Forty thousand kilometers under quantum protection.

Quantum key distribution (QKD) is a revolutionary cryptography response to the rapidly growing cyberattacks threat posed by quantum computing. Yet, the roadblock limiting the vast expanse of secure quantum communication is the exponential decay of the transmitted quantum signal with the distance. Today's quantum cryptography is trying to solve this problem by focusing on quantum repeaters. However, efficient and secure quantum repetition at sufficient distances is still far beyond modern technology. Here, we shift the paradigm and build the long-distance security of the QKD upon the quantum foundations of the Second Law of Thermodynamics and end-to-end physical oversight over the transmitted optical quantum states. Our approach enables us to realize quantum states' repetition by optical amplifiers keeping states' wave properties and phase coherence. The unprecedented secure distance range attainable through our approach opens the door for the development of scalable quantum-resistant communication networks of the future.

Relaxation electrodynamics of superinsulators.

Superinsulators offer a unique laboratory realizing strong interaction phenomena like confinement and asymptotic freedom in quantum materials. Recent experiments evidenced that superinsulators are the mirror-twins of superconductors with reversed electric and magnetic field effects. Cooper pairs and Cooper holes in the superinsulator are confined into neutral electric pions by electric strings, with the Cooper pairs playing the role of quarks. Here we report the non-equilibrium relaxation of the electric pions in superinsulating films. We find that the time delay [Formula: see text] of the current passage in the superinsulator is related to the applied voltage V via the power law, [Formula: see text], where [Formula: see text] is the effective threshold voltage. Two distinct critical exponents, [Formula: see text] and [Formula: see text], correspond to jumps from the electric Meissner state to the mixed state and to the superinsulating resistive state with broken charge confinement, respectively. The [Formula: see text] value establishes a direct experimental evidence for the electric strings' linear potential confining the charges of opposite signs in the electric Meissner state and effectively rules out disorder-induced localization as a mechanism for superinsulation. We further report the memory effects and their corresponding dynamic critical exponents arising upon the sudden reversal of the applied voltage. Our observations open routes for exploring fundamental strong interaction charge confinement via desktop experiments.

Time-dependent exchange creates the time-frustrated state of matter.

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system's temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

Supercapacitance and superinductance of TiN and NbTiN films in the vicinity of superconductor-to-insulator transition.

We investigate the low-temperature complex impedance of disordered insulating thin TiN and NbTiN films in the frequency region 400 Hz-1 MHz in close proximity to the superconductor-insulator transition (SIT). The frequency, temperature, and magnetic field dependencies of the real and imaginary parts of the impedance indicate that in full accord with the theoretical predictions and earlier observations, the films acquire self-induced electronic granularity and become effectively random arrays of superconducting granules coupled via Josephson links. Accordingly, the inductive component of the response is due to superconducting droplets, while the capacitive component results from the effective Josephson junctions capacitances. The impedance crosses over from capacitive to inductive behavior as films go across the transition.

Thermoelectric current in a graphene Cooper pair splitter.

Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

Hopfions emerge in ferroelectrics.

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, attract an intense attention in the diverse areas of physics ranging from high-energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while being of broad interest, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions are of fundamental importance for the electromagnetic behavior of the nanocomposits and can result in advanced functionalities of these materials.

[Formula: see text]-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain.

Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity ([Formula: see text]) and time-reversal ([Formula: see text]) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the [Formula: see text] symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the [Formula: see text]-symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.

Phase estimation algorithm for the multibeam optical metrology.

Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can be translated into the classical linear optical framework. The developed setup made of beam splitters, mirrors and phase shifters demonstrates how the classical coherence, similarly to the quantum coherence, poses a resource for obtaining information about the measurable physical quantities. Our study opens route to the reliable implementation of the small-scale unitary algorithms on path-encoded qudits, thus establishing an easily accessible platform for unitary computation.

Controllable skyrmion chirality in ferroelectrics.

Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. Our findings open the route for controlled chirality with potential applications in ferroelectric-based information technologies.

Superconducting phase transitions in disordered NbTiN films.

Suppression of superconductivity in disordered systems is a fundamental problem of condensed matter physics. Here we investigate superconducting niobium-titanium-nitride (Nb1-xTixN) thin films grown by the atomic layer deposition (ALD) with slightly different growth process parameters. We observe a smooth crossover from the disorder-driven superconductor-normal metal transition (SMT) to the superconductor-insulator transition (SIT) via the intermediate Bose metal state detected by the low-temperature saturation of the temperature dependence of the sheet resistance. We demonstrate that the SIT via the intervening Bose metal state occurs if the sheet resistance of the film in the maximum, Rmax prior to the superconducting drop of R(T), exceeds Rq = h/4e2.

Arrow of time and its reversal on the IBM quantum computer.

Uncovering the origin of the "arrow of time" remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. This poses a question of whether it is possible to develop protocols for circumventing the irreversibility of time and if so to practically implement these protocols. Here we show that, while in nature the complex conjugation needed for time reversal may appear exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.

Vogel-Fulcher-Tamman criticality of 3D superinsulators.

It has been believed that the superinsulating state, which is the low-temperature charge Berezinskii-Kosterlitz-Thouless (BKT) phase, can exist only in two dimensions. We develop a general gauge description of the superinsulating state and the related deconfinement transition of Cooper pairs and predict the existence of the superinsulating state in three dimensions (3d). We find that 3d superinsulators exhibit Vogel-Fulcher-Tammann (VFT) critical behavior at the phase transition. This is the 3d string analog of the Berezinski-Kosterlitz-Thouless (BKT) criticality for logarithmically and linearly interacting point particles in 2d. Our results show that singular exponential scaling behaviors of the BKT type are generic for phase transitions associated with the condensation of topological excitations.

Geometrical vortex lattice pinning and melting in YBaCuO submicron bridges.

Since the discovery of high-temperature superconductors (HTSs), most efforts of researchers have been focused on the fabrication of superconducting devices capable of immobilizing vortices, hence of operating at enhanced temperatures and magnetic fields. Recent findings that geometric restrictions may induce self-arresting hypervortices recovering the dissipation-free state at high fields and temperatures made superconducting strips a mainstream of superconductivity studies. Here we report on the geometrical melting of the vortex lattice in a wide YBCO submicron bridge preceded by magnetoresistance (MR) oscillations fingerprinting the underlying regular vortex structure. Combined magnetoresistance measurements and numerical simulations unambiguously relate the resistance oscillations to the penetration of vortex rows with intermediate geometrical pinning and uncover the details of geometrical melting. Our findings offer a reliable and reproducible pathway for controlling vortices in geometrically restricted nanodevices and introduce a novel technique of geometrical spectroscopy, inferring detailed information of the structure of the vortex system through a combined use of MR curves and large-scale simulations.

H-theorem in quantum physics.

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

Quantum-to-classical crossover near quantum critical point.

A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while non-dissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transition from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d + zΛ(T), where z is the dynamical exponent, and temperature-depending parameter Λ(T) ∈ [0, 1] decreases with the temperature such that Λ(T = 0) = 1 and Λ(T → ∞) = 0. Our findings lead to a unified picture of quantum critical phenomena including both dissipation- and dissipationless quantum dynamic effects and offer a quantitative description of the quantum-to-classical crossover.

Electronic transport in two-dimensional high dielectric constant nanosystems.

There has been remarkable recent progress in engineering high-dielectric constant two dimensional (2D) materials, which are being actively pursued for applications in nanoelectronics in capacitor and memory devices, energy storage, and high-frequency modulation in communication devices. Yet many of the unique properties of these systems are poorly understood and remain unexplored. Here we report a numerical study of hopping conductivity of the lateral network of capacitors, which models two-dimensional insulators, and demonstrate that 2D long-range Coulomb interactions lead to peculiar size effects. We find that the characteristic energy governing electronic transport scales logarithmically with either system size or electrostatic screening length depending on which one is shorter. Our results are relevant well beyond their immediate context, explaining, for example, recent experimental observations of logarithmic size dependence of electric conductivity of thin superconducting films in the critical vicinity of superconductor-insulator transition where a giant dielectric constant develops. Our findings mark a radical departure from the orthodox view of conductivity in 2D systems as a local characteristic of materials and establish its macroscopic global character as a generic property of high-dielectric constant 2D nanomaterials.

Aharonov-Bohm oscillations in singly connected disordered conductors.

We show that the transport and thermodynamic properties of a singly connected disordered conductor exhibit quantum Aharonov-Bohm oscillations as a function of the total magnetic flux through the sample. The oscillations are associated with the interference contribution from a special class of electron trajectories confined to the surface of the sample.

Resonant tunneling of fluctuation Cooper pairs.

Superconducting fluctuations have proved to be an irreplaceable source of information about microscopic and macroscopic material parameters that could be inferred from the experiment. According to common wisdom, the effect of thermodynamic fluctuations in the vicinity of the superconducting transition temperature, Tc, is to round off all of the sharp corners and discontinuities, which otherwise would have been expected to occur at Tc. Here we report the current spikes due to radiation-induced resonant tunneling of fluctuation Cooper pairs between two superconductors which grow even sharper and more pronounced upon approach to Tc. This striking effect offers an unprecedented tool for direct measurements of fluctuation Cooper pair lifetime, which is key to our understanding of the fluctuation regime, most notably to nature of the pseudogap state in high-temperature superconductors. Our finding marks a radical departure from the conventional view of superconducting fluctuations as a blurring and rounding phenomenon.

Rayleigh approximation to ground state of the Bose and Coulomb glasses.

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

Magnetic field-induced dissipation-free state in superconducting nanostructures.

A superconductor in a magnetic field acquires a finite electrical resistance caused by vortex motion. A quest to immobilize vortices and recover zero resistance at high fields made intense studies of vortex pinning one of the mainstreams of superconducting research. Yet, the decades of efforts resulted in a realization that even promising nanostructures, utilizing vortex matching, cannot withstand high vortex density at large magnetic fields. Here, we report a giant reentrance of vortex pinning induced by increasing magnetic field in a W-based nanowire and a TiN-perforated film densely populated with vortices. We find an extended range of zero resistance with vortex motion arrested by self-induced collective traps. The latter emerge due to order parameter suppression by vortices confined in narrow constrictions by surface superconductivity. Our findings show that geometric restrictions can radically change magnetic properties of superconductors and reverse detrimental effects of magnetic field.