arXiv subjects

Dmitriy S. Shapiro

Publications and source records attributed to Dmitriy S. Shapiro.

14 recordsLinked to original sources

arXiv2026

Quantum Simulation of Strongly Correlated Fermion-Phonon Models in Circuit QED

Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.

quant-ph↗

arXiv2025

Berezinskii-Kosterlitz-Thouless transitions in a topological superconductor-ferromagnet-superconductor junction

We investigate quantum phase transitions in a topological Josephson junction with an embedded ferromagnetic layer, revealing a rich landscape of critical phenomena. The low-energy excitations comprise Majorana fermions propagating along the junction, coupled to the magnons in the ferromagnet. Based on mean-field and renormalization group arguments, we predict Berezinskii-Kosterlitz-Thouless (BKT) transitions in this system, both in the case of a magnetic easy-plane and weak easy-axis anisotropy. In the latter case, this is based on an emergent effective easy-plane, spanned by the easy-axis and the component of the magnetization which couples to the Majoranas. We conclude by presenting a conjecture for the full phase diagram of the model. It covers BKT transitions as well as exotic multicritical and supersymmetric points known from related models of interacting real fermions and bosons.

cond-mat.mes-hall↗

arXiv2024

Digital-Analog Simulations of Schr\"odinger Cat States in the Dicke-Ising Model

The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a "no-go theorem''. Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system's free energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm that disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schr\"odinger cat state, which is a hallmark of the superradiant ground state in finite-size systems and can be unambiguously probed through the Wigner tomography of the resonator's field.

quant-ph↗

arXiv2023

Coulomb blockade of chiral Majorana and complex fermions far from equilibrium

We study charge transport in a single-electron transistor implemented as an interferometer such that the Coulomb blockaded middle island contains a circular chiral Majorana or Dirac edge mode. We concentrate on the regime of small conductance and provide an asymptotic solution in the limit of high transport voltage exceeding the charging energy. The solution is achieved using an instanton-like technique. The distinctions between Majorana and Dirac cases appears when the tunnel junctions are unequal. The main difference is in the offset current at high voltages which can be higher up to $50\%$ in Majorana case. It is caused by an additional particle-hole symmetry of the distribution function in the Majorana case. There is also an eye-catching distinction between the oscillations patterns of the current as a function of the gate charge. We conjecture this distinction survives at lower transport voltages as well.

cond-mat.mes-hall↗

arXiv2022

Cavity-QED of a quantum metamaterial with tunable disorder

We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows to change the number N of resonantly coupled qubits and also to introduce a disorder in their excitation frequencies with preassigned distributions. While increasing N, we demonstrate the expected $N^{1/2}$ scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.

quant-ph↗

arXiv2021

Transport of pseudothermal photons through an anharmonic cavity

Under nonequilibrium conditions, quantum optical systems reveal unusual properties that might be distinct from those in condensed matter. The fundamental reason is that photonic eigenstates can have arbitrary occupation numbers, whereas in electronic systems these are limited by the Pauli principle. Here, we address the steady-state transport of pseudothermal photons between two waveguides connected through a cavity with Bose-Hubbard interaction between photons. One of the waveguides is subjected to a broadband incoherent pumping. We predict a continuous transition between the regimes of Lorentzian and Gaussian chaotic light emitted by the cavity. The rich variety of nonequilibrium transport regimes is revealed by the zero-frequency noise. There are three limiting cases, in which the noise-current relation is characterized by a power-law, $S\propto J^γ$. The Lorentzian light corresponds to Breit-Wigner-like transmission and $γ=2$. The Gaussian regime corresponds to many-body transport with the shot noise ($γ=1$) at large currents; at low currents, however, we find an unconventional exponent $γ=3/2$ indicating a nontrivial interplay between multi-photon transitions and incoherent pumping. The nonperturbative solution for photon dephasing is obtained in the framework of the Keldysh field theory and Caldeira-Leggett effective action. These findings might be relevant for experiments on photon blockade in superconducting qubits, thermal states transfer, and photon statistics probing.

quant-ph↗

arXiv2021

Microwave response of a chiral Majorana interferometer

We consider an interferometer based on artificially induced topological superconductivity and chiral 1D Majorana fermions. The (non-topological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency dependent impedance between the island and the earth. Namely, charging and discharging of the island is controlled by the time-delayed interference of chiral Majorana excitations in both normal and Andreev channels. We argue that microwave measurements provide a direct way to observe the physics of 1D chiral Majorana modes.

cond-mat.mes-hall↗

arXiv2018

Excess equilibrium noise in topological SNS junction between chiral Majorana liquids

We consider a Josephson contact mediated by 1D chiral modes on a surface of a 3D topological insulator with superimposed superconducting and magnetic layers. The system represents an interferometer in which 1D chiral Majorana modes on the boundaries of superconducting electrodes are linked by ballistic chiral Dirac channels. We investigate the noise of the Josephson current as a function of the dc phase bias and the Aharonov-Bohm flux. Starting from the scattering formalism, a Majorana representation of the Keldysh generating action for cumulants of the transmitted charge is found. At temperatures higher than the Thouless energy $E_{\rm Th}$, we obtain the usual Johnson-Nyquist noise, $4G_0 k_{\rm B}T$, characteristic for a single-channel wire with $G_0 \equiv e^2/(2π\hbar)$. At lower temperatures the behavior is much richer. In particular, the equilibrium noise is strongly enhanced to a temperature-independent value $\sim G_0 E_{\rm Th}$ if the Aharonov-Bohm and superconducting phases are both close to $2πn$, which are points of emergent degeneracy in the ground state of the junction. The equilibrium noise is related to the Josephson junction's impedance via the fluctuation-dissipation theorem. In a striking contrast to usual Josephson junctions (tunnel junctions between two $s$-wave superconductors), the real part of the impedance does not vanish, reflecting the gapless character of Majorana modes in the leads.

cond-mat.supr-con↗

arXiv2017

Many-body synchronization of interacting qubits by engineered ac-driving

In this work we introduce the many-body synchronization of an interacting qubit ensemble which allows one to switch dynamically from many-body-localized (MBL) to an ergodic state. We show that applying of $π$-pulses with altering phases, one can effectively suppress the MBL phase and, hence, eliminate qubits disorder. The findings are based on the analysis of the Loschmidt echo dynamics which shows a transition from a power-law decay to more rapid one indicating the dynamical MBL-to-ergodic transition. The technique does not require to know the microscopic details of the disorder.

cond-mat.dis-nn↗

arXiv2017

Thermoelectric transport in junctions of Majorana and Dirac channels

We investigate the thermoelectric current and heat conductance in a chiral Josephson contact on a surface of a 3D topological insulator, covered with superconducting and magnetic insulator films. The contact consists of two junctions of Majorana and Dirac channels next to two superconductors. Geometric asymmetry results in a supercurrent without a phase bias. The interference of Dirac fermions causes oscillations of the electric and heat currents with an unconventional period $2Φ_0=h/e$ as functions of the Aharonov-Bohm flux. Due to the gapless character of Majorana modes, there is no threshold for the thermoelectric effect and the current-flux relationship is non-sinusoidal. Depending on the magnetic flux, the direction of the electric current can be both from the hot to cold lead and vice versa.

cond-mat.mes-hall↗

arXiv2016

Role of qubit-cavity entanglement for switching dynamics of quantum interfaces in superconductor metamaterials

We study quantum effects of strong driving field applied to dissipative hybrid qubit-cavity system which are relevant for a realization of quantum gates in superconducting quantum metamaterials. We demonstrate that effects of strong and non-stationary drivings have significantly quantum nature and can not be treated by means of mean-field approximation. This is shown from a comparison of steady state solution of the standard Maxwell-Bloch equations and numerical solution of Lindblad equation on a density matrix. We show that mean-field approach provides very good agreement with the density matrix solution at not very strong drivings $f f^*$ a growing value of quantum correlations between fluctuations in qubit and photon sectors changes a behavior of the system. We show that in regime of non-adiabatic switching on of the driving such a quantum correlations influence a dynamics of qubit and photons even at weak $f$.

quant-ph↗

arXiv2015

Current-phase relation and $h/e$-periodic critical current of a chiral Josephson contact between 1D Majorana modes

We explore a long Josephson contact transporting Cooper pairs between 1D charge-neutral chiral Majorana modes in the leads via charged Dirac chiral modes in the normal region. We investigate the regimes of (i) transparent contacts and (ii) tunnel junctions implemented in 3D topological insulator/superconductor/magnet hybrid structures. The setup acts as a SQUID controlled by the magnetic flux enclosed by the chiral loop of the normal region. This chirality leads to the fractional $h/e$-periodic pattern of critical current. The current-phase relation can have sawtooth-like shape with spikes at unusual even phases of $2πn$.

cond-mat.supr-con↗

arXiv2015

Synchronization of qubit ensemble under optimized $π$-pulse driving

We propose technique of simultaneous excitation of disordered qubits providing an effective suppression of inhomogeneous broadening in their spectral density. The technique is based on applying of optimally chosen $π$-pulse with non-rectangular smooth shape. We study excitation dynamics of an off-resonant qubit subjected to strong classical electromagnetic driving field with the fast reference frequency and slow envelope. Within this solution we optimize the envelope to achieve a preassigned accuracy in qubit synchronization.

cond-mat.dis-nn↗

arXiv2015

Dispersive Response of a Disordered Superconducting Quantum Metamaterial

We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulations are in agreement with the results of the recently reported experiment.

cond-mat.supr-con↗