arXiv subjects

K. S. Tikhonov

Publications and source records attributed to K. S. Tikhonov.

32 records · Page 2Linked to original sources

arXiv2017

Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations

We developed general approach to the calculation of power-law infrared asymptotics of spin-spin correlation functions in the Kitaev honeycomb model with different types of perturbations. We have shown that in order to find these correlation functions, one can perform averaging of some bilinear forms composed out of free Majorana fermions, and we presented the method for explicit calculation of these fermionic densities. We demonstrated how to derive an effective Hamiltonian for the Majorana fermions, including the effects of perturbations. For specific application of the general theory, we have studied the effect of the Dzyaloshinskii-Moriya anisotropic spin-spin interaction; we demonstrated that it leads, already in the second order over its relative magnitude $D/K$, to a power-law spin correlation functions, and calculated dynamical spin structure factor of the system. We have shown that an external magnetic field $h$ in presence of the DM interaction, opens a gap in the excitation spectrum of magnitude $Δ\propto D h$.

cond-mat.str-el↗

arXiv2017

Noiseless signal shaping and cluster state generation with quantum memory cell

In this article, we employ multimode radiation of a synchronously pumped optical parametric oscillator (SPOPO) to build a cluster state through a conversion on the base of quantum memory cell. We demonstrate that by choosing an appropriate driving field we can ensure the effective writing of the only one supermode from the entire set of the SPOPO squeezed supermodes. Further, by changing the driving field profile at the readout, we convert the time profile of the retrieved signal while maintaining its quantum state. We demonstrate the possibilities of using the presented scheme by the example of creating a four-mode linear cluster state of light.

quant-ph↗

arXiv2016

Preservation of quantum correlations in femtosecond light pulse train within atomic ensemble

In this paper, we examined a possibility of preservation of a substantially multimode radiation in a single cell of quantum memory. As a light source we considered a synchronously pumped optical parametric oscillator (SPOPO). As it was shown in [1-4], SPOPO radiation has a large number of the correlated modes making it attractive for the purposes of the quantum communication and computing. We showed that these correlations can be mapped on the longitudinal spin waves of the memory cell and be restored later in the readout light. The efficiencies of the writing and readout depend on the mode structure of the memory determined by a mechanism of the light-matter interaction under consideration (the non-resonance Raman interaction) and by the profile of the driving light field. We showed that like the initial light pulse train, the restored one can be represented by a set of squeezed supermodes. The mapping of the quantum multimode correlations on the material medium offers opportunities to manipulate the quantum states within the memory cell followed by the reading of the transformed state.

quant-ph↗

arXiv2016

Long-range spin correlations in a honeycomb spin model with magnetic field

We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x \propto h_z^2$. Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $δk \propto h_z^2$. We also compute the dynamic structure factor $S(\mathbf{p},ω)$; in the vicinity of $\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},ω)-S(\mathbf{p}_K,ω)\propto\sqrt{ω^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.

cond-mat.str-el↗

arXiv2016

Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary

We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally tree-like structure without a boundary (random regular graph) where extended wavefunctions are ergodic.

cond-mat.dis-nn↗

arXiv2016

Anderson localization on random regular graphs

A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system, where $N_c$ is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their inverse participation ratio scales as $1/N$.

cond-mat.dis-nn↗

arXiv2016

Storage and conversion of quantum-statistical properties of light in the resonant quantum memory on tripod atomic configuration

We have considered theoretically the feasibility of the broadband quantum memory based on the resonant tripod-type atomic configuration. In this case, the writing of a signal field is carried out simultaneously into two channels, and characterized by an excitation of two spin waves of the atomic ensemble. With simultaneous read out from both channels quantum properties of the original signal are mapped on the retrieval pulse no worse than in the case of memory based on Lambda-type atomic configuration. At the same time new possibilities are opened up for manipulation of quantum states associated with sequential reading out (and/or sequential writing) of signal pulses. For example, the pulse in squeezed state is converted into two partially entangled pulses with partially squeezed quadratures. Alternatively, two independent signal pulses with orthogonal squeezed quadratures can be converted into two entangled pulses.

quant-ph↗

arXiv2014

Admittance of a long diffusive SNS junction

The dynamical properties of hybrid normal metal/superconductor structures have recently come into research focus both experimentally and theoretically. Recent experimental studies of the coherent admittance $% Y(ω)$ of SNS rings as function of the phase difference $ϕ_{0}$ are still not fully understood. Here we concentrate on the linear response regime, calculating $Y(ω)$ by solving Usadel equations, linearised in electric field. Although partially reproducing previously known results, we find qualitatively different behaviour in the collisionless regime of $τ_{in}^{-1}\ll ω\lesssim E_{Th}$ and high temperature $T\gg E_{Th}$ and low temperature $T\lesssim E_{Th}$ near the minigap closing $ϕ_{0}\sim π$. We find that the dissipative part $\mbox{Re}Y(ω)$ peaks when the minigap closes (at a phase difference of $π$) even at high temperatures, when the equilibrium supercurrent is fully suppressed.

cond-mat.supr-con↗

arXiv2013

Spin resonance in Luttinger liquid with spin-orbit interaction

Spin-orbit interaction in quantum wires leads to a spin resonance at low temperatures, even in the absence of an external dc magnetic field. We study the effect of electron-electron interaction on the resonance. This interaction is strong in quantum wires. We show that the electron-electron interaction changes the shape of the resonance curve and produces an additional cusp at the plasmon frequency. However, except for very strong electron-electron interaction these changes are weak since this interaction by itself does not break the spin-rotation symmetry that is violated weakly by the spin-orbit interaction and external magnetic field.

cond-mat.str-el↗

arXiv2013

Spectral non-uniform temperature, non-local heat transfer, and the spin Seebeck effect

We present a theory of the spin Seebeck effect driven by subthermal non-local phonon heat transfer and spectral non-uniform temperature distribution. The theory explains the non-local behavior of the effect arising from the fact that phonons that store the energy (thermal) and the phonons that transfer it (subthermal) are located in different parts of the spectrum and have very different kinetics. This gives rise to a spectral phonon distribution function that deviates from local equilibrium along the substrate and is sensitive to boundary conditions. The theory also predicts a non-magnon origin of the effect in ferromagnetic metals in agreement with observations in recent experiments. Equilibration of the heat flow out of the substrate to the Pt probe and backwards leads to a measurable vertical spin-current produced by the spin polarized electrons dragged by the local thermal phonons. We predict specific sample length limits and other dependencies that can be probed experimentally, and obtain the correct magnitude of the effect.

cond-mat.mes-hall↗

arXiv2011

Disordered electron liquid in double quantum well heterostructures: Renormalization group analysis and dephasing rate

We report a detailed study of the influence of the electron-electron interaction on physical observables (conductance, etc.) of a disordered electron liquid in double quantum well heterostructure. We find that even in the case of common elastic scattering off electrons in both quantum wells, the asymmetry in the electron-electron interaction across and within quantum wells decouples them at low temperatures. Our results are in quantitative agreement with recent transport experiments on the gated double quantum well Al$_x$Ga$_{1-x}$As/GaAs/Al$_x$Ga$_{1-x}$As heterostructures.

cond-mat.mes-hall↗

arXiv2010

Quantum spin metal state on a decorated honeycomb lattice

We present a modification of exactly solvable spin-(1/2) Kitaev model on the decorated honeycomb lattice, with a ground state of "spin metal" type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi-circle those size depends on the ratio of exchange couplings. Low-temperature heat capacity C(T) and dynamic spin susceptibility χ(ω,T) are calculated in the case of small Fermi-circle. Whereas C(T)\sim T at low temperatures as it is expected for a Fermi-liquid, spin excitations are gapful and χ(ω,T) demonstrate unusual behaviour with a power-law peak near the resonance frequency. The corresponding exponent as well as the peak shape are calculated.

cond-mat.str-el↗

arXiv2009

AC Josephson effect in the long voltage-biased SINIS junction

Theory of non-stationary coherent effects is developed for superconductor-normal-superconductor (SNS) structures with relatively strong normal scattering on S/N interfaces (interface resistance is large compared to intrinsic resistance of N metal). Analitical expressions are found for the time-dependent anomalous Green functions induced in the N region under the fixed-voltage-bias. The amplitude of the current oscillations is determined in non-equilibrium conditions. Non-stationary correction to the distribution function is calculated in high-temperature limit and found to be slowly decreasing with the temperature, leading to the dominance of the second-harmonic term in the Josepshon current at high temperatures and low voltage.

cond-mat.supr-con↗

arXiv2008

Proximity-induced superconductivity in graphene

We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T_c, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T<<T_c, and zero magnetic field, the density of states is characterized by a small gap E_g<T_c resulting from the collective proximity effect. Transverse magnetic field H_g(T) E_g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H_{g2}(T).

cond-mat.mes-hall↗