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 $\omega \simeq \omega_q$, where $\omega_q$ 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, $D(\omega)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(\omega)$ 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 $D(\omega)$. 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 $D(\omega)$. These transitions are manifestations of nonequilibrium steady states of an array of qubits achieved in this regime.Comment: 7 pages and 6 figure

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 $\pi$- 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.Comment: 10 pages, 9 figures and 2 Appendice

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 $\hat \zeta$ 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 $\hat \zeta$: 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 particula

Critical current of a long Josephson junction in the presence of a perturbing Abrikosov vortex

We investigate theoretically how the proximity of an Abrikosov vortex influences the physical properties of a long Josephson junction. We find that ␦I c , the contribution to the critical current associated with the presence of the vortex, is generally positive ͑the critical current is increased͒ and is crucially dependent on the specific boundary conditions satisfied by the transport current. In the case in which the latter has a bulk component in the vicinity of the vortex, ␦I c is proportional to the coupling between the vortex and the junction. The situation is however more complex when the transport current is purely a surface phenomenon. In this case ␦I c strongly depends on the distance between the vortex and the edges of the junction, and is in general much smaller than that of the bulk current case unless a special commensurability condition is met. In particular we show that a contribution to ␦I c proportional to is obtained in this case only when an integer number of Josephson vortices can be accommodated between the location of the vortex and one of the edges of the junction

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

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 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 $_0$. 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

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 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 $_0$. 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

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.Comment: 30 pages, 5 figure

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