arXiv subjects

Mikhail V. Fistul

Publications and source records attributed to Mikhail V. Fistul.

13 recordsLinked to original sources

arXiv2026

Nematic Phase Transitions in 1D Flat Band Condensates

We investigate the ground-state properties of one-dimensional Gross-Pitaevskii flat-band lattices which are parametrized through their compact localized state (CLS) amplitudes. We uncover a CLS geometry-driven phase transition into a macroscopically degenerate nematic state with broken time-reversal symmetry. The transition is marked by the appearance of constant-density flat-band states and a vanishing sound velocity. We demonstrate that even infinitesimal onsite interactions can destabilize a $k=0$ plane wave condensate, driving the system into a nematic manifold, which persists for any interaction strength. For the particular choice of constant density CLSs which can tile the lattice, we identify additional families of continuously degenerate ground states characterized by vanishing phase stiffness. Utilizing Bogoliubov-de Gennes excitations and parallel tempering, we show that these tiling phases are thermally selected at low temperatures via an order-by-disorder mechanism. We exemplify our findings for different classes of flat bands. Our findings also reveal that the sound velocity in flat-band condensates is a sensitive probe of the underlying nematic phase transitions.

cond-mat.stat-mech↗

arXiv2026

Quantum dynamics of two $XX$ interacting PT-symmetric non-Hermitian qubits: enhancement of quantum annealing

Quantum information platforms enable analog quantum simulations, such as quantum annealing, offering a promising route to solving complex combinatorial optimization problems. Here, we propose a quantum information architecture based on networks of interacting parity-time (PT)-symmetric non-Hermitian qubits. While the dynamics of individual PT-symmetric qubits have been experimentally demonstrated across multiple platforms including NV centers, superconducting circuits, and trapped-ion systems yet coherent dynamics in interacting systems remain largely unexplored. To address this issue we theoretically investigate stationary and time-dependent Hamiltonians relevant to quantum annealing using a minimal model of two interacting XX-coupled PT-symmetric non-Hermitian qubits. We analyze both symmetry-preserving and symmetry-broken regimes and demonstrate that adding even tiny PT-symmetric non-Hermitian terms in the qubits Hamiltonian allows to greatly enhance the probability of reaching the ground state after annealing.

quant-ph↗

arXiv2024

Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: an effective XX spin chain with long-range interaction

We study theoretically a variety of collective quantum phases occurring in frustrated saw-tooth chains of Josephson junctions embedded in a dissipationless transmission line. The basic element of a system, i.e., the triangular superconducting cell, contains two $0$- and one $π$- Josephson junctions characterized by $E_J$ and $αE_J$ Josephson energies, accordingly. In the frustrated regime the low energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex/antivortex). The direct embedding of $π$-Josephson junctions in a transmission line allows to establish a short/long-range interaction between (anti)vortices of well separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective $XX$ spin model with an exchange spin-spin interaction decaying with the distance $x$ as $x^{-β}$, and the local $\hat σ_{x,n}$-terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that in long arrays as $N \gg \ell_0 \simeq \sqrt{C/C_0}$, where $C$ and $C_0$ are capacitances of $0$-Josephson junction and transmission line, accordingly, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic ($P$), compressible superfluid ($CS$) and weakly compressible superfluid ($w$-$CS$) states.

quant-ph↗

arXiv2023

Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints

Geometrical frustration in correlated systems can give rise to a plethora of novel ordered states and intriguing phases. Here, we analyze theoretically vertex-sharing frustrated Kagome lattice of Josephson junctions and identify various classical and quantum phases. The frustration is provided by periodically arranged $0$- and $π$- Josephson junctions. In the frustrated regime the macroscopic phases are composed of different patterns of vortex/antivortex penetrating each basic element of the Kagome lattice, i.e., a superconducting triangle interrupted by three Josephson junctions. We obtain that numerous topological constraints, related to the flux quantization in any hexagon loop, lead to highly anisotropic and long-range interaction between well separated vortices (antivortices). Taking into account this interaction and a possibility of macroscopic "tunneling" between vortex and antivortex in single superconducting triangles we derive an effective Ising-type spin Hamiltonian with strongly anisotropic long-range interaction. In the classically frustrated regime we calculate numerically the temperature-dependent spatially averaged spins polarization, $\overline{m}(T)$, characterizing the crossover between the ordered and disordered vortex/antivortex states. In the coherent quantum regime we analyze the lifting of the degeneracy of the ground state and the appearance of the highly entangled states.

quant-ph↗

arXiv2023

Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{PT}$-symmetric circuit QED

Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate \textit{non-Hermitian} systems. We apply our results to an exemplary $\mathcal{PT}$--symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as $|ω_r-Ω| \ll ω_r$, where $Ω$ and $ω_r$ are qubits and resonator frequencies, respectively, providing well-defined groups of quasi-degenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator, $g$, and the gain (loss) parameter $γ$, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify $\mathcal{PT}$--symmetry broken and unbroken phases, trace the formation of Exceptional Points of the second and the third order, and provide a complete phase diagram $g-γ$ of low-lying resonant states. We relate the formation of Exceptional Points to the additional $\mathcal{P}$-pseudo-Hermitian symmetry of the system and show that non-hermiticity mixes the "dark" and the "bright" states, which has a direct experimental consequence.

quant-ph↗

arXiv2023

Formation of Exceptional Points in pseudo-Hermitian Systems

Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of pseudo-Hermitian Hamiltonian as the strength of Hermiticity-breaking terms turns on. Using general symmetry arguments, we characterize the separate energy levels by a topological $\mathbb{Z}_2$ index which corresponds to the signs $\pm 1$ of the eigenvalues of pseudo-metric operator $\hat ζ$ in the absence of Hermiticity-breaking terms. After that, we show explicitly that the formation of second-order $\textit{EP}$s is governed by this $\mathbb{Z}_2$-index: only the pairs of levels with $\textit{opposite}$ index can provide second-order $\textit{EP}$s. Our general analysis is accompanied by a detailed study of $\textit{EP}$s appearance in an exemplary $\mathcal{P}\mathcal{T}$-symmetric pseudo-Hermitian system with parity operator in the role of $\hat ζ$: a transverse-field Ising spin chain with a staggered imaginary longitudinal field. Using analytically computed parity indices of all the levels, we analyze the eigenspectrum of the model in general, and the formation of third-order $\textit{EP}$s in particular

quant-ph↗

arXiv2021

Fluxons in high-impedance long Josephson junctions

The dynamics of fluxons in long Josephson junctions is a well-known example of soliton physics and allows for studying highly nonlinear relativistic electrodynamics on a microscopic scale. Such fluxons are supercurrent vortices that can be accelerated by a bias current up to the Swihart velocity, which is the characteristic velocity of electromagnetic waves in the junction. We experimentally demonstrate slowing down relativistic fluxons in Josephson junctions whose bulk superconducting electrodes are replaced by thin films of a high kinetic inductance superconductor. Here, the amount of magnetic flux carried by each supercurrent vortex is significantly smaller than the magnetic flux quantum $ Φ_0 $. Our data show that the Swihart velocity is reduced by about one order of magnitude compared to conventional long Josephson junctions. At the same time, the characteristic impedance is increased by an order of magnitude, which makes these junctions suitable for a variety of applications in superconducting electronics.

cond-mat.supr-con↗

arXiv2021

Anderson localization of excitations in disordered Gross-Pitaevskii lattices

We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the weak and strong interaction regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov-de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For strong interactions, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective strong interaction field equations for the excitations and generalize to higher dimensions.

cond-mat.dis-nn↗

arXiv2019

Electromagnetic waves propagation through an array of superconducting qubits: manifestations of non-equilibrium steady states of qubits

We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as the frequency of EWs $ω\simeq ω_q$, where $ω_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency dependent transmission coefficient of EWs, $D(ω)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(ω)$ in both cases of a single qubit and chains composed of a large number of densely arranged qubits. However, in narrow frequency regions a chain of qubits allows the resonant transmission of EWs with greatly enhanced $D(ω)$. In the nonlinear regime realized for a moderate power of applied microwave radiation, we predict and analyze various transitions between states characterized by high and low values of $D(ω)$. These transitions are manifestations of nonequilibrium steady states of an array of qubits achieved in this regime.

quant-ph↗

arXiv2018

Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades

We use a novel unitary map toolbox -- discrete time quantum walks originally designed for quantum computing -- to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment $m_2 \sim t^{1/3}$ (with time in units of a characteristic scale $t_0$) up to the largest computed times of the order of $10^8$. A fundamental question remained as to whether this process can continue ad infinitum, or has to slow down. Current experimental devices are not capable to even reach 1\textpertenthousand ~of the reported computational horizons. With our toolbox, we outperform previous computational results and observe that the universal subdiffusion persists over additional four decades reaching 'astronomic' times $2\cdot 10^{12}$. Such a dramatic extension of previous computational horizons suggests that subdiffusion is universal, and that the toolbox can be efficiently used to assess other hard computational many-body problems.

cond-mat.dis-nn↗

arXiv2014

Josephson phase diffusion in small Josephson junctions: a strongly nonlinear regime

I present a theoretical study of current-voltage characteristics ($I$-$V$ curves ) of small Josephson junctions. In the limit of a small Josephson coupling energy $E_J \ll k_B T$ the thermal fluctuations result in a stochastic dependence of the Josephson phase $φ$ on time, i.e the Josephson phase diffusion. These thermal fluctuations destroy the superconducting state, and the low-voltage resistive state is characterized by a nonlinear $I$-$V$ curve. Such $I$-$V$ curve is determined by the resonant interaction of ac Josephson current with the Josephson phase oscillations excited in the junction. The main frequency of ac Josephson current is $ω=eV/\hbar$, where $V$ is the voltage drop on the junction. In the phase diffusion regime the Josephson phase oscillations show a broad spectrum of frequencies. The average $I$-$V$ curve is determined by the time-dependent correlations of the Josephson phase. By making use of the method of averaging elaborated in Ref. M. V. Fistul and G. F. Giuliani, Phys. Rev. B 56, 788 (1997), for Josephson junctions with randomly distributed Abrikosov vortices I will be able to obtain two regimes: a linear regime as the amplitudes of excited phase oscillations are small, and a strongly nonlinear regime as both the amplitudes of excited Josephson phase oscillations and the strength of resonant interaction are large. The latter regime can be realized in the case of low dissipation. The crossover between these regimes is analyzed.

cond-mat.supr-con↗

arXiv2013

A multi-stable switchable metamaterial

The field of metamaterial research revolves around the idea of creating artificial media that interact with light in a way unknown from naturally occurring materials. This is commonly achieved by creating sub-wavelength lattices of electronic or plasmonic structures, so-called meta-atoms, that determine the interaction between light and metamaterial. One of the ultimate goals for these tailored media is the ability to control their properties in-situ which has led to a whole new branch of tunable and switchable metamaterials. Many of the present realizations rely on introducing microelectromechanical actuators or semiconductor elements into their meta-atom structures. Here we show that superconducting quantum interference devices (SQUIDs) can be used as fast, intrinsically switchable meta-atoms. We found that their intrinsic nonlinearity leads to simultaneously stable dynamic states, each of which is associated with a different value and sign of the magnetic susceptibility in the microwave domain. Moreover, we demonstrate that it is possible to switch between these states by applying a nanosecond long pulse in addition to the microwave probe signal. Apart from potential applications such as, for example, an all-optical metamaterial switch, these results suggest that multi-stability, which is a common feature in many nonlinear systems, can be utilized to create new types of meta-atoms.

cond-mat.mes-hall↗

arXiv2011

Conversion of self-assembled monolayers into nanocrystalline graphene: Structure and electric transport

Graphene-based materials have been suggested for applications ranging from nanoelectronics to nanobiotechnology. However, the realization of graphene-based technologies will require large quantities of free-standing two-dimensional (2D) carbon materials with tuneable physical and chemical properties. Bottom-up approaches via molecular self-assembly have great potential to fulfil this demand. Here, we report on the fabrication and characterization of graphene made by electron-radiation induced cross-linking of aromatic self-assembled monolayers (SAMs) and their subsequent annealing. In this process, the SAM is converted into a nanocrystalline graphene sheet with well defined thickness and arbitrary dimensions. Electric transport data demonstrate that this transformation is accompanied by an insulator to metal transition that can be utilized to control electrical properties such as conductivity, electron mobility and ambipolar electric field effect of the fabricated graphene sheets. The suggested route opens broad prospects towards the engineering of free-standing 2D carbon materials with tuneable properties on various solid substrates and on holey substrates as suspended membranes.

cond-mat.mes-hall↗