arXiv subjects

V. V. Konotop

Publications and source records attributed to V. V. Konotop.

At least 55 records · Page 3Linked to original sources

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

Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials

Exact solutions for the generalized nonlinear Schrödinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic modulations in the space of complex potentials and nonlinearity coefficients. Examples of stable and unstable solutions are given. We also demonstrated numerically the existence of stable dissipative breathers in the presence of an additional parabolic trap.

nlin.PS↗

arXiv2010

Three-dimensional rogue waves in non-stationary parabolic potentials

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of (1+1)-dimensional case. As an example, we illustrated our technique using two lowest order rational solutions of the NLS equation as seeding functions to obtain rogue wave-like solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wave-like solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and BECs.

nlin.SI↗

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↗

arXiv2010

All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms

A standing-wave control field applied to a three-level atomic medium in a planar hollow-core photonic crystal waveguide creates periodic variations of linear and nonlinear refractive indexes of the medium. This property can be used for efficient steering of light. In this work we study, both analytically and numerically, the dynamics of probe optical beams in such structures. By properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of spatial gap solitons, thus providing desirable change in direction of the beam propagation without inducing appreciable diffraction. Due to the significant enhancement of the nonlinearity, such self-focusing of the probe beam can be reached at extremely weak light intensities.

physics.optics↗

arXiv2009

Rabi oscillations of matter wave solitons in optical lattices

Inter-band Rabi oscillations of gap soliton matter waves induced by time dependent periodic forces in combined linear and nonlinear optical lattices are for the first time demonstrated. It is shown that under suitable conditions these oscillations can become long-lived. By switching off the external force at proper time it is possible to create either pure (stationary macroscopically populated) gap soliton states or linear combination of two gap solitons with appreciably long life-time.

cond-mat.other↗

arXiv2009

Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices

It is shown that the one-dimensional nonlinear Schrödinger equation with a dissipative periodic potential, nonlinear losses and linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes a Bose-Einstein condensate with inelastic two- and three-body interactions loaded in an optical lattice with losses due to inelastic interactions of the atoms with photons.

cond-mat.other↗

arXiv2009

Dynamical localization of gap-solitons by time periodic forces

The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic modulation of the nonlinearity in space to eliminate nonexistence regions of gap-solitons in reciprocal space. We show that when this condition is achieved, the observation of dynamical localization in true nonlinear regime becomes possible. The results apply to all systems described by the periodic nonlinear Schrödinger equation, including Bose-Einstein condensates of ultracold atoms trapped in optical lattices and arrays of waveguides or photonic crystals in nonlinear optics.

cond-mat.other↗

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

Surface Solitons in Three Dimensions

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site "horseshoe"-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anti-continuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface this increased stability region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.

nlin.PS↗

arXiv2008

Long-living Bloch oscillations of matter waves in optical lattices

It is shown that by properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of a localized wavepacket in a periodic potential. The results are supported both by analytical and numerical investigations and are interpreted in terms of matter wave dynamics displaying dozens of oscillation periods without any visible distortion of the wave packet.

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

Field patterns in periodically modulated optical parametric amplifiers and oscillators

Spatially localized and periodic field patterns in periodically modulated optical parametric amplifiers and oscillators are studied. In the degenerate case (equal signal and idler beams) we elaborate the systematic method of construction of the stationary localized modes in the amplifiers, study their properties and stability. We describe a method of constructing periodic solutions in optical parametric oscillators, by adjusting the form of the external driven field to the given form of either signal or pump beams.

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↗

arXiv2007

Partial delocalization of two-component condensates in optical lattices

We study management of localized modes in two-component (spinor) Bose-Einstein condensates embedded in optical lattices by changing interspecies interactions. By numerical integration of the coupled Gross-Pitaevskii equations, we find three different regimes of the delocalizing transition: i) the partial delocalization when the chemical potential of one of the components collapses with a gap edge and the respective component transforms into a Bloch state, while the other component remains localized; ii) the partial delocalization as consequence of instability of one of the components; and iii) the situation where the vector soliton reaches limits of the existence domain. It is shown that there exists a critical value for interspecies scattering length, below which solutions can be manipulated and above which one of the components is irreversibly destroyed.

cond-mat.other↗

arXiv2007

Surface modes and breathers in finite arrays of nonlinear waveguides

We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one-- and two--dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.

cond-mat.other↗

arXiv2007

Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present non-standard possibilities, among which we mention a quasi-linear regime, where the pulse dynamics obeys essentially the linear Schr{ö}dinger equation. We analyze the properties of such models both in connection with their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

cond-mat.other↗