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arXiv2013

Dicke Quantum Spin and Photon Glass in Optical Cavities: Non-equilibrium theory and experimental signatures

In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter, and could evolve into a "cavity glass microscope" for frustrated quantum systems out-of-equilibrium. Here we develop the non-equilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class however is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin glass physics onto a "photon glass" makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function $g^{(2)}(τ)$.

cond-mat.quant-gas↗

arXiv2013

Microscopic characterization of Lévy flights of light in atomic vapors

We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is characteristic of a superdiffusive behavior, where rare but very long steps (Lévy flights) dominate the transport properties.

physics.atom-ph↗

arXiv2013

Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder

Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.

cond-mat.quant-gas↗

arXiv2013

Backscattering echo of correlated wave packets

We present an analytical theory describing a novel phenomenon of enhanced backscattering corresponding to the spatial refocussing of a spread-out correlated wave packet due to a brief interaction with a disordered potential. Our theory is validated by numerical simulations and explains the physics observed in recent experiments on cold atom transport in disorder.

cond-mat.dis-nn↗

arXiv2014

Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media

Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves have not been investigated so far. We study theoretically the polarization and coherence properties of electromagnetic waves produced by a dipole source in a three-dimensional uncorrelated disordered medium. The spatial field correlation matrix is calculated analytically using a multiple scattering theory for polarized light. This allows us to provide a formal description of the light depolarization process in terms of "polarization eigenchannels" and to derive analytical formulas for the spatial coherence of multiply-scattered light.

physics.optics↗

arXiv2014

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Quantum walk (QW) in presence of lattice disorders leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a scheme to realize the discrete time QW by placing a pair of superconducting qubits on each site of a 1D lattice and treating an excitation as a walker. It is also shown that lattice disorders can be introduced and fully controlled within this scheme by tuning the qubit parameters. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signature of localized and delocalized regimes can be detected with existing superconducting technology.

quant-ph↗

arXiv2014

Entangling Power of Disordered Quantum Walks

We investigate how the introduction of different types of disorder affects the generation of entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional quantum random walks (QRW). Disorder is modeled by adding another random feature to QRW, i.e., the quantum coin that drives the system's evolution is randomly chosen at each position and/or at each time step, giving rise to either dynamic, fluctuating, or static disorder. The first one is position-independent, with every lattice site having the same coin at a given time, the second has time and position dependent randomness, while the third one is time-independent. We show for several levels of disorder that dynamic disorder is the most powerful entanglement generator, followed closely by fluctuating disorder. Static disorder is the less efficient entangler, being almost always less efficient than the ordered case. Also, dynamic and fluctuating disorder lead to maximally entangled states asymptotically in time for any initial condition while static disorder has no asymptotic limit and, similarly to the ordered case, has a long time behavior highly sensitive to the initial conditions.

quant-ph↗

arXiv2014

Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases

We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a $π$-flux square lattice, in the presence of a weak correlated disorder such that the disorder fluctuations do not couple the two Dirac points of the lattices. We numerically and theoretically investigate the time evolution of the momentum distribution of such quasi-particles when they are initially prepared in a quasi-monochromatic wave packet with a given mean momentum. The parallel transport of the pseudo-spin degree of freedom along scattering paths in momentum space generates a geometrical phase which alters the interference associated with reciprocal scattering paths. In the massless case, a well-known dip in the momentum distribution develops at backscattering (respective to the Dirac point considered) around the transport mean free time. This dip later vanishes in the honeycomb case because of trigonal warping. In the massive case, the dynamical phase of the scattering paths becomes crucial. Its interplay with the geometrical phase induces an additional transient broken reflection symmetry in the momentum distribution. The direction of this asymmetry is a property of the Dirac point considered, independent of the energy of the wave packet. These Berry phase effects could be observed in current cold atom lattice experiments.

cond-mat.dis-nn↗

arXiv2018

Time crystals: analysis of experimental conditions

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.

cond-mat.quant-gas↗

arXiv2017

Skyrmion Gas Manipulation for Probabilistic Computing

The topologically protected magnetic spin configurations known as skyrmions offer promising applications due to their stability, mobility and localization. In this work, we emphasize how to leverage the thermally driven dynamics of an ensemble of such particles to perform computing tasks. We propose a device employing a skyrmion gas to reshuffle a random signal into an uncorrelated copy of itself. This is demonstrated by modelling the ensemble dynamics in a collective coordinate approach where skyrmion-skyrmion and skyrmion-boundary interactions are accounted for phenomenologically. Our numerical results are used to develop a proof-of-concept for an energy efficient ($\simμ\mathrm{W}$) device with a low area imprint ($\simμ\mathrm{m}^2$). Whereas its immediate application to stochastic computing circuit designs will be made apparent, we argue that its basic functionality, reminiscent of an integrate-and-fire neuron, qualifies it as a novel bio-inspired building block.

cond-mat.mes-hall↗

arXiv2022

Wigner-Weyl description of light absorption in disordered semiconductor alloys using the localization landscape theory

The presence of disorder in semiconductors can dramatically change their physical properties. Yet, models faithfully accounting for it are still scarce and computationally inefficient. We present a mathematical and computational model able to simulate the optoelectronic response of semiconductor alloys of several tens of nanometer sidelength, while at the same time accounting for the quantum localization effects induced by the compositional disorder at the nano-scale. The model is based on a Wigner-Weyl analysis of the structure of electron and hole eigenstates in phase space made possible by the localization landscape theory. After validation against eigenstates-based computations in 1D and 2D, our model is applied to the computation of light absorption in 3D InGaN alloys of different compositions. We obtain the detailed structures of the absorption tail below the average bandgap and the Urbach energies of all simulated compositions. Moreover, the Wigner-Weyl formalism allows us to define and compute 3D maps of the effective locally absorbed power at all frequencies. Finally the proposed approach opens the way to generalize this method to all energy-exchange processes such as radiative and non-radiative recombination in realistic devices.

cond-mat.dis-nn↗

arXiv2022

Noise-induced dynamical localization and delocalization

We investigate the effect of a two-level jump process or random telegraph noise on a square wave driven tight-binding lattice. In the absence of the noise, the system is known to exhibit dynamical localization for specific ratios of the amplitude and the frequency of the drive. We obtain an exact expression for the probability propagator to study the stability of dynamical localization against telegraph noise. Our analysis shows that in the presence of noise, a proper tuning of the noise parameters destroys dynamical localization of the clean limit in one case, while it induces dynamical localization in an otherwise delocalized phase of the clean model. Numerical results help verify the analytical findings. A study of the dynamics of entanglement entropy from an initially half-filled state offers complementary perspective.

cond-mat.dis-nn↗

arXiv2021

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with $1/r^6$ power-law interactions and positional disorder. Using the semi-classical discrete truncated Wigner approximation (dTWA) method, we investigate the time evolution of the magnetization and ensemble-averaged single-spin purity for a strongly disordered system after initializing the system in an out-of-equilibrium state. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian. Furthermore, a systematic analysis allows us to quantitatively show that, for all the scenarios considered, the stretch power lies close to the one analytically obtained in the Ising limit. This indicates that glassy relaxation behavior occurs widely in disordered quantum spin systems, independent of the particular symmetries and integrability of the Hamiltonian.

cond-mat.dis-nn↗

arXiv2010

The three-dimensional gauge-glass model

We investigate the temperature-disorder (T-S) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts A_xy at the bonds, by numerical Monte Carlo simulations. We consider the uncorrelated phase-shift distribution P(A_xy)\sim \exp[(cos A_xy)/S], which has the pure XY model and the uniform distribution of random shifts as extreme cases at S=0 and S->infty respectively, and which gives rise to equal magnetic and overlap correlation functions when T=S. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small S) and a glassy phase at large disorder (large S). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives only rise to very slowly decaying scaling corrections. The glassy critical behavior along the finite-temperature paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large critical exponent nu=3.2(4). These transition lines meet at a multicritical point M, located at T=S=0.7840(2). The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T=0 axis, which is slightly reentrant.

cond-mat.dis-nn↗

arXiv2011

An integrable modification of the critical Chalker-Coddington network model

We consider the Chalker-Coddington network model for the Integer Quantum Hall Effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models, with two loop flavours. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra, and parameterised by the loop fugacity $n$. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-Gas theory, whereas the other two branches (3,4) couple the two loop flavours, and relate to an $SU(2)_r \times SU(2)_r / SU(2)_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n= -2\cos[π/(r+2)]$ where $r$ is a positive integer. The truncated Chalker-Coddington model is the $n=0$ point of branch 4. By numerical diagonalisation, we find that its universality class is neither an analytic continuation of the WZW coset, nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.

cond-mat.dis-nn↗

arXiv2012

A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions

We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.

cond-mat.dis-nn↗

arXiv2013

Theoretical assessment on the possibility of constraining point defect energetics by pseudo-phase transition pressures

Making use of the energetics and equations of state of defective uranium dioxide that calculated with first-principles method, we demonstrate a possibility of constraining the formation energy of point defects by measuring the transition pressures of the corresponding pseudo-phase of defects. The mechanically stable range of fluorite structure of UO2, which dictates the maximum possible pressure of relevant pseudo-phase transitions, gives rise to defect formation energies that span a wide band and overlap with the existing experimental estimates. We reveal that the knowledge about pseudo-phase boundaries can not only provide important information of energetics that is helpful for reducing the scattering in current estimates, but also be valuable for guiding theoretical assessments, even to validate or disprove a theory. In order to take defect interactions into account and to extrapolate the physical quantities at finite stoichiometry deviations to that near the stoichiometry, we develop a general formalism to describe the thermodynamics of a defective system. We also show that it is possible to include interactions among defects in a simple expression of point defect model (PDM) by introducing an auxiliary constant mean-field. This generalization of the simple PDM leads to great versatility that allows one to study nonlinear effects of stoichiometry deviation on materials' behavior. It is a powerful tool to extract the defect energetics from finite defect concentrations to the dilute limit. Besides these, the full content of the theoretical formalism and some relevant and interesting issues, including reentrant pseudo-transition, multi-defect coexistence, charged defects, and possible consequence of instantaneous defective response in a quantum crystal, are explored and discussed.

cond-mat.mtrl-sci↗

arXiv2013

Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order

The ordering of the three-dimensional isotropic {\it XY} spin glass with the nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution and the non-self-averageness parameter, {\it etc}, for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of the spin-chirality decoupling, {\it i.e.}, the CG and the SG order occurring at two separated temperatures, $0<T_{SG}<T_{CG}$, is obtained from the glass order parameter, which is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length drop-off of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents $ν_{CG}=1.36^{+0.15}_{-0.37}$ and $η_{CG}=0.26^{+0.29}_{-0.26}$, and the SG exponents $ν_{SG}=1.22^{+0.26}_{-0.06}$ and $η_{SG}=-0.54^{+0.24}_{-0.52}$. The obtained exponents are close to those of the Heisenberg SG, but are largely different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with the previous reports. Such a 1RSB feature is again in common with that of the Heisenberg SG, but is different from the Ising one, which may be the cause of the difference in the CG critical properties from the Ising SG ones despite of a common $Z_2$ symmetry.

cond-mat.dis-nn↗