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## Fluctuations and photon statistics in a quantum metamaterial near a superradiant transition

The analysis of single-mode photon fluctuations and their counting statistics at the superradiant phase transition is presented. The study concerns the equilibrium Dicke model in a regime where the Rabi frequency, related to a coupling of the photon mode with a finite-number qubit environment, plays the role of the transition's control parameter. We use the effective Matsubara action formalism based on the representation of Pauli operators as bilinear forms with complex and Majorana fermions. Then, we address fluctuations of superradiant order parameter and quasiparticles. The average photon number, the fluctuational Ginzburg-Levanyuk region of the phase transition, and Fano factor are evaluated. We determine the cumulant-generating function which describes a full counting statistics of equilibrium photon number. Exact numerical simulation of the superradiant transition demonstrates quantitative agreement with analytical calculations.

A numerical method of simulations for the evolution operators (propagators) of coupled qubits was developed on the basis of Magnus representation. The propagator of a multi-qubit system can be expressed by a N × N matrix whose size increases as N = 2^n with the number of qubits n . Therefore, the standard approach to the propagator calculation requires the involvement of numerically expensive procedures. We have shown that the calculations of the propagator at the current time can be reduced to the inversion of the Vandermonde matrix, which occurs when constructing interpolation polynomials. In this case, due to the recurrence relations, the number of required flops increases only as ~ O(N^2) (in opposite to ~ O(N^3) flops for the matrix of the general form). This fact allows us to speed up the calculation of the propagator for multi-qubit systems.

Introducing of topological insulator concept for fluctuating valence compound – samarium hexaboride – has recently initiated a new round of studies aimed to clarify the nature of the ground state in this extraordinary system with strong electron correlations. Here we discuss the data of magnetic resonance in the pristine single crystals of SmB6 measured in 60 GHz cavity experiments at temperatures 1.8–300 K. The microwave study as well as the DC resistivity and Hall effect measurements performed for the different states of SmB6 [110] surface prove definitely the existence of the layer with metallic conductivity increasing under lowering temperature below 5 K. Four lines with the g-factors g ≈ 2 are found to contribute to the ESR-like absorption spectrum that may be attributed to intrinsic paramagnetic centers on the sample’s surface, which are robust with respect to the surface treatment. The temperature dependence of integrated intensity I(T) for main paramagnetic signal is found to demonstrate anomalous critical behavior I(T) ~ (T* − T)ν with characteristic temperature T* = 5.34 ± 0.05 K and exponent ν = 0.38 ± 0.03 indicating possible magnetic transition at the SmB6 [110] surface. Additional resonant magnetoabsorption line, which may be associated with either donorlike defects or cyclotron resonance mode corresponding to the mass mc ~ 1.2m0, is reported.

Simulation of the entangled (Bell) states generation of two qubits by using of unipolar picoseconds pulses was performed. As an example, a system of two coupled superconducting flux qubits interacting with fluxons that integrated with a Josephson transmission line has been considered. The influence of the pulse shape and quantum noise on the accuracy of the Bell states initialization and the way to control of nonlocal entangled states are discussed.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.