Hybrid Boson Sampling.

We propose boson sampling from a system of coupled photons and Bose-Einstein condensed atoms placed inside a multi-mode cavity as a simulation process testing the quantum advantage of quantum systems over classical computers. Consider a two-level atomic transition far-detuned from photon frequency. An atom-photon scattering and interatomic collisions provide interactions that create quasiparticles and excite atoms and photons into squeezed entangled states, orthogonal to the atomic condensate and classical field driving the two-level transition, respectively.

Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap.

We describe boson sampling of interacting atoms from the noncondensed fraction of Bose-Einstein-condensed (BEC) gas confined in a box trap as a new platform for studying computational ♯P-hardness and quantum supremacy of many-body systems. We calculate the characteristic function and statistics of atom numbers via the newly found Hafnian master theorem. Using Bloch-Messiah reduction, we find that interatomic interactions give rise to two equally important entities-eigen-squeeze modes and eigen-energy quasiparticles-whose interplay with sampling atom states determines the behavior of the BEC gas.

Multi-Qubit Bose-Einstein Condensate Trap for Atomic Boson Sampling.

We propose a multi-qubit Bose-Einstein-condensate (BEC) trap as a platform for studies of quantum statistical phenomena in many-body interacting systems. In particular, it could facilitate testing atomic boson sampling of the excited-state occupations and its quantum advantage over classical computing in a full, controllable and clear way. Contrary to a linear interferometer enabling Gaussian boson sampling of non-interacting non-equilibrium photons, the BEC trap platform pertains to an interacting equilibrium many-body system of atoms.

Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix.

We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of any-value diagonals on top of a uniform matrix (for k=1,2 and 3) and the method for deriving such recurrence relations, which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear-time computing; and finding their asymptotics in a large-matrix-size limit. The latter problem is an open fundamental problem.

Unification of the Nature's Complexities via a Matrix Permanent-Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity.

We reveal the analytic relations between a matrix permanent and major nature's complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem.

Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap's Form and Boundary Conditions in the Thermodynamic Limit.

We analytically calculate the statistics of Bose-Einstein condensate (BEC) fluctuations in an interacting gas trapped in a three-dimensional cubic or rectangular box with the Dirichlet, fused or periodic boundary conditions within the mean-field Bogoliubov and Thomas-Fermi approximations. We study a mesoscopic system of a finite number of trapped particles and its thermodynamic limit. We find that the BEC fluctuations, first, are anomalously large and non-Gaussian and, second, depend on the trap's form and boundary conditions.

Enhancing acceleration radiation from ground-state atoms via cavity quantum electrodynamics.

When ground-state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The reason is a strong nonadiabatic effect at cavity boundaries and its interplay with the standard Unruh effect. The cavity field at steady state is still described by a thermal density matrix under most conditions.

Resonant second-order nonlinear optical processes in quantum cascade lasers.

We demonstrate an efficient intracavity nonlinear interaction of laser modes in a specially adapted quantum cascade laser. A two-wavelength quantum cascade laser structure emitting at wavelengths of 7.1 and 9.

Coherent radiation from neutral molecules moving above a grating.

We predict and study the effect of parametric self-induced excitation of a molecule moving above the dielectric or conducting medium with periodic grating. In this case the radiation reaction force modulates the molecular transition frequency which results in a parametric instability of dipole oscillations even from the level of quantum or thermal fluctuations. The present mechanism of instability of electrically neutral molecules is different from that of the well-known Smith-Purcell and transition radiation in which a moving charge and its oscillating image create an oscillating dipole.