When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb interactions - in which particle-hole dipoles are emergent excitations - and for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and dephasing rates ($T_2$ times), and their dependence on frequency, temperature, and polarization. Systems in both two and three dimensions are considered, along with the dimensional crossover in quasi-two dimensional geometries. A rich set of scaling laws is found.
The effects of dilution disorder and random-displacement disorder are analyzed for dipolar-coupled magnetic moments confined in a plane, which were originally placed on the square lattice. In order to distinguish the different phases, new order parameters are derived and parallel tempering Monte Carlo simulations are performed for a truncated dipolar Hamiltonian to obtain the phase diagrams for both types of disorder. We find that both dilution disorder and random-displacement disorder give similar phase diagrams, namely disorder at small enough temperatures favors a so-called microvortex phas…
We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the syste…
We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in the two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem claiming the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical t…
We study the behavior of a quantum dipolar Bose condensate with the Lee-Huang-Yang quantum corrections at zero temperature in the presence of weak disorder potential. We solve the underlying nonlocal Gross-Pitaevskii equation using a perturbative theory. The role of both the Lee-Huang-Yang term and the disorder potential on the condensed fraction, the equation of state, the compressibility and the superfluid density is deeply analyzed. Surprisingly, we find that the Lee-Huang-Yang quantum corrections not only arrest the dipolar implosion but also lead to reduce the condensate fluctuations due …
Quantum information processing often uses systems with dipolar interactions. We use a nuclear spin-based quantum simulator, to study the spreading of information in such a dipolar-coupled system and how perturbations to the dipolar couplings limit the spreading, leading to localization. In [Phys. Rev. Lett. 104, 230403 (2010)], we found that the system reaches a dynamic equilibrium size, which decreases with the square of the perturbation strength. Here, we study the impact of a disordered Hamiltonian with dipolar 1/r^3 interactions. We show that the expansion of the coherence length of the cl…
Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of $\sim 10^6$ electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color cent…
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to resul…
A recent theory of magnetoresistance in positionally disordered organic semiconductors is extended to include exchange and dipolar couplings between polarons. Analytic results are discovered when the hyperfine, exchange, and dipolar interactions have little time to operate between hopping events. We find an angle-of-field dependence of the magnetoresistance that agrees with previous experiments and numerical simulations. In addition we report new magnetoresistive behavior that critically depends upon the amount of anisotropy in the dipolar interaction.
The physics of the spin glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. While most theoretical studies have focused on the Edwards-Anderson model of Ising spins with only discrete `up/down' directions, such Ising systems are experimentally rare. LiHo$_{x}$Y$_{1-x}$F$_{4}$, where the Ho$^{3+}$ moments are well described by Ising spins, is an almost ideal Ising SG material. In LiHo$_{x}$Y$_{1-x}$F$_{4}$, the Ho$^{3+}$ moments interact predominantly via the inherently frustrated magnetostatic dipole…
Recently, Nattermann and Pokrovsky [PRL 100, 060402 (2008)] have proposed a scaling approach for studying Bose-Einstein condensates in strongly disordered traps. In this paper we implement their scaling argument in the framework of the variational method for solving the time dependent Gross-Pitaevskii equation. We consider atomic gases with both short range s-wave interaction and long range anisotropic dipolar interaction. The theory is addressed to the regime of strong disorder and weak interactions where the physics is dominated by the collective pinning due to the disorder. The phenomenon o…
In a recent letter [Phys. Rev. Lett. {\bf 75}, 2360 (1996)] we briefly discussed the existence and nature of ferroelectric order in positionally disordered dipolar materials. Here we report further results and give a complete description of our work. Simulations of randomly frozen and dynamically disordered dipolar soft spheres are used to study ferroelectric ordering in non-crystalline systems. We also give a physical interpretation of the simulation results in terms of short- and long-range interactions. Cases where the dipole moment has 1, 2, and 3 components (Ising, XY and XYZ models, resp…
Using the history-dependence of a dipolar glass hosted in a compositionally-disordered lithium-enriched potassium-tantalate-niobate (KTN:Li) crystal, we demonstrate scale-free optical propagation at tunable temperatures. The operating equilibration temperature is determined by previous crystal spiralling in the temperature/cooling-rate phase-space.
The standard one-parameter scaling theory predicts that all eigenstates in two-dimensional random lattices are weakly localized. We show that this claim fails in two-dimensional dipolar Frenkel exciton systems. The linear energy dispersion at the top of the exciton band, originating from the long-range inter-site coupling of dipolar nature, yields the same size-scaling law for the level spacing and the effective disorder seen by the exciton. This finally results in the delocalization of those eigenstates in the thermodynamic limit. Large scale numerical simulations allow us to perform a detail…
We investigate the physics of dipolar bosons in a two dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this paper, we consider the properties of the system beyond its ground state, finding that it is characterised by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and open…
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement wi…
We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass system. Entanglement in such systems attains significantly high values, after quenched averaging, and has a stable positive value for arbitrary times. Complex systems with long range interactions, such as ion chains or dipolar atomic gases, can be modeled by neural network Hamiltonians. In such systems, we find the characteristic time of persistence of quenched a…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent an…
The rare-earth material $\mathrm{LiHoF_4}$ is believed to be an experimental realization of the celebrated (dipolar) Ising model, and upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by non-magnetic Y ions, disorder can be introduced into the system giving rise to a dipolar disordered magnet and at high disorders to a spin-glass. Indeed, this material has been scrutinized experimentally, numerically and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the …
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipol…
Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent "classical" properties of a system (e.g. diffusivity, viscosity, compressibility) from a generic microscopic quantum Hamiltonian. Here, we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconv…
We model the optical dynamics in linear Frenkel exciton systems governed by scattering on static disorder and lattice vibrations, and calculate the temperature dependent fluorescence spectrum and lifetime. The fluorescence Stokes shift shows a nonmonotonic behavior with temperature, which derives from the interplay of the local band-edge level structure and thermal equilibration. The model yields excellent fits to experiments performed on linear dye aggregates.
Quantum states cohere and interfere. Quantum systems composed of many atoms arranged imperfectly rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent clusters of spins by driving the system beyond its linear response regime at a single frequency and measuring the resulting "hole" in the overall linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the disordered Ising magnet, $\mathrm…
The low-frequency vibrations of glasses are markedly different from those of crystals. These vibrations have recently been categorized into two types: spatially extended vibrations, whose vibrational density of states (vDOS) follows a non-Debye quadratic law, and quasilocalized vibrations (QLVs), whose vDOS follows a quartic law. The former are explained by elasticity theory with quenched disorder and microscopic replica theory as being a consequence of elastic instability, but the origin of the latter is still debated. Here, we show that the latter can also be directly derived from elasticity…
Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian $\propto 1/r^α$ in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function $R_2(ω)$ in a finite syst…
Spin dynamics in low dimensional magnetic systems has been of fundamental importance for a long time and has currently received an impetus owing to the emerging field of nanoelectronics. Knowledge of the spin wave lifetimes, in particular, can be favorable for future potential applications. We investigate the low-temperature spin wave excitations in two-dimensional disordered ferromagnetic systems, with a particular focus on the long wavelength magnon lifetimes. A semi-analytical Green's functions based approach is used to determine the dynamical spectral functions, for different magnetic impu…
Effects of two-body dipolar interactions on the effective permittivity/conductivity of a binary, symmetric, random dielectric composite are investigated in a self-consistent framework. By arbitrarily splitting the singularity of the Green tensor of the electric field, we introduce an additional degree of freedom into the problem, in the form of an unknown "inner" depolarization constant. Two coupled self-consistent equations determine the latter and the permittivity in terms of the dielectric contrast and the volume fractions. One of them generalizes the usual Coherent Potential condition to m…
Three dimensional Dirac semimetals are stable against weak potential disorder, but not against strong disorder. In the language of renormalization group, such stability stems from the irrelevance of weak disorder in the vicinity of the noninteracting Gaussian fixed point. However, beyond a threshold, potential disorder can take Dirac semimetals into a compressible diffusive metallic phase through a quantum phase transition (QPT), where density of states at zero energy, quasiparticle lifetime and metallic conductivity at $T=0$, are finite. Universal behavior of such unconventional QPT is descri…
Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant transmission and contribute to the conductivity. The rest of the eigenvalues are not associated with peaks in transmission and the amplitudes of their wave functions do not exhibit a significant maxima within the sample. Moreover, unlike ordinary states, the lifetimes of these `hidden' modes either remain constant or even decrease (depending on the coupling wit…
