arXiv subjects

D. N. Maksimov

Publications and source records attributed to D. N. Maksimov.

25 records · Page 2Linked to original sources

arXiv2018

NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition

We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions is slowly increased and, simultaneously, the inter-well tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the number of atoms.

cond-mat.quant-gas↗

arXiv2018

Propagating bound states in the continuum in dielectric gratings

We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged ether on top or on the both sides of the slab. Based on the Fourier modal approach we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-side grating possesses either mirror or glide symmetry the Bloch bound states are stable to variation of parameters as far as the above symmetries are preserved.

physics.optics↗

arXiv2015

Bound states in the continuum in open acoustic resonators

We consider bound states in the continuum (BSC) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct-cavity structures. We demonstrate numerically that under variation of the length of the cavity multiple BSCs occur due to the Friedrich-Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

physics.class-ph↗

arXiv2014

Wannier-Stark states in double-periodic lattices I: one-dimensional lattices

We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark problem and the driven two-level system in the strong-coupling regime.

quant-ph↗

arXiv2014

Wannier-Stark states in double-periodic lattices II: two-dimensional lattices

We analyze the Wannier-Stark spectrum of a quantum particle in tilted two-dimensional lattices with the Bloch spectrum consisting of two subbands, which could be either separated by a finite gap or connected at the Dirac points. For rational orientations of the static field given by an arbitrary superposition of the translation vectors the spectrum is a ladder of energy bands. We obtain asymptotic expressions for the energy bands in the limit of large and weak static fields and study them numerically for intermediate field strength. We show that the structure of energy bands determines the rate of spreading of a localized wave packets which is the quantity measured in laboratory experiments. It is shown that wave-packet dispersion becomes a fractal function of the field orientation in the long-time regime of ballistic spreading.

quant-ph↗

arXiv2013

Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field II: Electric breakdown

We analyze dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau-Zener tunneling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau-Zener tunneling leads to appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.

cond-mat.mes-hall↗

arXiv2008

Quantum stress in chaotic billiards

This article reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor $T_{αβ}(x,y)$ for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as $ψ= u+iv$. With the assumption that $u$ and $v$ are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components $T_{αβ}$. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schroedinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogues. Hence we report on microwave measurements for an open 2D cavity and how the quantum stress tensor analogue is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for $T_{αβ}(x,y)$ is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

cond-mat.mes-hall↗