arXiv subjects

A. Stefanov

Publications and source records attributed to A. Stefanov.

15 recordsLinked to original sources

arXiv2025

Calibration features of a polarimetric backscattering setup with a beamsplitter

We address the problem of calibrating a polarimetric backscattering setup that includes a beamsplitter, taking its optical properties into account. Using Fisher information, we justify a specific calibration configuration involving reference optical elements for the maximum likelihood method and demonstrate its effectiveness through Monte Carlo simulations. This approach leads to higher precision, as the described set of measurements allows the beamsplitter to be treated as an integral part of the setup, without requiring separate processing or reconfiguration of the setup for the beamsplitter calibration. Furthermore, we emphasize the significance of considering the beamsplitter's optical properties by proposing a test to estimate the error that arises from neglecting these properties during the calibration procedure.

physics.optics↗

arXiv2025

Testing classicality of gravity by gravitation decoherence

Here we discuss an influence of an external weak gravitational field on the gravitational self-decoherence effect with help of the stochastic extension of regularized Shrödinger-Newton equation in a curved background. We derive the master equation and demonstrate that it leads to the experimentally verifiable conclusions about applicability of the classical description of the weak gravitation field. Namely, a presence of oscillating terms in the otherwise purely exponential decay of the coherence would indicate classicality of gravity for the case.

hep-ph↗

arXiv2022

Emulation of quantum measurements with mixtures of coherent states

We propose a methodology to emulate quantum phenomena arising from any non-classical quantum state using only a finite set of mixtures of coherent states. This allows us to successfully reproduce well-known quantum effects using resources that can be much more feasibly generated in the laboratory. We present a simple procedure to experimentally carry out quantum-state emulation with coherent states, illustrate it emulating multi-photon NOON states with few phase-averaged coherent states, and demonstrate its capabilities in observing fundamental quantum-mechanical effects, such as the Hong-Ou-Mandel effect, violating Bell inequalities and witnessing quantum non-classicality.

quant-ph↗

arXiv2022

Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations

In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schr{ö}dinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension $d=2$, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent $p$, there exists a progressively narrowing range of stable frequencies. Finally, above the critical $p$ all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor $b$ and nonlinearity power $p$.

nlin.PS↗

arXiv2019

Reconstructing compound objects by quantum imaging with higher-order correlation functions

Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons. However, quantum imaging generally leads to nonlinear estimation problems. The complexity of these problems rapidly increases with the number of parameters describing the object. We suggest a way to drastically reduce the complexity for a wide class of problems. The key point of our approach is connecting the features of the Fisher information with the parametric locality of the problem, and building the efficient iterative inference scheme reconstructing only a subset of the whole set of parameters in each step. This iterative scheme is linear on the total number of parameters. This scheme is applied to quantum near-field imaging, the inference procedure is developed resulting in super-resolving reconstruction of grey compound transmission objects. The functionality of the method is demonstrated with experimental data obtained by measurements of higher-order correlation functions for imaging with entangled twin-photons and pseudo-thermal light sources. By analyzing the informational content of the measurement, it becomes possible to predict the existence of optimal photon correlations providing for the best image resolution in the super-resolution regime. This prediction is experimentally confirmed. It is also shown how an estimation bias stemming from image features may drastically improve the resolution.

quant-ph↗

arXiv2014

Traveling Waves and their Tails in Locally Resonant Granular Systems

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem. or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) of the problem in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, that will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of resonance conditions is identified for which solutions with genuinely monotonic decaying tails arise.

nlin.PS↗

arXiv2014

Non-Locality of Experimental Qutrit Pairs

The insight due to John Bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day. We describe an experiment, and its analysis, displaying non-locality of entangled qutrit pairs. The non-locality of such systems, as compared to qubit pairs, is of particular interest since it potentially opens the door for tests of bipartite non-local behavior independent of probabilistic Bell inequalities, but of deterministic nature.

quant-ph↗

arXiv2014

On the spectral stability of kinks in some PT-symmetric variants of the classical Klein-Gordon Field Theories

In the present work we consider the introduction of PT-symmetric terms in the context of classical Klein-Gordon field theories. We explore the implication of such terms on the spectral stability of coherent structures, namely kinks. We find that the conclusion critically depends on the location of the kink center relative to the center of the PT-symmetric term. The main result is that if these two points coincide, the kink's spectrum remains on the imaginary axis and the wave is spectrally stable. If the kink is centered on the "lossy side" of the medium, then it becomes stabilized. On the other hand, if it becomes centered on the "gain side" of the medium, then it is destabilized. The consequences of these two possibilities on the linearization (point and essential) spectrum are discussed in some detail.

nlin.PS↗

arXiv2011

On the existence of solitary traveling waves for generalized Hertzian chains

We consider the question of existence of "bell-shaped" (i.e. non-increasing for x>0 and non-decreasing for x<0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p=3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formulation of the problem. More specifically, we construct an appropriate energy functional, for which we show that the constrained minimization problem over bell-shaped entries has a solution. We also provide an alternative proof of the Friesecke-Wattis result [Comm. Math. Phys 161, 394 (1994)], by using the same approach (but where the minimization is not constrained over bell-shaped curves). We briefly discuss and illustrate numerically the implications on the doubly exponential decay properties of the waves, as well as touch upon the modifications of these properties in the presence of a finite precompression force in the model.

nlin.PS↗

arXiv2008

Asymptotic stability of small solitons in the discrete nonlinear Schrodinger equation in one dimension

Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schrodinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dispersive decay estimates from Pelinovsky & Stefanov (2008) and the arguments of Mizumachi (2008) for a continuous nonlinear Schrodinger equation in one dimension. Numerical simulations suggest that the actual decay rate of perturbations near the asymptotically stable solitons is higher than the one used in the analysis.

nlin.PS↗

arXiv2008

On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension

Based on the recent work \cite{KKK} for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator $$ H ϕ= (-\De + V)ϕ=-(ϕ_{n+1} + ϕ_{n-1} - 2 ϕ_n) + V_n ϕ_n. $$ We show that under appropriate decay conditions on the general potential (and a non-resonance condition at the spectral edges), the spectrum of $H$ consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates $$ \|e^{i t H} P_{\rm a.c.}(H)\|_{l^2_σ \to l^2_{-σ}} \lesssim t^{-3/2} $$ for any fixed $σ> {5/2}$ and any $t > 0$, where $P_{\rm a.c.}(H)$ denotes the spectral projection to the absolutely continuous spectrum of $H$. In addition, based on the scattering theory for the discrete Jost solutions and the previous results in \cite{SK}, we find new dispersive estimates $$ \|e^{i t H} P_{\rm a.c.}(H) \|_{l^1\to l^\infty}\lesssim t^{-1/3}. $$ These estimates are sharp for the discrete Schrödinger operators even for $V = 0$.

math-ph↗

arXiv2007

Experimental Demonstration of Decoherence-Free One-Way Information Transfer

We report the experimental demonstration of a one-way quantum protocol reliably operating in the presence of decoherence. Information is protected by designing an appropriate decoherence-free subspace for a cluster state resource. We demonstrate our scheme in an all-optical setup, encoding the information into the polarization states of four photons. A measurement-based one-way information-transfer protocol is performed with the photons exposed to severe symmetric phase-damping noise. Remarkable protection of information is accomplished, delivering nearly ideal outcomes.

quant-ph↗

arXiv2007

Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices

We consider the problem of the existence of a dynamical barrier of ``mass'' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrodinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schrodinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schrodinger equation.

nlin.PS↗

arXiv2005

Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.

cond-mat.supr-con↗

arXiv2004

Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations

We show decay estimates for the propagator of the discrete Schrödinger and Klein-Gordon equations in the form $\norm{U(t)f}{l^\infty}\leq C (1+|t|)^{-d/3}\norm{f}{l^1}$. This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant $l^p$ norms. The analytical decay estimates are corroborated with numerical results.

nlin.PS↗