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V. S. Shchesnovich

Publications and source records attributed to V. S. Shchesnovich.

At least 37 records · Page 2Linked to original sources
arXiv2011

Generators of nonclassical states by combination of the linear coupling of boson modes, Kerr nonlinearity and the strong linear losses

We show that the generators of quantum states of light can be built by employing the Kerr nonlinearity, a strong linear absorption or losses and the linear coupling of optical modes. Our setup can be realized, for instance, with the use of the optical fiber technology. We consider in detail the simplest cases of three and four coupled modes, where a strongly lossy mode is linearly coupled to other linear and nonlinear modes. In the three-mode design, our scheme emulates the third-order nonlinear absorption, allowing for generation of the single photon states, or the two-photon absorption allowing to generate the phase states. In the four-mode design, the scheme emulates a non-local absorption which produces an entangled state of two uncoupled modes. We also note that in the latter case and in the case of the phase states generation the output state is in the linear modes, which prevents its subsequent degradation by the strong losses accompanying the strong Kerr nonlinearity.

quant-ph↗
arXiv2011

Linear and nonlinear Zeno effects in an optical coupler

It is shown that in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a counter-intuitive enhancement of transparency of the coupler with the increase of the dissipation and represents an optical analogue of the quantum Zeno effect. Experimental realization of the phenomenon based on the use of the chalcogenide glasses is proposed. The system allows for observation of the cross-over between the linear and nonlinear Zeno effects, as well as effective manipulation of light transmission through the coupler.

physics.optics↗
arXiv2010

The three-site Bose-Hubbard model subject to atom losses: the boson-pair dissipation channel and failure of the mean-field approach

We employ the perturbation series expansion for derivation of the reduced master equations for the three-site Bose-Hubbard model subject to strong atom losses from the central site. The model describes a condensate trapped in a triple-well potential subject to externally controlled removal of atoms. We find that the $π$-phase state of the coherent superposition between the side wells decays via two dissipation channels, the single-boson channel (similar to the externally applied dissipation) and the boson-pair channel. The quantum derivation is compared to the classical adiabatic elimination within the mean-field approximation. We find that the boson-pair dissipation channel is not captured by the mean-field model, whereas the single-boson channel is described by it. Moreover, there is a matching condition between the zero-point energy bias of the side wells and the nonlinear interaction parameter which separates the regions where either the single-boson or the boson-pair dissipation channel dominate. Our results indicate that the $M$-site Bose-Hubbard models, for $M>2$, subject to atom losses may require an analysis which goes beyond the usual mean-field approximation for correct description of their dissipative features. This is an important result in view of the recent experimental works on the single site addressability of condensates trapped in optical lattices.

cond-mat.quant-gas↗
arXiv2010

Control of the Bose-Einstein condensate by dissipation. Nonlinear Zeno effect

We show that controlled dissipation can be used as a tool for exploring fundamental phenomena and managing mesoscopic systems of cold atoms and Bose-Einstein condensates. Even the simplest boson-Josephson junction, that is, a Bose-Einstein condensate in a double-well trap, subjected to removal of atoms from one of the two potential minima allows one to observe such phenomena as the suppression of losses and the nonlinear Zeno effect. In such a system the controlled dissipation can be used to create desired macroscopic states and implement controlled switching among different quantum regimes.

cond-mat.quant-gas↗
arXiv2009

Mesoscopic quantum switching of a Bose-Einstein condensate in an optical lattice governed by the parity of the number of atoms

It is shown that for a $N$-boson system the parity of $N$ can be responsible for a qualitative difference in the system response to variation of a parameter. The nonlinear boson model is considered, which describes tunneling of boson pairs between two distinct modes $X_{1,2}$ of the same energy and applies to a Bose-Einstein condensate in an optical lattice. By varying the lattice depth one induces the parity-dependent quantum switching, i.e. $X_1\to X_2$ for even $N$ and $X_1\to X_1$ for odd $N$, for arbitrarily large $N$. A simple scheme is proposed for observation of the parity effect on the \textit{mesoscopic scale} by using the bounce switching regime, which is insensitive to the initial state preparation (as long as only one of the two $X_l$ modes is significantly populated), stable under small perturbations and requires an experimentally accessible coherence time.

cond-mat.quant-gas↗
arXiv2009

Quantum switching at a mean-field instability of a Bose-Einstein condensate in an optical lattice

It is shown that bifurcations of the mean-field dynamics of a Bose-Einstein condensate can be related with the quantum phase transitions of the original many-body system. As an example we explore the intra-band tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two selftrapping states or from a selftrapping state to a superposition of the macroscopically populated selftrapping states with the step-like variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system.

cond-mat.other↗
arXiv2008

Optical pulse propagation in a switched-on photonic lattice: Rabi effect with the roles of light and matter interchanged

A light pulse propagating in a suddenly switched on photonic lattice, when the central frequency lies in the photonic band gap, is an analog of the Rabi model where the two-level system is the two resonant (i.e. Bragg-coupled) Fourier modes of the pulse, while the photonic lattice serves as a monochromatic external field. A simple theory of these Rabi oscillations is given and confirmed by the numerical solution of the corresponding Maxwell equations. This is a direct, i.e. temporal, analog of the Rabi effect, additionally to the spatial analog in optical beam propagation described in Opt. Lett. 32, 1920 (2007). An additional high-frequency modulation of the Rabi oscillations reflects the lattice-induced energy transfer between the electric and magnetic fields of the pulse.

physics.optics↗
arXiv2008

Fock-space quantum particle approach for the two-mode boson model describing BEC trapped in a double-well potential

We develop the Fock-space many-body quantum approach for large number of bosons, when the bosons occupy significantly only few modes. The approach is based on an analogy with the dynamics of a single particle of either positive or negative mass in a quantum potential, where the inverse number of bosons plays the role of Planck constant. As application of the method we consider the Bose-Einstein condensate in a double-well trap. The ground state of positive mass particle corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BEC above the threshold for symmetry breaking, the ground state is a cat state and we relate this fact to the double-well shape of the quantum potential for the positive mass quantum particle. The tunneling energy splitting between the local Fock states of the cat state is shown to be extremely small for the nonlinearity parameter just above the critical value and exponentially decreasing with the number of atoms. In the repulsive case, the phase locked ($π$-phase) macroscopic quantum self-trapping of BEC is related to the double-well structure of the potential for the negative mass quantum particle. We also analyze the running phase macroscopic quantum self-trapping state and show that it is subject to quantum collapses and revivals. Moreover, the quantum dynamics just before the first collapse of the running phase shows exponential growth of dispersion of the quantum phase distribution which may explain the growth of the phase fluctuations seen in the experiment on the macroscopic quantum self-trapping.

cond-mat.other↗
arXiv2008

Nonlinear tunneling of BEC in an optical lattice: signatures of quantum collapse and revival

Quantum theory of the intraband resonant tunneling of a Bose-Einstein condensate loaded in a twodimensional optical lattice is considered. It is shown that the phenomena of quantum collapse and revival can be observed in the fully quantum problem. The mean-field limit of the theory is analyzed using the WKB approximation for discrete equations, establishing in this way a direct connection between the two approaches conventionally used in very different physical contexts. More specifically we show that there exist two different regimes of tunneling and study dependence of quantum collapse and revival on the number of condensed atoms.

cond-mat.other↗
arXiv2008

Nonlinear intraband tunneling of BEC in a cubic three-dimensional lattice

The intra-band tunneling of a Bose-Einstein condensate between three degenerate high-symmetry X-points of the Brillouin zone of a cubic optical lattice is studied in the quantum regime by reduction to a three-mode model. The mean-field approximation of the deduced model is described. Compared to the previously reported two-dimensional (2D) case [Phys. Rev. A 75, 063628 (2007)], which is reducible to the two-mode model, in the case under consideration there exist a number of new stable stationary atomic distributions between the X-points and a new critical lattice parameter. The quantum collapses and revivals of the atomic population dynamics are absent for the experimentally realizable time span. The 2D stationary configurations, embedded into the 3D lattice, turn out to be always unstable, while existence of a stable 1D distribution, where all atoms populate only one X-state, may serve as a starting point in the experimental study of the nonlinear tunneling in the 3D lattice.

cond-mat.other↗
arXiv2007

Nonlinear tunneling in two-dimensional lattices

We present thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices considering different initial atomic distributions in the highly symmetric states. For analytical description of the condensate before instabilities are developed, we derive several few-mode models, analyzing both essentially nonlinear and quasi-linear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide accurate description of the tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise a two-mode model may give only useful qualitative hints for understanding tunneling but does not reproduce many features of the phenomenon. This reflects crucial role of the instabilities developed due to two-body interactions resulting in non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer.

cond-mat.other↗
arXiv2006

Zener tunneling in two-dimensional photonic lattices

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as was studied recently in experiments for optically-induced photonic lattices [H. Trompeter et al., Phys. Rev. Lett. \textbf{96}, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in a generic case of the Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, the higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.

cond-mat.other↗
arXiv2004

Dynamics of Bose-Einstein condensates in cigar-shaped traps

Gross-Pitaevskii equation for Bose-Einstein condensate confined in elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low density limit our results reproduce the known formulae. In the high density case our description of solitons goes beyond the standard approach based on the nonlinear Schrödinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. Korteweg-de Vries equation for weakly nonlinear waves is derived and existence of bright solitons on a constant background is predicted for the dense enough condensate with repulsive interaction between the atoms.

cond-mat.soft↗
arXiv2003

Polarization scattering by soliton-soliton collisions

Collision of two solitons of the Manakov system is analytically studied. Existence of a complete polarization mode switching regime is proved and the parameters of solitons prepared for polarization switching are found.

solv-int↗
arXiv2003

General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multi-soliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. \textbf{110}, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to non-elementary zeros generically describe the simultaneous breakup of a pumping wave $(u_3)$ into the other two components ($u_1$ and $u_2$) and merger of $u_1$ and $u_2$ waves into the pumping $u_3$ wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping $u_3$ wave into the $u_1$ and $u_2$ components, and the reverse process. In the non-generic cases, these two-soliton solutions could describe the elastic interaction of the $u_1$ and $u_2$ waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. \textbf{69}, 1654 (1975)] and Kaup [Stud. Appl. Math. \textbf{55}, 9 (1976)].

nlin.SI↗
arXiv2002

Noncoaxial multivortices in the complex sine-Gordon theory on the plane

We construct explicit multivortex solutions for the complex sine-Gordon equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the previously found (coaxial) multivortices, the new solutions comprise $n$ single vortices placed at arbitrary positions (but confined within a finite part of the plane.) All multivortices, including the single vortex, have an infinite number of parameters. We also show that, in contrast to the coaxial complex sine-Gordon multivortices, the axially-symmetric solutions of the Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not} belong to a broader family of noncoaxial multivortex configurations.

nlin.SI↗
arXiv2001

Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to previously utilised Inverse Scattering-based perturbation techniques, our approach is valid for arbitrarily large driving strengths and damping coefficients. We show that, contrary to suggestions made in literature, the complexity observed in the soliton's dynamics cannot be accounted for just by its coupling to the long-wavelength radiation.

nlin.PS↗