Microscopic description of tunneling systems in a structural model glass

Finding defects in glasses through machine learning

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Due to their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

Microscopic observation of two-level systems in a metallic glass model

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

Nanoscopic Charge Fluctuations in a Gallium Phosphide Waveguide Measured by Single Molecules

We present efficient evanescent coupling of single organic molecules to a gallium phosphide (GaP) subwavelength waveguide (nanoguide) decorated with microelectrodes. By monitoring their Stark shifts, we reveal that the coupled molecules experience fluctuating electric fields. We analyze the spectral dynamics of different molecules over a large range of optical powers in the nanoguide to show that these fluctuations are light-induced and local. A simple model is developed to explain our observations based on the optical activation of charges at an estimated mean density of 2.5×10^{22}  m^{-3} in the GaP nanostructure. Our work showcases the potential of organic molecules as nanoscopic sensors of the electric charge as well as the use of GaP nanostructures for integrated quantum photonics.

Depletion of Two-Level Systems in Ultrastable Computer-Generated Glasses

Amorphous solids exhibit quasiuniversal low temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create in silico glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than k_{B}T_{Q}, with T_{Q} the temperature below which quantum effects are relevant (T_{Q}≈1  K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore the real-space nature of tunneling defects, and find that they are mostly localized to a few atoms, but are occasionally dramatically delocalized.

Vibrational density of states and specific heat in glasses from random matrix theory

The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s at least, it is a well-established experimental fact that the specific heat of glasses is instead just linear in T at T∼1 K and presents a pronounced peak when normalized by T^{3}, known as the boson peak. Here we present an approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random-matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus.

Quantifying non-Markovianity for a chromophore-qubit pair in a super-Ohmic bath

An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe the quantum dynamics of a chromophore-qubit in a super-Ohmic bath. Utilizing a measure of non-Markovianity based on dynamical fixed points, we study the effects of the environmental temperature and the coupling strength on the non-Markovian behavior of the chromophore in a super-Ohmic bath. It is found that an increase in the temperature results in a reduction in the backflow information from the environment to the chromophore, and therefore, a suppression of non-Markovianity. In the weak coupling regime, increasing the coupling strength will enhance the non-Markovianity, while the effect is reversed in the strong coupling regime.

Dissipative dynamics of two-level systems in low temperature glasses

An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe dynamics of a central chromophore embedded in a bath of two-level systems commonly found in low-temperature glasses. By treating the Hamiltonian in the polaron frame, we can account for initial nonequilibrium bath states as well as the spatially correlated environmental effect. Relevant realistic situations are explored by adopting parameters from previous experiments. It is found that the temperature of the boson bath has a substantial effect on the population relaxation and the decoherence process, and a higher temperature also results in a higher saturation value of the entanglement entropy, while the coupling between the chromophore and the TLS has an effect that goes counter to that of the temperature.

Disorder influenced absorption line shapes of a chromophore coupled to two-level systems

We have carried out a theoretical and numerical study of disorder-induced changes in the absorption line shape of a chromophore embedded in a host matrix. The stochastic sudden jump model is employed wherein the host matrix molecules are treated as noninteracting two-level systems (TLSs) occupying points on a three-dimensional lattice with randomly oriented dipole moments. By systematically controlling the degree of positional disorder (α) attributed to them, a perfectly crystalline (α = 0) or a glassy environment (α = 1) or a combination of the two is obtained. The interaction between the chromophore and the TLSs is assumed to be of the dipole-dipole form. With an increase in α, the broadening of the absorption line shape was found to follow a power-law behavior. More importantly, it is revealed in the long-time limit that the resultant line shape is Gaussian in the absence of disorder but transforms to Lorentzian for a completely disordered environment. For an arbitrarily intermediate value of α, the resultant line shape can be approximately fitted by a linear combination of Gaussian and Lorentzian components. The Lorentzian profile for the disordered medium is attributed to the chomophore-TLS pairs with vanishingly small separation between them.

Multilevel tunnelling systems and fractal clustering in the low-temperature mixed alkali-silicate glasses

The thermal and dielectric anomalies of window-type glasses at low temperatures (T < 1 K) are rather successfully explained by the two-level systems (2LS) standard tunneling model (STM). However, the magnetic effects discovered in the multisilicate glasses in recent times, magnetic effects in the organic glasses, and also some older data from mixed (SiO₂)_1−x(K₂O)_x and (SiO₂)_1−x(Na₂O)_x glasses indicate the need for a suitable extension of the 2LS-STM. We show that—not only for the magnetic effects, but also for the mixed glasses in the absence of a field—the right extension of the 2LS-STM is provided by the (anomalous) multilevel tunnelling systems (ATS) proposed by one of us for multicomponent amorphous solids. Though a secondary type of TS, different from the standard 2LS, was invoked long ago already, we clarify their physical origin and mathematical description and show that their contribution considerably improves the agreement with the experimental data. In spite of dealing with low-temperature properties, our work impinges on the structure and statistical physics of glasses at all temperatures.

Nonlinear quantum optomechanics via individual intrinsic two-level defects

We propose to use the intrinsic two-level system (TLS) defect states found naturally in integrated optomechanical devices for exploring cavity QED-like phenomena with localized phonons. The Jaynes-Cummings-type interaction between TLS and mechanics can reach the strong coupling regime for existing nano-optomechanical systems, observable via clear signatures in the optomechanical output spectrum. These signatures persist even at finite temperature, and we derive an explicit expression for the temperature at which they vanish. Further, the ability to drive the defect with a microwave field allows for realization of phonon blockade, and the available controls are sufficient to deterministically prepare non-classical states of the mechanical resonator.

Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by molecular dynamics simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the nonlinear density response function, chi4(t). The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that a further increase in polydispersity lowers the glass forming ability.

Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport

In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.

Microscopic Description of the Low-Temperature Anomalies in Silica and Lithium Silicate via Computer Simulations

Information about the nature of the low-temperature anomalies and in particular the properties of the tunneling systems in silica and lithium silica glasses are revealed via computer simulations. The potential energy landscape of these systems is systematically explored for adjacent pairs of local minima which may act as double-well potentials (DWPs) at low temperatures. Three different types of DWPs are distinguished, related to perfectly coordinated silica, intrinsic silica defects, and extrinsic defects. Their properties such as the spatial extension and the dipole moment are characterized in detail. Furthermore, the absolute number of tunneling systems, that is, symmetric DWPs, is estimated. The results are compared with dielectric echo, specific heat, and acoustic experiments on Suprasil I and Suprasil W. A semiquantitative agreement for all relevant features is obtained.

What is moving in silica at 1 K? A computer study of the low-temperature anomalies

Though the existence of two-level systems (TLS) is widely accepted to explain low-temperature anomalies in many physical observables, knowledge about their properties is very rare. For silica, which is one of the prototype glass-forming systems, we elucidate the properties of the TLS via computer simulations by applying a systematic search algorithm. We get specific information in the configuration space, i.e., about relevant energy scales, the absolute number of TLS, and electric dipole moments. Furthermore, important insight about the real-space realization of the TLS can be obtained. Comparison with experimental observations is included.

Theory of single-molecule spectroscopy: beyond the ensemble average

Single-molecule spectroscopy (SMS) is a powerful experimental technique used to investigate a wide range of physical, chemical, and biophysical phenomena. The merit of SMS is that it does not require ensemble averaging, which is found in standard spectroscopic techniques. Thus SMS yields insight into complex fluctuation phenomena that cannot be observed using standard ensemble techniques. We investigate theoretical aspects of SMS, emphasizing (a) dynamical fluctuations (e.g., spectral diffusion, photon-counting statistics, antibunching, quantum jumps, triplet blinking, and nonergodic blinking) and (b) single-molecule fluctuations in disordered systems, specifically distribution of line shapes of single molecules in low-temperature glasses. Special emphasis is given to single-molecule systems that reveal surprising connections to Levy statistics (i.e., blinking of quantum dots and single molecules in glasses). We compare theory with experiment and mention open problems. Our work demonstrates that the theory of SMS is a complementary field of research for describing optical spectroscopy in the condensed phase.

Lévy statistics for random single-molecule line shapes in a glass

We demonstrate that the statistical behavior of random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at T=2 K is described by Lévy statistics as predicted theoretically by Barkai, Silbey, and Zumofen [Phys. Rev. Lett. 84, 5339 (2000)]. This behavior is a manifestation of the long-range interaction between two-level systems in the glass and the single molecule. A universal amplitude ratio is investigated, which shows that the standard tunneling model assumptions are compatible with the experimental data.

Tunneling state anisotropy in a single grain decagonal quasicrystal

We present low-temperature measurements, between 20 mK and 20 K, of the sound velocity variations in a single grain of the decagonal quasicrystal Al-Ni-Co. We have used acoustic shear waves of frequency 70 MHz propagating in the quasicrystalline planes with two different polarizations: parallel and perpendicular to the quasicrystalline planes. Our results show the presence of tunneling states (TSs) with a strong difference of the phonon-TS coupling for the two polarizations, which reveals a strong anisotropy of distribution of the orientations of the TSs in the sample. This result gives direct evidence that TSs are generated by the quasicrystalline structure itself.

Path-integral study of a two-dimensional Lennard-Jones glass

The glass transition in a quantum Lennard-Jones mixture is investigated by constant-volume path-integral simulations. Particles are assumed to be distinguishable, and the strength of quantum effects is varied by changing variant Planck's over 2pi from zero (the classical case) to one (corresponding to a highly quantum-mechanical regime). Quantum delocalization and zero point energy drastically reduce the sensitivity of structural and thermodynamic properties to the glass transition. Nevertheless, the glass transition temperature T(g) can be determined by analyzing the phase space mobility of path-integral centroids. At constant volume, the T(g) of the simulated model increases monotonically with increasing variant Planck's over 2pi. Low temperature tunneling centers are identified, and the quantum versus thermal character of each center is analyzed. The relation between these centers and soft quasilocalized harmonic vibrations is investigated. Periodic minimizations of the potential energy with respect to the positions of the particles are performed to determine the inherent structure of classical and quantum glassy samples. The geometries corresponding to these energy minima are found to be qualitatively similar in all cases. Systematic comparisons for ordered and disordered structures, harmonic and anharmonic dynamics, classical and quantum systems show that disorder, anharmonicity, and quantum effects are closely interlinked.

Energy landscape view of fracture and avalanches in disordered materials

Molecular simulations are carried out to probe how strain-induced changes in the energy landscape are related to fracture processes in disordered systems. The simulations address a two-dimensional system that consists of 9952 particles with a distribution of sizes, and the changes in the structure and properties with strain are determined with the system constrained to an energy minimum. As the system is strained, local minima of the energy landscape are found to flatten out and disappear, which causes discontinuous structural rearrangements. These structural rearrangements, which correspond to avalanche events, lead to void nucleation and crack growth in discrete steps.

Potential energy landscape of a model glass former: thermodynamics, anharmonicities, and finite size effects

It is possible to formulate the thermodynamics of a glass forming system in terms of the properties of inherent structures, which correspond to the minima of the potential energy and build up the potential energy landscape in the high-dimensional configuration space. In this work we quantitatively apply this general approach to a simulated model glass-forming system. We systematically vary the system size between N=20 and N=160. This analysis enables us to determine for which temperature range the properties of the glass former are governed by the regions of the configuration space, close to the inherent structures. Furthermore, we obtain detailed information about the nature of anharmonic contributions. Moreover, we can explain the presence of finite size effects in terms of specific properties of the energy landscape. Finally, determination of the total number of inherent structures for very small systems enables us to estimate the Kauzmann temperature.