state simulations. For example, we may iteratively eliminate short-range entanglement in a so-called entanglement renormalization scheme so that the entangled ground state is mapped to a product state and then resolved exactly. This idea can be adapted to hybrid quantum-classical algorithms and speed up the simulation of strongly correlated quantum many-body systems.

In the first part of this dissertation, we investigate eigenstate entanglement scaling in quantum many-body systems and characterize the crossover from the ground-state entanglement regime at low energies and small subsystem sizes to extensive volume laws at high energies or large subsystem sizes. We first establish a weak eigenstate thermalization hypothesis (ETH) for translation-invariant systems, argue that the entanglement entropies of (almost) all energy eigenstates are described by a single crossover function whenever the (weak) ETH applies, and point out the universal scaling properties in the quantum critical regime. We then comprehensively confirm these scaling properties by analyzing large classes of quantum many-body systems. Particularly, we give the eigenstate entanglement scaling functions in analytical form for critical one-dimensional systems based on conformal field theory and for $d$-dimensional fermionic systems with Fermi surfaces. For $d=1,2,3$ non-interacting fermions, the scaling functions are numerically verified, and for $d=1,2,3$ harmonic lattice models (free scalar field theory), they are numerically determined. ETH is confirmed with Monte Carlo methods by sampling energy eigenstates or squeezed states for fermions or bosons with $d=1,2$. We also probe and confirm the described scaling properties and the applicability of the ETH in integrable and non-integrable interacting spin-1/2 chains by using exact diagonalization. All the evidence appearing here strongly suggests the existence of crossover functions. Their transition from ground-state scaling to extensive scaling, as well as the universal scaling properties in quantum-critical regimes, are generic.

In the second part of this dissertation, we present a quantum-classical tensor network state algorithm for condensed matter systems. First, we describe this algorithm, which is based on the multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimizations. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. We show that the number of required qubits is independent of the system size, increasing only to logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translational invariance can be used to make the computational cost square-logarithmic with respect to the system size and to describe the thermodynamic limit. The method is particularly attractive for ion-trap devices with ion shuttling capabilities. We then demonstrate it numerically for MERA with Trotterized disentanglers and isometries and find that the computational cost of such MERA quantum eigensolvers is substantially lower than that of the corresponding classical algorithms. In particular, numerical results in various strongly-correlated quantum magnet models show that it has a polynomial quantum advantage over the classical approach. In the experimental implementation, small angles in the employed two-qubit quantum gates are advantageous. We find that, by adding an angle penalty term to the energy functional, the average absolute values of the angles can be moderately reduced without significantly affecting the energy accuracies. Finally, we propose that the Trotter-type circuit in each tensor can be replaced by a parallel random circuit. However, this replacement does not seem to result in further gains as long as the tensor-network bond dimensions are small.

Item Open Access Electron Transport through Carbon Nanotube Quantum Dots in A Dissipative Environment(2012) Mebrahtu, Henok TesfamariamThe role of the surroundings, or environment , is essential in understanding funda- mental quantum-mechanical concepts, such as quantum measurement and quantum entanglement. It is thought that a dissipative environment may be responsible for certain types of quantum (i.e. zero-temperature) phase transitions. We observe such a quantum phase transition in a very basic system: a resonant level coupled to a dissipative environment. Specifically, the resonant level is formed by a quantized state in a carbon nanotube, and the dissipative environment is realized in resistive leads; and we study the shape of the resonant peak by measuring the nanotube electronic conductance.

In sequential tunneling regime, we find the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weakly than the conventional T-1. Moreover, the observed scaling signals a close connec- tion between fluctuations that influence tunneling phenomenon and macroscopic models of the electromagnetic environment.

In the resonant tunneling regime (temperature smaller than the intrinsic level width), we characterize the resonant conductance peak, with the expectation that the width and height of the resonant peak, both dependent on the tunneling rate, will be suppressed. The observed behavior crucially depends on the ratio of the coupling between the resonant level and the two contacts. In asymmetric barriers the peak width approaches saturation, while the peak height starts to decrease.

Overall, the peak height shows a non-monotonic temperature dependence. In sym- metric barriers case, the peak width shrinks and we find a regime where the unitary conductance limit is reached in the incoherent resonant tunneling. We interpret this behavior as a manifestation of a quantum phase transition.

Finally, our setup emulates tunneling in a Luttinger liquid (LL), an interacting one-dimensional electron system, that is distinct from the conventional Fermi liquids formed by electrons in two and three dimensions. Some of the most spectacular properties of LL are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Our setup allows us to address many prediction of resonant tunneling in a LL, which have not been experimentally tested yet.

Item Open Access Electronic and Spin Correlations in Asymmetric Quantum Point Contacts(2014) Zhang, HaoA quantum point contact (QPC) is a quasi-one dimensional electron system, for which the conductance is quantized in unit of $2e^2/h$. This conductance quantization can be explained in a simple single particle picture, where the electron density of states cancels the electron velocity to a constant. However, two significant features in QPCs were discovered in the past two decades, which have drawn much attention: the 0.7 effect in the linear conductance and zero-bias-anomaly (ZBA) in the differential conductance. Neither of them can be explained by single particle pictures.

In this thesis, I will present several electron correlation effects discovered in asymmetric QPCs, as shown below:

The linear conductance of our asymmetric QPCs shows conductance resonances. The number of these resonances increases as the QPC channel length increases. The quantized conductance plateau is also modulated by tuning the gate voltage of the QPCs. These two features, observed in the linear conductance, are ascribed to the formation of quasi-bound states in the QPCs, which is further ascribed to the electron-correlation-induced barriers.

The differential conductance for long channel QPCs shows the zero-bias-anomaly for every other linear conductance resonance valley, suggesting a near even-odd behavior. This even-odd law can be interpreted within the electron-correlation-induced barrier picture, where the quasi-localized non-zero spin in the quasi-bound state (Kondo-like) couples to the Fermi sea in the lead. For a specific case, triple-peak structure is observed in the differential conductance curves, while the electron filling number is still even, suggesting a spin triplet formation at zero magnetic field.

Small differential conductance oscillations as a function of bias voltage were discovered and systematically studied in an asymmetric QPC sample. These oscillations are significantly suppressed in a low in-plane magnetic field, which is completely unexpected. The oscillations are washed out when the temperature is increased to 0.8K. Numerical simulation, based on the thermal smearing of the Fermi distribution, was performed to simulate the oscillation behavior at high temperatures, using the low temperature data as an input. This simulation agrees with the oscillations off zero-bias region, but does not agree with the temperature evolution of the structure near zero-bias. Based on the above oscillation characteristics, all simple single particle pictures were carefully considered, and then ruled out. After exhausting all these pictures, we think these small oscillations are related to novel electronic and spin correlations.

Item Open Access Fermion Bag Approach for Hamiltonian Lattice Field Theories(2018) Huffman, EmilieUnderstanding the critical behavior near quantum critical points for strongly correlated quantum many-body systems remains intractable for the vast majority of scenarios. Challenges involve determining if a quantum phase transition is first- or second-order, and finding the critical exponents for second-order phase transitions. Learning about where second-order phase transitions occur and determining their critical exponents is particularly interesting, because each new second-order phase transition defines a new quantum field theory.

Quantum Monte Carlo (QMC) methods are one class of techniques that, when applicable, offer reliable ways to extract the nonperturbative physics near strongly coupled quantum critical points. However, there are two formidable bottlenecks to the applicability of QMC: (1) the sign problem and (2) algorithmic update inefficiencies. In this thesis, I overcome both these difficulties for a class of problems by extending the fermion bag approach recently developed by Shailesh Chandrasekharan to the Hamiltonian formalism and by demonstrating progress using the example of a specific quantum system known as the $t$-$V$ model, which exhibits a transition from a semimetal to an insulator phase for a single flavor of four-component Dirac fermions.

I adapt the fermion bag approach, which was originally developed in the context of Lagrangian lattice field theories, to be applicable within the Hamiltonian formalism, and demonstrate its success in two ways: first, through solutions to new sign problems, and second, through the development of new efficient QMC algorithms. In addressing the first point, I present a solution to the sign problem for the $t$-$V$ model. While the $t$-$V$ model is the simplest Gross-Neveu model of the chiral Ising universality class, the specter of the sign problem previously prevented its simulation with QMC for 30 years, and my solution initiated the first QMC studies for this model. The solution is then extended to many other Hamiltonian models within a class that involves fermions interacting with quantum spins. Some of these models contain an interesting quantum phase transition between a massless/semimetal phase to a massive/insulator phase in the so called Gross-Neveu universality class. Thus, the new solutions to the sign problem allow for the use of the QMC method to study these universality classes.

The second point is addressed through the construction of a Hamiltonian fermion bag algorithm. The algorithm is then used to compute the critical exponents for the second-order phase transition in the $t$-$V$ model. By pushing the calculations to significantly larger lattice sizes than previous recent computations ($64^2$ sites versus $24^2$ sites), I am able to compute the critical exponents more reliably here compared to earlier work. I show that the inclusion of these larger lattices causes a significant shift in the values of the critical exponents that was not evident for the smaller lattices. This shift puts the critical exponent values in closer agreement with continuum $4-\epsilon$ expansion calculations. The largest lattice sizes of $64^2$ at a comparably low temperature are reachable due to efficiency gains from this Hamiltonian fermion bag algorithm. The two independent critical exponents I find, which completely characterize the phase transition, are $\eta=.51(3)$ and $\nu=.89(1)$, compared to previous work that had lower values for these exponents. The finite size scaling fit is excellent with a $\chi^2/DOF=.90$, showing strong evidence for a second-order critical phase transition, and hence a non-perturbative QFT can be defined at the critical point.

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 Granular Impact Dynamics: Grain Scale to Macroscale(2014) Clark, AbeGranular impact, where a foreign object strikes a granular material like sand, is common in nature and industry. Due to experimental difficulties in obtaining sufficiently fast data at the scale of a single grain, a description of this process which connects to physics at the grain-scale is lacking. In this thesis, I will present data from a series of two-dimensional granular impact experiments. By cutting each grain out of a photoelastic material and using a very fast camera, we obtain data on the intruder trajectory, as well as the particle flow and force response of the granular material. Past experiments have shown that the decelerating force on an intruder moving through a granular medium is often well captured by a force law which is dominated by a velocity-squared drag force. Using the intruder trajectories, as well as the flow and force response of the granular material, I will demonstrate that, while these force laws describe the intruder trajectories on slow time scales, the instantaneous force on the intruder is highly fluctuating in space and time. I will particularly focus on the velocity-squared drag force, showing that it arises from random, locally normal collisions with chain-like clusters of particles which send energy and momentum away into the granular material. In this regime, the particles and intruder reach a kind of adiabatic steady state, where the particle motion scales linearly with the intruder speed. However, for impact velocities which are fast compared to the rate of momentum transfer within the granular material, the system response qualitatively changes, behaving like an elastic solid with a shock-like response at impact.

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 Investigating the Ground States of Triangular Antiferromagnet Quantum Spin Liquid Candidates(2021) Steinhardt, William MThe pursuit of the quantum spin liquid (QSL) state has been at the fore of condensed matter physics for several decades. In this exotic state of matter, spins remain dynamic in the zero temperature limit while retaining a high degree of entanglement. QSLs may play a role in quantum computing and high temperature conductivity, and are predicted to host exotic quasiparticle excitations. The first system proposed to host the QSL state was a triangular antiferromagnet, and variations of these materials are still being proposed as candidate systems decades later.

Here I present work aimed at shedding light on the ground states of two closely related spin S=1/2 triangular antiferromagnets, YbMgGaO4 and YbZnGaO4. These materials garnered great interest in recent years for showing many experimental signatures associated with QSL phenomena in a variety of measurements. However, both possess a high degree of disorder due to nominally perfect site mixing between the non-magnetic cations, and there is an ongoing debate about the role of this disorder in the spin liquid features.

We used a combination of inelastic and diffuse neutron scattering, and tunnel diode oscillator, cantilever torque, and SQUID magnetometry measurements that seek to advance our understanding of the possible spin liquid behaviors in these materials by constraining the exchange parameters of their Hamiltonians. These measurements have further served as a guide for theoretical studies performed by our collaborators. Plausible ground states are suggested for these materials in the disorder-free limit, and efforts are made to address nuances with respect to the role of frustration, disorder, and thermal and quantum mechanical fluctuations that all play important roles in the spin liquid phenomena in these and other QSL candidates, as well as the rich phase diagram of anisotropic triangular antiferromagnets.

Item Open Access Novel Tensor Network Methods for Interacting Quantum Matter and Its Dynamical Response(2020) Binder, MoritzThe simulation of interacting quantum matter remains challenging. The Hilbert space dimension required to describe the physics grows exponentially with the system size, yet many interesting collective phenomena emerge only for large enough systems. Tensor network methods allow for the simulation of quantum many-body systems by reducing the effective number of degrees of freedom in controlled approximations. For one-dimensional lattice models, algorithms employing matrix product states (MPS) are currently regarded as the most powerful numerical techniques. For example, density matrix renormalization group (DMRG) algorithms can be used to efficiently compute precise approximations for ground states of local Hamiltonians. The computation of finite-temperature properties and dynamical response functions is more challenging, yet crucial for a complete understanding of the physics and for comparisons with experiments.

In the first part of this dissertation, we introduce and demonstrate novel matrix product state techniques. First, we present an improved version of the minimally entangled typical thermal states (METTS) algorithm, a sampling approach for the simulation of thermal equilibrium. Our modification allows the use of symmetries in the MPS operations, which renders the algorithm significantly more efficient and makes the finite-temperature simulation of previously inaccessible models possible. Then, we introduce a new technique utilizing infinite matrix product states (iMPS) with infinite boundary conditions for the computation of response functions. These quantities are of great importance as their Fourier transform yields spectral functions or dynamic structure factors, which give detailed insights into the low-lying excitations of a model and can be directly compared to experimental data. Our improved algorithm allows to significantly reduce the number of required time-evolution runs in the simulations.

In the second part of this dissertation, we study the physics of the bilinear-biquadratic spin-1 chain in detail. Our new scheme for the simulation of response functions enables us to compute high-resolution dynamic structure factors for the model, which we use as a starting point to explore the low-lying excitations in all quantum phases of the rich phase diagram. Comparing our numerical data to exact results and field-theory approximations, we gain insights into the nature of the relevant excitations. In the Haldane phase, the model can be mapped to a continuum field theory, the non-linear sigma model (NLSM). We find that the NLSM does not capture the influence of the biquadratic term correctly and gives only unsatisfactory predictions for the relevant physical quantities. However, several features in the Haldane phase can be explained by a non-interacting approximation for two- and three-magnon states. Moving into the extended critical phase, we explain the observed contraction of the multi-soliton continua from the Uimin-Lai-Sutherland point by comparison with a field-theory description. In addition, we discover new excitations at higher energies and find that their dispersions are described by simple cosine-functions in the purely biquadratic limit. We characterize them as elementary one-particle excitations and relate them to the integrable Temperley-Lieb chain. The Temperley-Lieb chain can also be used to describe the physics at the opposite biquadratic point, which places the model in the gapped dimerized phase. Here, the excitation spectrum is related to that of an anisotropic spin-1/2 chain. In the ferromagnetic phase, the two-magnon excitations can be computed exactly and contain bound and resonant states in addition to two-particle continua.

Finally, we address the extraction of spectral functions or dynamic structure factors from real-time response functions computed with MPS techniques. In the time evolution, the computation costs grow with time, hence the response function can only be evaluated up to some maximum time. As the spectral functions are obtained by Fourier transform from the time to the frequency domain, this limits the frequency resolution of the result. Here, we introduce and discuss new approaches for the extraction of dynamic structure factors from the limited response-function data.

Item Open Access Out of Equilibrium Superconducting States in Graphene Multiterminal Josephson Junctions(2022) Arnault, Ethan GreggMultiterminal Josephson junctions have attracted attention, driven by the promise that they may host synthetic topological phase of matter and provide insight into Floquet states. Indeed, the added complexity of the additional contacts in multiterminal Josephson junctions greatly expands its parameter space, allowing for unexpected results. This work sheds light onto the out of equilibrium superconducting states that can exist within a ballistic multiterminal Josephson junction. The application of a microwave excitation produces unexpected fractional Shapiro steps, which are a consequence of the multiterminal circuit network. The application of a finite voltage reveals a robust cos 2φ supercurrent along the multiplet biasing condition nV1=-mV2. This supercurrent is found to be born from the RCSJ equations and has a stability condition analogous to Kapitza’s pendulum. Finally, the injection of hot carriers poisons supercurrent contributions from the Andreev spectrum, revealing a continuum mediated supercurrent.

Item Open Access Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes(2016) Belley, Catherine Cronin MarcouxLimit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Item Open Access Pull-out Experiment in Granular Material(2018) Zhang, YueTwo-dimensional impact experiments by Clark et al. identified the source of inertial drag to be caused by ‘collisions’ with a latent force network, leading to large fluctuations of the force experienced by the impactor. These collisions provided the major drag on an impacting intruder until the intruder was nearly at rest. As a complement, we consider controlled pull-out experiments where a buried intruder is pulled out of a material, starting from rest. This provides a means to better understand the non-inertial part of the drag force, and to explore the mechanisms associated with the force fluctuations. The pull out process is a time reversed version of the impact process. In order to visualize this pulling process, we use 2D photoelastic disks from which circular intruders of different radii are pulled out. We check the effect of the initial depth of the intruder, as well as the widths and friction of boundaries. We present results about the dynamics of the intruder and the structures of the force chains inside the granular system as captured by high speed imaging. Before conducting the pull-out dynamic experiments, we first measured the critical pulling force that is needed to pull the intruder out. Under gradually increasing upward pulling force, a steadily strengthening force network forms in response to small displacements of intruder, then eventually fails and the intruder exits the material in a rapid event. We find that just before failure, the force chains bend in a way that is consistent with recent predictions by Blumenfeld and Ma. We found the boundary width together with friction plays an important role in this static pre-failure experiment. However, the system boundary does not have much effect on the dynamics of the intruder once the pull-out process starts.

Item Open Access Quantum Critical Phenomena of Relativistic Fermions in 1+1d and 2+1d(2022) Liu, HanqingIn this dissertation, we study the phase structures and the quantum critical phenomena of relativistic lattice fermions with $\O(2N_f)$ symmetry in one and two spatial dimensions, motivated by the ability to perform efficient Monte Carlo simulations. Close to a quantum critical point, physics is universal and can be described by continuum quantum field theories. We perform a perturbative analysis of all independent four-fermion interactions allowed by the $\O(2N_f)$ symmetry near the free-fermion fixed point. We then analyze the resulting continuum field theories using various techniques. In one spatial dimension, we use the powerful tools from conformal field theory and non-abelian bosonization to understand the renormalization group flows, the correlation functions, and the spectra. In the case of $N_f=2$, we find that by tuning a Hubbard coupling, our model undergoes a second-order phase transition, which can be described by an $\SU(2)_1$ Wess-Zumino-Witten model perturbed by a marginal coupling. We confirm these results using the meron-cluster algorithm, and locate the critical point precisely using exact diagonalization based on the spectrum of the Wess-Zumino-Witten model. In two spatial dimensions, we analyze the model using $\varepsilon$ expansion, large $N_f$ expansion and effective potential methods. In the case of $N_f=2$, we find a novel critical point where the anti-ferromagnetic order and superconducting-CDW order become simultaneously quantum critical, which seems to have been missed in literature. We compare these predictions with the numerical results obtained using the fermion-bag algorithm by Emilie Huffman.

Item Open Access Shape Effects on Jamming of Granular Materials(2012) Farhadi, SomayehIn this work, we have focused on the jamming properties of systems composed of semi-2D elliptical shaped particles. In order to study these systems, we have performed three types of experiments: Couette shear, biaxial isotropic compression, and biaxial pure shear. In each experimental scheme, we take data for both systems of ellipses an bi-disperse disks, in order to probe the effect of broken spherical symmetry at the particle scale, on the global behavior. We use two synchronized cameras to capture the flow of particles and the local stress at the same time.

In Couette experiments, we study the rheological properties, as well as the stress fluctuations for very large strains (up to 20 revolutions of the inner wheel). The system is sheared for densities below the isotropic jamming point (point J). From these studies we learn that over a small range of packing fractions, ($0.85 \leq \phi \leq 0.86$),

systems of ellipses demonstrate exceptionally slow dynamical evolution when they are sheared. For

fixed density, and starting from an essentially unstressed state, the application of shear strain leads to

first a growth of average particle displacements in the system through a Reynolds dilatancy effect,

and then for very large strains, a steady decrease in particle displacements. In an intermediate

range of shear strains, the system exists in effectively meta-stable states for a very long time

before relaxing to an unjammed state, in which the flow of particles stops completely, and the

stress fluctuations drop to zero. The strain scale for this relaxation depends on the global packing

fraction. We characterize this slow dynamics by measuring the evolution of mean velocity, density,

and orientational order throughout the experiments. In a similar set of experiments performed on

disks, slow relaxation was observed as well. However, the increasing average displacement build-up

before relaxation, which was observed in ellipses, did not occur for disks. This suggests that the

slow relaxation towards an unjammed state in ellipses is associated with the possibility of small and

slow changes in their orientations, which then allow a more efficient packing.

In order to study the stress fluctuations, we implement photoelastic properties of the particles. We are able to track the $g^{2}$ (a measure of local stress) of each particle throughout the entire experiment.

Unlike disks, the power spectra of $g^2$, $P(\omega)$, is not rate invariant for ellipses. In other words, all curves of $R P(\omega)$ vs. $\omega / R$ (where $R$ is the shear rate) with different values of $R$, collapse to a single curve for disks, but not for ellipses.

The rate invariance of spectra was previously studied for sheared spherical glass beads and semi-2D pentagonal particles. This is the first experimental work in which the fluctuations of granular systems composed of elongated particles is addressed.

We have also studied the formation and destruction of stress avalanches during Couette shear in both systems of disks and ellipses. In particular, we introduce measures which characterize the size and shape of stress avalanches. Analysis of these measures shows that the build-up and release of stress in both systems of disks and ellipses have similar distributions which indicates that the deformation of particles in a Couette cell does not resemble stick-slip behavior. We also find that the build-up and release of stress is faster is larger avalanches.

Cyclic isotropic compression is performed on semi-2D systems of bi-disperse disks and identical ellipses with aspect ratio 2, which are composed of photoelastic particles. In each compression cycle, the system is compressed with a total strain of $1.6\%$ and then expanded to the initial state. After completion of each half cycle, the system is allowed to relax, then imaged by two synchronized cameras. The packing fraction, $\phi$, of compressed states are chosen above the isotopic jamming point (point J). In both systems of disks and ellipses, we observed relaxation of global stress over long compression cycles. We find that the global stress drops with a power law over time ($\sigma \sim C t^{-A}$). The exponent of decay, $A$, drops linearly with increasing $\phi$, and hits zero at $\phi \simeq 0.89$ for disks, and $\phi \simeq 0.93$ for ellipses. Above these packing fractions, the system is stable with respect to its global stress.

In order to understand the origin of this slow stress dilation, we have studied the structural changes of the system, including Falk-Langer measures of affine and non-affine deformations, as well as average contact per particle.