Condensed Matter

Ultrasonic wave attenuation({\alpha}) measurement by pulse-echo method exhibits pronounced dependence on experimental conditions. It is shown to be an inherent characteristic of the method itself. Estimation of {\alpha} from the component wave amplitudes in the frequency scale gives more accurate and consistent value. This technique, viz., the Fourier Spectrum Pulse-Echo (FSPE) is demonstrated to determine the ultrasonic velocity(v) and attenuation constant({\alpha}) in ultrapure de-ionized water at room temperature (250C) at 1MHz and 2 MHz wave frequency.

The reported results for ultrasonic wave attenuation constant ({\alpha}) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant ({\alpha}) at 1MHz frequency in tri-distilled water at room temperature (25oC). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, {\alpha} and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values.

The rigid double-torus torsional oscillator (TO) is constructed to reduce any elastic effects in-herent to complicate TO structures, allowing explicit probing for a genuine supersolid signature. We investigated the frequency- and temperature-dependent response of the rigid double-torus TO containing solid 4He with 0.6 ppb 3He and 300 ppb 3He. We did not find evidence to support the frequency-independent contribution proposed to be a property of supersolid helium. The frequency-dependent contribution which comes from the simple elastic effect of solid helium coupled to TO is essentially responsible for the entire response. The magnitude of the period drop is linearly proportional to f 2 , indicating that the responses observed in this TO are mostly caused by the overshoot of `soft' solid helium against the wall of the torus. Dissipation of the rigid TO is vastly suppressed compared to those of non-rigid TOs.

We present a new method to compute resonance Raman spectra based on ab initio level calculations using the frequency-dependent Placzek approximation. We illustrate the efficiency of our hybrid quantum-classical method by calculating the Raman spectra of several materials with different crystal structures. Results obtained from our approach agree very well with experimental data in the literature. We argue that our method offers an affordable and far more accurate alternative to the widely used static Placzek approximation.

We study the extended Bose-Hubbard model with nearest-neighbor and next-nearest-neighbor (V, V ??) repulsive interactions on a square lattice by using the quantum Monte Carlo method. Unlike the case of strong V ??where the ground states can be striped solids or striped supersolids, we focus on weak V ??<V/2 and small hoppings and find that, in the thermodynamic limit, incommensurate solids of fractional densities varying from 1/4 to 1/2 can be stabilized. We also show that the incommensurate solids, which are characterized by a continuous set of wave vectors changing from (?,?/2) (or (?/2,?) ) to (?,?) , can be understood by a mechanism of domain wall formation. The related ground-state phase diagram and thermal phase transitions are also discussed.

We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize the d -wave superfluid, which shares the same pairing symmetry with high- T c materials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that the role of bound states is more subtle: when a macroscopic object moves in superfluid 3 He at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.

Faraday rotation being a dispersive effect, is commonly considered as the method of choice for non-destructive detection of spin states. Nevertheless Faraday rotation is inevitably accompanied by spin-flips induced by Raman scattering, which compromises non-destructive detection. Here, we derive an explicit general relation relating the Faraday rotation and the spin-flip Raman scattering cross-sections, from which precise criteria for non-destructive detection are established. It is shown that, even in ideal conditions, non-destructive measurement of a single spin can be achieved only in anisotropic media, or within an optical cavity.

The self-consistent GW{\Gamma} method satisfies the Ward-Takahashi identity (i.e., the gauge invariance or the local charge continuity) for arbitrary energy ( ω ) and momentum ( q ) transfers. Its self-consistent first-principles treatment of the vertex Γ= Γ v or Γ W is possible to first order in the bare ( v ) or dynamically-screened ( W ) Coulomb interaction. It is developed within a linearized scheme and combined with the Bethe-Salpeter equation (BSE) to accurately calculate photoabsorption spectra (PAS) and photoemission (or inverse photoemission) spectra (PES) simultaneously. The method greatly improves the PAS of Na, Na 3 , B 2 , and C 2 H 2 calculated using the standard one-shot G 0 W 0 + BSE method that results in significantly redshifted PAS by 0.8-3.1 eV, although the PES are well reproduced already in G 0 W 0 .

The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge.