arXiv subjects

Andrey Grankin

Publications and source records attributed to Andrey Grankin.

At least 19 recordsLinked to original sources

arXiv2026

Bogolyubov excitons as a microscopic origin of two-level systems

Two-level systems (TLS) are a leading source of decoherence and dielectric loss in Josephson-junction qubits, yet their microscopic origin remains unresolved. We propose an intrinsic, purely electronic TLS candidate: subgap bound states of Bogolyubov quasiparticles. We show that, in a model of a conventional superconductor with electron-electron attraction in the $s$-wave channel and repulsion in higher-angular-momentum channels, the latter produce an effective attraction between Bogolyubov quasiparticles, forming bound states. These Bogolyubov excitons resemble Bardasis--Schrieffer excitons but are driven by repulsive interactions. Bulk Bogolyubov excitons are not easily detectable through single-particle tunneling or other conventional probes, but we show that surface excitons couple to an external electric field and behave as two-level systems. We examine an idealized model of a bulk superconductor proximity-coupled to a two-dimensional repulsive metal, which could represent an external metallic or semiconductor layer or an underscreened region of the superconductor. The two levels correspond to the absence and presence of a single exciton, which carries an electric dipole moment and exhibits an avoided crossing with a resonator, as observed for TLS. Because this mechanism requires no defects and cannot be eliminated by screening or annealing, it suggests that TLS-like excitations may be intrinsic to superconductors.

cond-mat.supr-con↗

arXiv2026

Signatures of quantum chaos in phonon-polariton billiards

We use scanning near-field optical microscopy to image hyperbolic phonon polaritons in hexagonal boron nitride (hBN) billiards with integrable and chaotic geometries. In Sinai billiards, we observe irregular mode patterns consistent with quantum scarring, together with an unexpected sensitivity to weak probe perturbations. These random-wave features coexist with non-chaotic one-dimensional boundary modes arising from nontrivial polariton reflection at the billiard edge. As the billiard boundary becomes increasingly complex, the Fourier transforms of the measured signals evolve toward ring-like structures consistent with Berry's random-wave conjecture. We develop a numerical framework based on the Helmholtz equation with generalized boundary conditions that encode angle-dependent reflection phase shifts. The calculated level statistics exhibit a crossover from Poisson-like behavior in integrable billiards to Wigner-Dyson-like behavior in chaotic geometries, with small deviations from the canonical form arising from nonlinear boundary conditions that require self-consistent bulk-boundary analysis. Theoretical analysis based on dissipative Green's functions qualitatively reproduces the near-field data. These results establish mesoscopic van der Waals billiards as a rich platform for studying generalized chaotic dynamics of hybrid light-matter polaritons.

cond-mat.mes-hall↗

arXiv2026

Tunable viscosity across the BCS-BEC crossover

Tunable interactions make ultracold quantum gases a unique platform for exploring hydrodynamic properties in the strongly correlated regime. Of particular interest are turbulent flows possible in the regime of high Reynolds numbers. Since the system size and flow velocity are limited in experimentally realistic systems, we propose an alternative approach to enhance the Reynolds numbers in an ultracold Fermi gas by minimizing the shear viscosity in the vicinity of the Feshbach resonance. By employing the Keldysh formulation of the linear response theory, we theoretically demonstrate that the shear viscosity can vary by several orders of magnitude in the vicinity of the BCS-BEC crossover. It is also shown that while Drude-like contributions generally dominate at large Feshbach detunings, higher-order vertex corrections, including the Maki-Thompson contribution, become significant and suppress singular behavior in the near-resonant regime. Our results provide a roadmap for achieving tunable Reynolds numbers in ultracold quantum fluids, which can serve as table-top turbulence simulators.

cond-mat.quant-gas↗

arXiv2026

Fluctuation engineering in cavity quantum materials

Coupling tailored electromagnetic fluctuations to materials provides a resource for controlling correlated quantum matter. By structuring the frequency, spatial, and modal distribution of fluctuations through a new generation of cavity quantum materials, vacuum and thermal spectra can shift phase boundaries and stabilize or suppress orders. This review organizes the field around a fluctuation-focused perspective, surveying a practical design toolbox and recent milestones, and outlining theory-experiment challenges in realistic, multimode, beyond-long-wavelength regimes. We highlight photonic observables and map opportunities for equilibrium and driven control across superconducting, magnetic, moire, and topological platforms.

cond-mat.mes-hall↗

arXiv2025

Fractional Chern insulator edges: crystalline effects and optical measurements

Edge states of chiral topologically ordered phases are commonly described by chiral Luttinger liquids, effective theories that are exact only in the hydrodynamic limit. Motivated by recent bulk observations of fractional Chern insulators (FCIs) in two-dimensional materials and by synthetic realizations in ultracold atoms, we revisit this framework and quantify deviations from the hydrodynamic limit due to lattice effects. Using a combination of analytical arguments and numerical simulations, we disentangle universal from nonuniversal edge properties. We outline experimental probes in excitonic FCIs and in ultracold atom systems, and in particular propose time-resolved edge spectroscopy to directly access the predicted exponents and velocities.

cond-mat.str-el↗

arXiv2025

Optical engineering and detection of magnetism in moir\'e semiconductors

We present a general framework for optically inducing, controlling, and probing spin states in moir\'e systems. In particular, we demonstrate that applying Raman optical drives to moir\'e transition metal dichalcogenide bilayers can realize a class of spin models, with magnetic interactions tunable via the optical parameters. The resulting interaction anisotropy, controlled by the polarizations of the drives, enables access to magnetic states that are inaccessible in undriven moir\'e bilayers. Furthermore, we establish direct connections between the resulting spin correlations and experimentally observable optical signals. Our work paves the way for future studies on the optical control and detection on strongly correlated quantum systems.

cond-mat.str-el↗

arXiv2025

Enhanced Cooper pairing in nano-patterned metals

Nano-patterning has been shown to be a powerful tool for manipulating the vibrational modes of elastic structures, with applications such as optical-mechanical mode coupling. Inspired by these recent developments in phononic band engineering, we propose a nano-patterning scheme to enhance the superconducting transition temperature $T_c$ in phonon-mediated nano-film superconductors, such as aluminum. Using the finite element method, we simulate the lattice vibrational modes of nano-patterned films within the Debye model. Our results show that periodic nano-patterning softens the lattice vibrational modes compared to bulk films. It also increases the density of states at high energies, resulting in a couple of percent enhancement in $T_c$. Moreover, we investigate connections to Weyl's law and provide an experimental design prescription to optimize nano-patterning for further enhancement of the superconducting transition temperature.

cond-mat.supr-con↗

arXiv2025

Negative superfluid density and spatial instabilities in driven superconductors

We consider excitation of Higgs modes via the modulation of the BCS coupling within the Migdal-Eliashberg-Keldysh theory of time-dependent superconductivity. Despite the presence of phonons, which break integrability, we observe Higgs amplitude oscillations reminiscent of the integrable case. The dynamics of quasiparticles follows from the effective Bogolyubov-de Gennes equations, which represent a Floquet problem for the Bogoliubov quasiparticles. We find that when the Floquet-Bogoliubov bands overlap, the homogeneous solution formally leads to a negative superfluid density, which is no longer proportional to the amplitude of the order parameter. This result indicates an instability, which we explore using spatially-resolved BdG equations. Spontaneous appearance of spatial inhomogeneities in the order parameter is observed and they first occur when the superfluid density becomes unphysical. We conclude that the homogeneous solution to time-dependent superconductivity is generally unstable and breaks up into a complicated spatial landscape via an avalanche of topological excitations.

cond-mat.supr-con↗

arXiv2024

Diagnosing electronic phases of matter using photonic correlation functions

In the past couple of decades, there have been significant advances in measuring quantum properties of light, such as quadratures of squeezed light and single-photon counting. Here, we explore whether such tools can be leveraged to probe electronic correlations in the many-body quantum regime. Specifically, we show that it is possible to probe certain spin, charge, and topological orders in an electronic system by measuring the correlation functions of scattered photons. We construct a mapping from the correlators of the scattered photons to those of a correlated insulator, particularly for Mott insulators described by a single-band Fermi-Hubbard model at half-filling. We show that frequency filtering before photodetection plays a crucial role in determining this mapping. We find that if the ground state of the insulator is a gapped spin liquid, a photon-pair correlation function, i.e., $G^{(2)}$, can detect the presence of anyonic excitations with fractional mutual statistics. Moreover, we show that correlations between electromagnetic quadratures can be used to detect expectation values of static spin chirality operators on both the kagome and triangular lattices, thus being useful in detecting chiral spin liquids. More generally, we show that a series of hitherto unmeasured spin-spin and spin-charge correlation functions of the material can be extracted from photonic correlations. This work opens up access to probe correlated materials, beyond the linear response paradigm, by detecting quantum properties of scattered light.

cond-mat.str-el↗

arXiv2024

Surface-mediated ultra-strong cavity coupling of two-dimensional itinerant electrons

Engineering phases of matter in cavities requires effective light-matter coupling strengths that are on the same order of magnitude as the bare system energetics, coined the ultra-strong coupling regime. For models of itinerant electron systems, which do not have discrete energy levels, a clear definition of this regime is outstanding to date. Here we argue that a change of the electronic mass exceeding $10\%$ of its bare value may serve as such a definition. We propose a quantitative computational scheme for obtaining the electronic mass in relation to its bare vacuum value and show that coupling to surface polariton modes can induce such mass changes. Our results have important implications for cavity design principles that enable the engineering of electronic properties with quantum light.

cond-mat.str-el↗

arXiv2024

Enhanced Cooper Pairing via Random Matrix Phonons in Superconducting Grains

There is rich experimental evidence that granular superconductors and superconducting films often exhibit a higher transition temperature, $T_{c}$, than that in bulk samples of the same material. This paper suggests that this enhancement hinges on random matrix phonons mediating Cooper pairing more efficiently than bulk phonons. We develop the Eliashberg theory of superconductivity in chaotic grains, calculate the random phonon spectrum and solve the Eliashberg equations numerically. Self-averaging of the effective electron-phonon coupling constant is noted, which allows us to fit the numerical data with analytical results based on a generalization of the Berry conjecture. The key insight is that the phonon density of states, and hence $T_{c}$, shows an enhancement proportional to the ratio of the perimeter and area of the grain - the Weyl law. We benchmark our results for aluminum films, and find an enhancement of $T_{c}$ of about $10\%$ for a randomly-generated shape. A larger enhancement of $T_{c}$ is readily possible by optimizing grain geometries. We conclude by noticing that mesoscopic shape fluctuations in realistic granular structures should give rise to a further enhancement of global $T_{c}$ due to the formation of a percolating Josephson network.

cond-mat.supr-con↗

arXiv2024

Collective optical properties of moir\'e excitons

We propose that excitons in moir\'e transition metal dichalcogenide bilayers offer a promising platform for investigating collective radiative properties. While some of these optical properties resemble those of cold atom arrays, moir\'e excitons extend to the deep subwavelength limit, beyond the reach of current optical lattice experiments. Remarkably, we show that the collective optical properties can be exploited to probe certain correlated electron states without requiring subwavelength spatial resolution. Specifically, we illustrate that the Wigner crystal states of electrons doped into these bilayers act as an emergent periodic potential for excitons. Moreover, the collective dissipative excitonic bands and their associated Berry curvature can reveal various charge orders that emerge at the corresponding electronic doping. Our study provides a promising pathway for future research on the interplay between collective effects and strong correlations involving moir\'e excitons.

cond-mat.mes-hall↗

arXiv2024

Integrable-to-Thermalizing Crossover in Non-Equilibrium Superconductors

Motivated by the experiment by M. Budden {\em et al.} [Nature Physics {\bf 17}, 611 (2021)], who observed signatures of long-lived photo-induced superconductivity, we develop an accurate analytical/computational approach to non-equilibrium superconductivity following a quench. We consider the BCS-Holstein model, which includes both integrable local electron-electron interactions and integrability-breaking electron-phonon coupling. We develop Keldysh-Eliashberg theory on the Kadanoff-Baym contour, which enables us to describe non-equilibrium dynamics of the superconductor. We consider a quench in interactions, which results in a dynamic transition from the initial superconducting state to a normal thermal state in the end of the evolution. It is shown that the dynamics contain two stages: The early-time integrable behavior, involving coherent oscillations of the superconducting order parameter, crosses over to the late-time ergodic dynamics exhibiting a thermal decay into an equilibrium state. In the former regime, our computational approach both reproduces exact analytical results on the integrable dynamics of the order parameter and generalizes those to the case of an initial thermal state. The method also succeeds for the first time in describing both integrable-to-thermalizing crossover and the late-time thermal decay, which is shown to be consistent with the time-dependent Ginzburg-Landau theory (with the exponential decay time dependent on the density of quasiparticle excitations). We observe the electron distribution function approaching the Fermi-Dirac thermal distribution at final stages. The details of two-time non-equilibrium dynamics depend on the density of quasiparticles in the initial state and the integrability-breaking parameters, which under certain conditions may result in a long-lived transient superconductivity consistent with experiment.

cond-mat.supr-con↗

arXiv2023

Extended Josephson junction qubit system

Circuit quantum electrodynamics (QED) has emerged as a promising platform for implementing quantum computation and simulation. Typically, junctions in these systems are of a sufficiently small size, such that only the lowest plasma oscillation is relevant. The interplay between the Josephson effect and charging energy renders this mode nonlinear, forming the basis of a qubit. In this work, we introduce a novel QED architecture based on extended Josephson Junctions (JJs), which possess a non-negligible spatial extent. We present a comprehensive microscopic analysis and demonstrate that each extended junction can host multiple nonlinear plasmon modes, effectively functioning as a multi-qubit interacting system, in contrast to conventional JJs. Furthermore, the phase modes exhibit distinct spatial profiles, enabling individual addressing through frequency-momentum selective coupling to photons. Our platform has potential applications in quantum computation, specifically in implementing single- and two-qubit gates within a single junction. We also investigate a setup comprising several driven extended junctions interacting via a multimode electromagnetic waveguide. This configuration serves as a powerful platform for simulating the generalized Bose-Hubbard model, as the photon-mediated coupling between junctions can create a lattice in both real and synthetic dimensions. This allows for the exploration of novel quantum phenomena, such as topological phases of interacting many-body systems.

quant-ph↗

arXiv2023

Chiral Flat-Band Optical Cavity with Atomically Thin Mirrors

A fundamental requirement for photonic technologies is the ability to control the confinement and propagation of light. Widely utilized platforms include two-dimensional (2D) optical microcavities in which electromagnetic waves are confined between either metallic or distributed Bragg reflectors. Recently, transition metal dichalcogenides hosting tightly bound excitons with high optical quality have emerged as promising atomically thin mirrors. In this work, we propose and experimentally demonstrate a sub-wavelength 2D nano-cavity using two atomically thin mirrors with degenerate resonances. Angle-resolved measurements show a flat band, which sets this system apart from conventional photonic cavities. Remarkably, we demonstrate how the excitonic nature of the mirrors enables the formation of chiral and tunable optical modes upon the application of an external magnetic field. Moreover, we show the electrical tunability of the confined mode. Our work demonstrates a mechanism for confining light with high-quality excitonic materials, opening perspectives for spin-photon interfaces, and chiral cavity electrodynamics.

physics.optics↗

arXiv2022

Boson Sampling for Generalized Bosons

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

quant-ph↗

arXiv2022

Dark Andreev States in Superconductors

The conventional Bardeen-Cooper-Schrieffer (BCS) model of superconductivity assumes a frequency-independent order parameter, which allows a relatively simple description of the superconducting state. In particular, its excitation spectrum readily follows from the Bogoliubov-de-Gennes (BdG) equations. A more realistic description of a superconductor is the Migdal-Eliashberg theory, where the pairing interaction, the order parameter, and electronic self-energy are strongly frequency dependent. This work combines these ingredients of phonon-mediated superconductivity with the standard BdG approach. Surprisingly, we find qualitatively new features such as the emergence of a shadow superconducting gap in the quasiparticle spectrum at energies close to the Debye energy. We show how these features reveal themselves in standard tunneling experiments. Finally, we also predict the existence of additional high-energy bound states, which we dub "dark Andreev states."

cond-mat.supr-con↗

arXiv2022

Interplay of hyperbolic plasmons and superconductivity

Hyperbolic plasmons are collective electron excitations in layered conductors. They are of relevance to a number of superconducting materials, including the cuprates and layered hyperbolic metamaterials [V. N. Smolyaninova, et al. Scientific Reports 6, 34140 (2016)]. This work studies how the unusual dispersion of hyperbolic plasmons affects Cooped pairing. We use the Migdal-Eliashberg equations, which are solved both numerically and analytically using the Grabowski-Sham approximation, with consistent results. We do not find evidence for plasmon-mediated pairing within a reasonable parameter range. However, it is shown that the hyperbolic plasmons can significantly reduce the effects of Coulomb repulsion in the Cooper channel leading to an enhancement of the transition temperature originating from other pairing mechanisms. In the model of a hyperbolic material composed of identical layers, we find this enhancement to be the strongest in the $d$-wave channel. We also discuss strategies for engineering an optimal hyperbolic plasmon background for a further enhancement of superconductivity in both $s$-wave and $d$-wave channels.

cond-mat.supr-con↗