arXiv subjects

Alexander Moroz

Publications and source records attributed to Alexander Moroz.

At least 37 records · Page 2Linked to original sources

arXiv2019

Extreme defect sensitivity from large synthetic dimensionality

The geometric dimensionality of a physical system significantly impacts its fundamental characteristics. While experiments are fundamentally limited to the maximum of three spatial dimensions, there is a growing interest in harnessing additional synthetic dimensions. In our work, we introduce a new paradigm for the experimental realization of excitation dynamics associated with many-dimensional systems. Crucially, it relies solely on static one-dimensional equivalent structures with judiciously tailored parameters to faithfully reproduce the same optical spectrum and density of states of the high-dimensional system to be represented. In order to showcase the capabilities of our approach, we fabricate 1D photonic lattices that exhibit the characteristic non-monotonic excitation decays associated with quantum walks in up to 7D square lattices. Furthermore, we find that a new type of bound state at the edge of the continuum emerges in higher-than-three dimensions and gives rise to a sharp localisation transition at defect sites. In a series of experiments, we implement the mapped equivalent lattices of up to 5D systems and observe an extreme increase of sensitivity with respect to the detuning of the respective anchor sites. Our findings demonstrate the feasibility and applicative potential of harnessing high-dimensional effects in planar photonics for ultra-sensitive switching or sensing. Notably, our general approach is by no means limited to optics, and can readily be adapted to a variety of other physical contexts, including cold atoms and superconducting qubits with exclusively nearest-neighbour interactions, promising to drive significant advances in different fields including quantum simulations and information processing.

physics.optics↗

arXiv2018

A unified treatment of polynomial sectors and constraint polynomials of the Rabi models

General concept of a gradation slicing is used to analyze polynomial solutions of ordinary differential equations (ODE) with polynomial coefficients, ${\cal L}ψ=0$, where ${\cal L}=\sum_l p_l(z) d_z^l$, $p_l(z)$ are polynomials, $z$ is a one-dimensional coordinate, and $d_z=d/dz$. It is not required that ODE is either (i) Fuchsian or (ii) leads to a usual Sturm-Liouville eigenvalue problem. General necessary and sufficient conditions for the existence of a polynomial solution are formulated involving constraint relations. The necessary condition for a polynomial solution of $n$th degree to exist forces energy to a $n$th baseline. Once the constraint relations on the $n$th baseline can be solved, a polynomial solution is in principle possible even in the absence of any underlying algebraic structure. The usefulness of theory is demonstrated on the examples of various Rabi models. For those models, a baseline is known as a Juddian baseline (e.g. in the case of the Rabi model the curve described by the $n$th energy level of a displaced harmonic oscillator with varying coupling $g$). The corresponding constraint relations are shown to (i) reproduce known constraint polynomials for the usual and driven Rabi models and (ii) generate hitherto unknown constraint polynomials for the two-mode, two-photon, and generalized Rabi models, implying that the eigenvalues of corresponding polynomial eigenfunctions can be determined algebraically. Interestingly, the ODE of the above Rabi models are shown to be characterized, at least for some parameter range, by the same unique set of grading parameters.

quant-ph↗

arXiv2016

Generalized Rabi models: diagonalization in the spin subspace and differential operators of Dunkl type

A discrete parity $\mathbb{Z}_2$ symmetry of a two parameter extension of the quantum Rabi model which smoothly interpolates between the latter and the Jaynes-Cummings model, and of the two-photon and the two-mode quantum Rabi models enables their diagonalization in the spin subspace. A more general statement is that the respective sets of $2\times 2$ hermitian operators of the Fulton-Gouterman type and those diagonal in the spin subspace are unitary equivalent. The diagonalized representation makes it transparent that any question about integrability and solvability can be addressed only at the level of ordinary differential operators of Dunkl type. Braak's definition of integrability is shown (i) to contradict earlier numerical studies and (ii) to imply that any physically reasonable differential operator of Fulton-Gouterman type is integrable.

quant-ph↗

arXiv2015

Comment on "New analytic solution of Schrödinger's equation"

Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is also contrasted with the method of comparison equations.

quant-ph↗

arXiv2015

On uniqueness of Heine-Stieltjes polynomials for second order finite-difference equations

A second order finite-difference equation has two linearly independent solutions. It is shown here that, like in the continuous case, at most one of the two can be a polynomial solution. The uniqueness in the classical continuous Heine-Stieltjes theory is shown to hold under broader hypotheses than usually presented. A difference between regularity condition and uniqueness is emphasized. Consistency of our uniqueness results is also checked against one of the Shapiro problems. An intrinsic relation between the Heine-Stieltjes problem and the discrete Bethe Ansatz equations allows one to immediately extend the uniqueness result from the former to the latter. The results have implications for nondegeneracy of polynomial solutions of physical models.

math-ph↗

arXiv2014

Quantum models with spectrum generated by the flows of polynomial zeros

A class {\cal R}_p of purely bosonic models is characterized having the following properties in the Bargmann Hilbert space of analytic functions: (i) wave function ψ(ε,z)=\sum_{n=0}^\infty ϕ_n(ε) z^n is the {\em generating function} for orthogonal polynomials ϕ_n(ε) of a discrete energy variable ε, (ii) any Hamiltonian \hat{H}_b\in {\cal R}_p has nondegenerate purely point spectrum that corresponds to infinite discrete support of measure dν(x) in the orthogonality relation of the polynomials ϕ_n, (iii) the support is determined exclusively by the points of discontinuity of ν(x), (iv) the spectrum of \hat{H}_b\in {\cal R}_p can be numerically determined as fixed points of monotonic flows of the zeros of orthogonal polynomials ϕ_n(\upepsilon), (v) one can compute practically an unlimited number of energy levels (e.g. 2^{53} in double precision). If a model of {\cal R}_p is exactly solvable, its spectrum can only assume one of four qualitatively different types. The results are applied to spin-boson quantum models that are, at least partially, diagonalizable and have at least single one-dimensional irreducible component in the spin subspace. Examples include the Rabi model and its various generalizations.

math-ph↗

arXiv2013

A hidden analytic structure of the Rabi model

The Rabi model describes the simplest interaction between a cavity mode with a frequency $ω_c$ and a two-level system with a resonance frequency $ω_0$. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to $Δ=ω_0/(2ω_c)=0$, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy $\upepsilon$, which are orthogonal on an equidistant lattice. A non-zero value of $Δ$ leads to non-classical discrete orthogonal polynomials $ϕ_{k}(\upepsilon)$ and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. {\em 1350} calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak's solution. Any first $n$ eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of $ϕ_{N}(\upepsilon)$ of at least the degree $N=n+n_t$. The value of $n_t>0$, which is slowly increasing with $n$, depends on the required precision. For instance, $n_t\simeq 26$ for $n=1000$ and dimensionless interaction constant $κ=0.2$, if double precision is required. Although we can rigorously prove our results only for dimensionless interaction constant $κ< 1$, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for $κ\ge 1$.

quant-ph↗

arXiv2013

On solvability and integrability of the Rabi model

Quasi-exactly solvable Rabi model is investigated within the framework of the Bargmann Hilbert space of analytic functions ${\cal B}$. On applying the theory of orthogonal polynomials, the eigenvalue equation and eigenfunctions are shown to be determined in terms of three systems of monic orthogonal polynomials. The formal Schweber quantization criterion for an energy variable $x$, originally expressed in terms of infinite continued fractions, can be recast in terms of a meromorphic function $F(z) = a_0 + \sum_{k=1}^\infty {\cal M}_k/(z-ξ_k)$ in the complex plane $\mathbb{C}$ with {\em real simple} poles $ξ_k$ and {\em positive} residues ${\cal M}_k$. The zeros of $F(x)$ on the real axis determine the spectrum of the Rabi model. One obtains at once that, on the real axis, (i) $F(x)$ monotonically decreases from $+\infty$ to $-\infty$ between any two of its subsequent poles $ξ_k$ and $ξ_{k+1}$, (ii) there is exactly one zero of $F(x)$ for $x\in (ξ_k,ξ_{k+1})$, and (iii) the spectrum corresponding to the zeros of $F(x)$ does not have any accumulation point. Additionally, one can provide much simpler proof of that the spectrum in each parity eigenspace ${\cal B}_\pm$ is necessarily {\em nondegenerate}. Thereby the calculation of spectra is greatly facilitated. Our results allow us to critically examine recent claims regarding solvability and integrability of the Rabi model.

quant-ph↗

arXiv2012

On the spectrum of a class of quantum models

The spectrum of any quantum model which eigenvalue equation reduces to a three-term recurrence, such as a displaced harmonic oscillator, the Jaynes-Cummings (JC) model, the Rabi model, and a generalized Rabi model, can be determined as zeros of a corresponding transcendental function F(x). The latter can be analytically determined as an infinite series defined solely in terms of the recurrence coefficients. The ease in obtaining the spectrum is of importance regarding recent experimental advances in preparing ultrastrongly interacting quantum systems, which can no longer be reliably described by the exactly solvable JC model. The relevant computer code has been made freely available online.

quant-ph↗

arXiv2012

On unorthodox solutions of the Bloch equations

A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number field, which makes it possible to find and classify all analytic solutions. Torrey's analytic solution in the form of exponentially damped harmonic oscillations [Phys. Rev. {\bf 76}, 1059 (1949)] is found to dominate the parameter space, which justifies its use at numerous occasions in magnetic resonance and in quantum optics of atoms, molecules, and quantum dots. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings $δ^2\lesssim (γ-γ_t)^2/27$ and small field strengths $Ω^2\lesssim 8 (γ-γ_t)^2/27$, where $γ$ and $γ_t$ describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectively. The unorthodox solutions being readily accessible experimentally are characterized by rather featureless time dependence.

quant-ph↗

arXiv2012

Comment on "Integrability of the Rabi model"

In his recent letter, Braak suggested that a regular spectrum of the Rabi model was given by the zeros of a transcendental function $G_\pm(x)$ (cf Eqs. (3)-(5) of Ref. [1]) and highlighted the role of the discrete $\mathbb{Z}_2$-symmetry, or parity, in determining $G_\pm(x)$. We show here to the contrary that one can define a transcendental function $F_0(x)$ and obtain the regular spectrum of the Rabi model as the zeros of $F_0(x)$ (see Fig. 1) without ever making use of the underlying $\mathbb{Z}_2$-symmetry of the model.

quant-ph↗

arXiv2011

A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates

An alternative representation of the quasistatic nonradiative rates of Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys. Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular dipole orientations. Given the distance d of a dipole from a sphere surface of radius a, the representations comprise four elementary analytic functions and a modified multipole series taking into account residual multipole contributions. The analytic functions could be arranged hierarchically according to decreasing singularity at the short distance limit d ---> 0, ranging from d^{-3} over d^{-1} to ln (d/a). The alternative representations exhibit drastically improved convergence properties. On keeping mere residual dipole contribution of the modified multipole series, the representations agree with the converged rates on at least 99.9% for all distances, arbitrary particle sizes and emission wavelengths, and for a broad range of dielectric constants. The analytic terms of the representations reveal a complex distance dependence and could be used to interpolate between the familiar d^{-3} short-distance and d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the representations could be especially useful for the qualitative and quantitative understanding of the distance behavior of nonradiative rates of fluorophores and semiconductor quantum dots involving nanometal surface energy transfer in the presence of metallic nanoparticles or nanoantennas. As a byproduct, a complete short-distance asymptotic of the quasistatic nonradiative rates is derived. The above results for the nonradiative rates translate straightforwardly to the so-called image enhancement factors Delta, which are of relevance for the surface-enhanced Raman scattering.

physics.chem-ph↗

arXiv2010

Non-radiative decay of a dipole emitter close to a metallic nanoparticle: Importance of higher-order multipole contributions

The contribution of higher-order multipoles to radiative and non-radiative decay of a single dipole emitter close to a spherical metallic nanoparticle is re-examined. Taking a Ag spherical nanoparticle (AgNP) with the radius of 5 nm as an example, a significant contribution (between 50% and 101% of the total value) of higher-order multipoles to non-radiative rates is found even at the emitter distance of 5 nm from the AgNP surface. On the other hand, the higher-order multipole contribution to radiative rates is negligible. Consequently, a dipole-dipole approximation can yield only an upper bound on the apparent quantum yield. In contrast, the non-radiative rates calculated with the quasistatic Gersten and Nitzan method are found to be in much better agreement with exact electrodynamic results. Finally, the size corrected metal dielectric function is shown to decrease the non-radiative rates near the dipolar surface plasmon resonance.

physics.chem-ph↗

arXiv2006

Quasi-periodic Green's functions of the Helmholtz and Laplace equations

A classical problem of free-space Green's function $G_{0Λ}$ representations of the Helmholtz equation is studied in various quasi-periodic cases, i.e., when an underlying periodicity is imposed in less dimensions than is the dimension of an embedding space. Exponentially convergent series for the free-space quasi-periodic $G_{0Λ}$ and for the expansion coefficients $D_{L}$ of $G_{0Λ}$ in the basis of regular (cylindrical in two dimensions and spherical in three dimension (3D)) waves, or lattice sums, are reviewed and new results for the case of a one-dimensional (1D) periodicity in 3D are derived. From a mathematical point of view, a derivation of exponentially convergent representations for Schlömilch series of cylindrical and spherical Hankel functions of any integer order is accomplished. The quasi-periodic Green's functions of the Laplace equation are obtained from the corresponding representations of $G_{0Λ}$ of the Helmholtz equation by taking the limit of the wave vector magnitude going to zero. The derivation of relevant results in the case of a 1D periodicity in 3D highlights the common part which is universally applicable to any of remaining quasi-periodic cases. The results obtained can be useful for numerical solution of boundary integral equations for potential flows in fluid mechanics, remote sensing of periodic surfaces, periodic gratings, in many contexts of simulating systems of charged particles, in molecular dynamics, for the description of quasi-periodic arrays of point interactions in quantum mechanics, and in various ab-initio first-principle multiple-scattering theories for the analysis of diffraction of classical and quantum waves.

math-ph↗

arXiv2005

Spectroscopic properties of a two-level atom interacting with a complex spherical nanoshell

Frequency shifts, radiative decay rates, the Ohmic loss contribution to the nonradiative decay rates, fluorescence yields, and photobleaching of a two-level atom radiating anywhere inside or outside a complex spherical nanoshell, i.e. a stratified sphere consisting of alternating silica and gold concentric spherical shells, are studied. The changes in the spectroscopic properties of an atom interacting with complex nanoshells are significantly enhanced, often more than two orders of magnitude, compared to the same atom interacting with a homogeneous dielectric sphere. The detected fluorescence intensity can be enhanced by 5 or more orders of magnitude. The changes strongly depend on the nanoshell parameters and the atom position. When an atom approaches a metal shell, decay rates are strongly enhanced yet fluorescence exhibits a well-known quenching. Rather contra-intuitively, the Ohmic loss contribution to the nonradiative decay rates for an atomic dipole within the silica core of larger nanoshells may be decreasing when the silica core - inner gold shell interface is approached. The quasistatic result that the radial frequency shift in a close proximity of a spherical shell interface is approximately twice as large as the tangential frequency shift appears to apply also for complex nanoshells. Significantly modified spectroscopic properties (see computer program (pending publication of this manuscript) freely available at http://www.wave-scattering.com) can be observed in a broad band comprising all (nonresonant) optical and near-infrared wavelengths.

quant-ph↗

arXiv2002

Metallo-dielectric diamond and zinc-blende photonic crystals

It is shown that small inclusions of a low absorbing metal can have a dramatic effect on the photonic band structure. In the case of diamond and zinc-blende photonic crystals, several complete photonic band gaps (CPBG's) can open in the spectrum, between the 2nd-3rd, 5th-6th, and 8th-9th bands. Unlike in the purely dielectric case, in the presence of small inclusions of a low absorbing metal the largest CPBG for a moderate dielectric constant (epsilon<=10) turns out to be the 2nd-3rd CPBG. The 2nd-3rd CPBG is the most important CPBG, because it is the most stable against disorder. For a diamond and zinc-blende structure of nonoverlapping dielectric and metallo-dielectric spheres, a CPBG begins to decrease with an increasing dielectric contrast roughly at the point where another CPBG starts to open--a kind of gap competition. A CPBG can even shrink to zero when the dielectric contrast increases further. Metal inclusions have the biggest effect for the dielectric constant 2<=epsilon<=12, which is a typical dielectric constant at near infrared and in the visible for many materials, including semiconductors and polymers. It is shown that one can create a sizeable and robust 2nd-3rd CPBG at near infrared and visible wavelengths even for a photonic crystal which is composed of more than 97% low refractive index materials (n<=1.45, i.e., that of silica glass or a polymer). These findings open the door for any semiconductor and polymer material to be used as genuine building blocks for the creation of photonic crystals with a CPBG and significantly increase the possibilities for experimentalists to realize a sizeable and robust CPBG in the near infrared and in the visible. One possibility is a construction method using optical tweezers, which is analyzed here.

cond-mat.mtrl-sci↗

arXiv2000

Absorption in periodic layered structures

Photonic band structure of metal-dielectric and semiconductor-dielectric layered structures are studied in the presence of a strong absorption. It is shown that absorption can enlarge some gaps by as much as 50%.

cond-mat↗

arXiv2000

Photonic crystals of coated metallic spheres

It is shown that simple face-centered-cubic (fcc) structures of both metallic and coated metallic spheres are ideal candidates to achieve a tunable complete photonic bandgap (CPBG) for optical wavelengths using currently available experimental techniques. For coated microspheres with the coating width to plasma wavelength ratio $l_c/λ_p \leq 10%$ and the coating and host refractive indices $n_c$ and $n_h$, respectively, between 1 and 1.47, one can always find a sphere radius $r_s$ such that the relative gap width $g_w$ (gap width to the midgap frequency ratio) is larger than 5% and, in some cases, $g_w$ can exceed 9%. Using different coatings and supporting liquids, the width and midgap frequency of a CPBG can be tuned considerably.

cond-mat↗