Interaction Of Two-level Systems Research Articles

High temperature superradiant phase transition in quantum structures with a complex network interface.

In the present work we propose a novel, to the best of our knowledge, quantum material concept, which enables superstrong and/or ultrastrong interaction of two-level systems with the photonic field in a complex network. Within the mean field approximation we examine phase transition to superradiance that results in two excitation (polariton) branches and is accompanied by the appearance of non-zero macroscopic polarization of two-level systems. We characterize the statistical properties of networks by the first, 〈k〉, and second normalized, ζ ≡ 〈k2〉/〈k〉, moments for node degree distribution. We have shown that the Rabi frequency is essentially enhanced due to the topology of the network within the anomalous domain where 〈k〉 and ζ sufficiently grow. The multichannel (multimode) structure of matter-field interaction leads superstrong coupling that provides primary behavior of the high temperature phase transition. The results obtained pave the way for the design of new photonic and polaritonic circuits, quantum networks for efficient processing quantum information at high (room) temperatures.

Distribution of two-level system couplings to strain and electric fields in glasses at low temperatures

The thermal, acoustic, and dielectric properties of glasses below 1 K are dictated by the interaction of two-level systems (TLS) with strain and electric fields. In a previous paper, we proposed a modified TLS model to quantitatively account for the universally small phonon scattering in glasses at low temperatures. A key ingredient of this model was a wide distribution of couplings between TLS and phonons, contrary to the standard model which assumes a single averaged value is sufficient. In this paper, we expand on this view and include couplings to strain as well as electric fields. We then compare our theoretical results to measurements obtained using superconducting qubits. We find that the predictions of the modified TLS model are more consistent with experiments than those of the standard model. For the distribution of couplings between TLS and the strain field, there is a better agreement with experiments if we include a random distribution of local strains. Such a distribution of local strains is consistent with those found from molecular dynamics simulations.

The phenomenon of nonstationary nutation in the system of two-level quantum wells of a periodic superlattice with strong magnetic quantization

We investigate the superposition of nonstationary nutation processes that arose during the interaction of two-level systems of quantum wells of a superlattice with two exciting coherent optical pulses with various resonance detunings. According to the model under consideration, dipole transitions in two-level systems of quantum wells under the action of exciting pulses occur between the Landau levels of the main mini-band of the superlattice conduction band. This gives a direct opportunity to study the controlled variation of the course of optical nutation processes, by changing the intensity of an external quantizing magnetic field.

Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial

Artificial cavity photon resonators with ultrastrong light-matter interactions are attracting interest both in semiconductor and superconducting systems because of the possibility of manipulating the cavity quantum electrodynamic ground state with controllable physical properties. We report here experiments showing ultrastrong light-matter coupling in a terahertz (THz) metamaterial where the cyclotron transition of a high-mobility two-dimensional electron gas (2DEG) is coupled to the photonic modes of an array of electronic split-ring resonators. We observe a normalized coupling ratio, Ω/ω(c) = 0.58, between the vacuum Rabi frequency, Ω, and the cyclotron frequency, ω(c). Our system appears to be scalable in frequency and could be brought to the microwave spectral range with the potential of strongly controlling the magnetotransport properties of a high-mobility 2DEG.

The anisotropic glass-like properties of disordered crystals

The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar. All these properties are described theoretically with reasonable quantitative accuracy by assuming that the amorphous solid contains dynamical defects that can be described at low temperatures as an ensemble of two-level systems (TLS), but the deep nature of these TLSs is not clarified yet. Moreover, glassy properties were found also in disordered crystals, quasicrystals, and even perfect crystals with a large number of atoms in the unit cell. In crystals, the glassy properties are not universal, like in amorphous materials, and also exhibit anisotropy. Recently it was proposed a model for the interaction of two-level systems with arbitrary strain fields (Phys. Rev. B 75, 64202, 2007), which was used to calculate the thermal properties of nanoscopic membranes at low temperatures. The model is also suitable for the description of anisotropic crystals. We describe here the results of the calculation of anisotropic glass-like properties in crystals of various lattice symmetries.

Anisotropic interaction of two-level systems with acoustic waves in disordered cubic crystals

We apply the model introduced in Phys. Rev. B 75, 064202 (2007), cond-mat/0610469, to calculate the anisotropy effect in the interaction of two level systems with phonons in disordered crystals. We particularize our calculations to cubic crystals and compare them with the available experimental data to extract the parameters of the model. With these parameters we calculate the interaction of the dynamical defects in the disordered crystal with phonons (or sound waves) propagating along other crystalographic directions, providing in this way a method to investigate if the anisotropy comes from the two-level systems being preferably oriented in a certain direction or solely from the lattice anisotropy with the two-level systems being isotropically oriented.

Interaction of two-level systems in amorphous materials with arbitrary phonon fields

To describe the interaction of the two-level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a $6\ifmmode\times\else\texttimes\fi{}6$ symmetric tensor of deformation potential parameters $[R]$. Taking into account the isotropy of the amorphous solid, we deduce that $[R]$ has only two independent parameters. We show how these two parameters can be calculated from experimental data, and we prove that for any amorphous bulk material, the average coupling of TLSs with longitudinal phonons is always stronger than the average coupling with transversal phonons (in standard notations, ${\ensuremath{\gamma}}_{l}>{\ensuremath{\gamma}}_{t}$).

Interaction-Driven Relaxation of Two-Level Systems in Glasses

We study how the elastic interaction of two-level systems contributes to their relaxational motion. Evaluating the Mori-Zwanzig memory function in terms of a perturbation series in powers of the couplings J(ij), we find a null result at second order, which means that interacting pairs of two-level systems do not give rise to relaxation, yet a finite relaxation rate does occur in fourth order; i.e., a diffusive band is formed by resonant triples. Our results provide a simple explanation for several puzzling experimental observations. Regarding the temperature dependence of the sound velocity deltanu approximately lnT in the kHz range, we find that its slope below and above the maximum takes opposite signs but the same absolute value, in agreement with the measured ratio 1 : - 1. Below the relaxation plateau, the internal friction is shown to vary linearly with T, in agreement with experiment.

Statistical Analysis of Spectra of Single Impurity Molecules and Dynamics of Disordered Solids: I. Distributions of Linewidths, Moments, and Cumulants

A review of recent results of studying the low-temperature dynamics of a disordered solid-state medium that were obtained by the method of single molecule spectroscopy (SMS) is presented. The studies were carried out with the use of the new approach of the statistical analysis of a large number of spectra of single molecules embedded into a medium under study as a microscopic spectral probe. The measurements were performed in the range 2–7 K. The use of SMS allowed us to avoid the information losses connected with the averaging over an ensemble of impurity molecules that is inherent in conventional spectral methods. For the example of the system studied (amorphous polyisobutylene doped with molecules of tetra-tert-butylterrylene), it was shown experimentally that, at low temperatures, the spectra of single impurity molecules in disordered media obey the Levy statistics. New microscopic information on the interaction of two-level systems and quasi-local low-frequency vibrational modes of the matrix with impurity molecules in a disordered medium was obtained.

Statistical Analysis of Spectra of Single Impurity Molecules and Dynamics of Disordered Solids: II. Manifestation of Interaction of Two-Level Systems with Impurity Molecules at Different Distances

Manifestations in the spectra of impurity chromophore molecules in a disordered solid matrix of the interaction of these molecules with two-level systems (TLSs) of the matrix are analyzed. The characteristic distances within the limits of which the interaction between TLSs and an impurity molecule leads, in the main, to either splitting or broadening of the spectrum, as well as the distance beginning with which this interaction is practically undetectable, are determined. Information about the effective value of the minimal distance between impurity molecules and TLSs, which is caused by nonzero sizes of the molecules and the TLSs, is presented. The analysis is performed by a statistical processing of experimental and model spectra of single tetra-tert-butylterrylene molecules in amorphous polyisobutylene at a temperature of 2 K, when the contribution of quasi-local low-frequency vibrational modes of the matrix to these spectra can be neglected.

Rotational echo in amorphous ferromagnets

The rotational echo in amorphous ferromagnets is investigated. It is conjectured that amorphous ferromagnets contain a group of molecules having a dipole moment, and the change in the orientation of these molecules gives rise to oscillations of the echo signal. The transverse relaxation time associated with the interaction of two-level systems through spin waves is calculated. The time dependence of the echo signal is investigated.

Dipole gap effects in low energy excitation spectrum of amorphous solids. Theory for dielectric relaxation

The long-range interaction of two-level systems in dielectric glasses influences the density of states and consequently the non-equilibrium dielectric response. The AC dielectric susceptibility is analyzed under rapid switching on of the DC electric field. The instantaneous increase of the dielectric susceptibility together with its subsequent logarithmic relaxation, observed experimentally, are explained in the framework of a model of weakly interacting two-level systems. The temperature and frequency dependences of the relaxation rate are found to be in a good agreement with the experimental data.

Dipole gap effects in low energy excitation spectrum of amorphous solids. Theory for dielectric relaxation

The influence of the long-range interaction of two-level systems in dielectric glasses on the density of low-energy excitations and the dielectric properties is studied. The AC dielectric susceptibiliy is analyzed under rapid switching on the external DC electric field. The instantaneous increase in the dielectric susceptibility and its subsequent logarithmic relaxation, recently observed in Ref. 1, are qualitatively explained in a framework of a weakly interacting two-level systems model. The temperature and frequency dependencies of the logarithmic relaxation rate are discussed.

Nonlinear resonant attenuation in glasses and spectral diffusion.

We have developed a quantitative theory of two nonlinear low-temperature phenomena in dielectric glasses for which interaction of two-level systems (TLS's) is responsible. They are the nonlinear resonant ultrasonic or microwave absorption and hole burning. General formulas are obtained for the critical intensity determining the onset of nonlinear behavior of resonant absorption and for the form of the burned hole with regard to the spectral diffusion. These formulas are investigated in detail for various limiting cases.