arXiv subjects

Vladimir V. Konotop

Publications and source records attributed to Vladimir V. Konotop.

At least 73 records · Page 4Linked to original sources

arXiv2018

Odd-time reversal $PT$ symmetry induced by anti-$PT$-symmetric medium

We introduce an optical system (a coupler) obeying parity-time ($PT$) symmetry with odd-time reversal, $T^2=-1$. It is implemented with two birefringent waveguides embedded in an anti-$PT$-symmetric medium. The system possesses properties which are untypical for most physical systems with the conventional even-time reversal. Having symmetry-protected degeneracy of the linear modes, the coupler allows for realization of a coherent switch operating with a superposition of binary states which are distinguished by their polarizations. When a Kerr nonlinearity is taken into account, each linear state, being double degenerated, bifurcates into several distinct nonlinear modes, some of which are dynamically stable. The nonlinear modes are characterized by amplitude and by polarization and come in $PT$-conjugate pairs.

physics.optics↗

arXiv2018

Observation and uses of position-space Bloch oscillations in an ultracold gas

We report the direct observation and characterization of position-space Bloch oscillations using an ultracold gas in a tilted optical lattice. While Bloch oscillations in momentum space are a common feature of optical lattice experiments, the real-space center-of-mass dynamics are typically too small to resolve. Tuning into the regime of rapid tunneling and weak force, we observe real-space Bloch oscillation amplitudes of hundreds of lattice sites, in both ground and excited bands. We demonstrate two unique capabilities enabled by tracking of Bloch dynamics in position space: measurement of the full position-momentum phase-space evolution during a Bloch cycle, and direct imaging of the lattice band structure. These techniques, along with the ability to exert long-distance coherent control of quantum gases without modulation, may open up new possibilities for quantum control and metrology.

cond-mat.quant-gas↗

arXiv2018

Coherent-perfect-absorber and laser for bound states in a continuum

It is shown that two fundamentally different phenomena, the bound states in continuum and the spectral singularity (or time-reversed spectral singularity), can occur simultaneously. This can be achieved, in particular, in a rectangular core dielectric waveguide with embedded active (or absorbing) layer. In such a system a two-dimensional bound state in a continuum is created in the plane of a waveguide cross section and it is emitted or absorbed along the waveguide core. The idea can be used for experimental implementation of a laser or a coherent-perfect-absorber for photonic bound state that resides in a continuous spectrum.

physics.optics↗

arXiv2017

Bound states in the continuum in a two-dimensional PT-symmetric system

We address a two-dimensional parity-time (PT)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses. We show that such a system admits bound states in the continuum (BICs) whose properties vary drastically with the orientation of the line separating amplifying and absorbing domains, which sets the direction of internal energy flow. When the flow is perpendicular to the chain of the waveguides, narrow BICs emerge when the standard defect mode, which is initially located in the finite gap, collides with another mode in a standard symmetry breaking scenario and its propagation constant enters the continuous spectrum upon increase of the strength of gain/losses. In contrast, when the energy flow is parallel to the chain of the waveguides, the symmetry gets broken even for a small strength of the gain/losses. In that case, the most rapidly growing mode emerges inside the continuous spectrum and realizes a weakly localized BIC. All BICs found here are the most rapidly growing modes, therefore they can be excited from noisy inputs and, importantly, should dominate the beam dynamics in experiments.

physics.optics↗

arXiv2017

Solitons in a Hamiltonian $PT$-symmetric coupler

We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose-Einstein condensates in nonlinear lattices are discussed.

nlin.PS↗

arXiv2017

Bound States in the Continuum in Spin-Orbit Coupled Atomic Systems

We show that the interplay between spin-orbit coupling and Zeeman splitting in atomic systems can lead to the existence of bound states in the continuum (BICs) supported by trapping potentials. Such states have energies falling well within the continuum spectrum, but nevertheless they are localized and fully radiationless. We report the existence of BICs, in some cases in exact analytical form, in systems with tunable spin-orbit coupling and show that the phenomenon is physically robust. We also found that BIC states may be excited in spin-orbit-coupled Bose-Einstein condensates, where under suitable conditions they may be metastable with remarkably long lifetimes.

nlin.PS↗

arXiv2017

Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling

We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose- Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for the existence of stable propagating solitons. Such states are found in the rotating frame, where the helicoidal SO coupling is reduced to a homogeneous one. In the absence of the Zeeman splitting, the coupled Gross-Pitaevskii equations describing localized states feature many properties of the integrable systems. In particular, four-parametric families of solitons can be obtained in the exact form. Such solitons interact elastically. Zeeman splitting still allows for the existence of two families of moving solitons, but makes collisions of solitons inelastic.

nlin.PS↗

arXiv2017

Phase transition through the splitting of self-dual spectral singularity in optical potentials

We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked in the most of previous studies scenario of the phase transition (known as $PT$-symmetry breaking in systems obeying parity-time symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial reflection, then no spectral singularity is possible. Our findings are illustrated with several examples including a $PT$-symmetric bilayer and other complex potentials discussed in recent literature.

physics.optics↗

arXiv2017

Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e. the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM-polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

physics.optics↗

arXiv2017

$CPT$-symmetric coupler with intermodal dispersion

A dual-core waveguide with balanced gain and loss in different arms and with intermodal coupling is considered. The system is not invariant under the conventional $PT$ symmetry but obeys $CPT$ symmetry where an additional spatial inversion $C$ corresponds to swapping the coupler arms. We show that second-order dispersion of coupling allows for unbroken $CPT$ symmetry and supports propagation of stable vector solitons along the coupler. Small-amplitude solitons are found in explicit form. The combined effect of gain-and-loss and dispersive coupling results in several interesting features which include a separation between the components in different arms, nontrivial dependence of stability of a soliton on its velocity, and the existence of more complex stationary two-hump solutions. Unusual decay dynamics of unstable solitons is discussed too.

physics.optics↗

arXiv2016

Stationary through-flows in a Bose-Einstein condensate with a PT-symmetric impurity

Superfluid currents in the boson condensate with a source and sink of particles are modelled by the PT-symmetric Gross-Pitaevskii equation with a complex potential. We demonstrate the existence of through-flows of the condensate --- stationary states with the asymptotically nonvanishing flux. The through-flows come in two broad varieties determined by the form of their number density distribution. One variety is described by dip-like solutions featuring a localised density depression; the other one comprises hump-like structures with a density spike in their core. We exemplify each class by exact closed-form solutions. For a fixed set of parameters of the PT-symmetric potential, stationary through-flows form continuous families parametrized by the strength of the background flux. All hump-like and some dip-like members of the family are found to be stable. We show that the through-flows can be controlled by varying the gain-and-loss amplitude of the complex potential and that these amplitude variations may produce an anomalous response of the flux across the gain-loss interface.

cond-mat.quant-gas↗

arXiv2016

Dynamic localization in optical and Zeeman lattices in the presence of spin-orbit coupling

The dynamic localization of a two-level atom in a periodic potential under the action of spin-orbit coupling and a weak harmonically-varying linear force is studied. We consider optical and Zeeman potentials that are either in-phase or out-of-phase in two spinor components, respectively. The expectation value for the position of the atom after one oscillation period of the linear force is recovered in authentic resonances or in pseudo-resonances. The frequencies of the linear force corresponding to authentic resonances are determined by the band structure of the periodic potential and are affected by the spin-orbit coupling. The width/dispersion of the wavepacket in authentic resonances is usually minimal. The frequencies corresponding to pseudo-resonances do not depend on the type of potential and on the strength of the spin-orbit coupling, while the evolution of excitations at the corresponding frequencies is usually accompanied by significant dispersion. Pseudo-resonances are determined by the initial phase of the linear force and by the quasi-momentum of the wavepacket. Due to the spinor nature of the system, the motion of the atom is accompanied by periodic, but not harmonic, spin oscillations. Under the action of spin-orbit coupling the oscillations of the wavepacket can be nearly completely suppressed in optical lattices. Dynamic localization in Zeeman lattices is characterized by doubling of the resonant oscillation periods due to band crossing at the boundary of the Brillouin zone. We also show that higher harmonics in the Fourier expansion of the energy band lead to effective dispersion, which can be strong enough to prevent dynamic localization of the Bloch wavepacket.

cond-mat.quant-gas↗

arXiv2016

Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling

We address Bloch oscillations of a spin-orbit coupled atom in periodic potentials of two types: Optical and Zeeman lattices. We show that in optical lattices the spin-orbit coupling allows controlling the direction of atomic motion and may lead to complete suppression of the oscillations at specific values of the coupling strength. In Zeeman lattices the energy bands are found to cross each other at the boundaries of the Brillouin zone, resulting in period-doubling of the oscillations. In all cases, the oscillations are accompanied by rotation of the pseudo-spin, with a dynamics that is determined by the strength of the spin-orbit coupling. The predicted effects are discussed also in terms of a Wannier-Stark ladder, which in optical lattices consist of two mutually-shifted equidistant sub-ladders.

cond-mat.quant-gas↗

arXiv2016

Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation

We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $δ$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys the parity-time symmetry. This configuration describes atomic Bose-Einstein condensates with local loading and local elimination of atoms, polaritonic condensates, or optical ring resonators with local pump and absorption. We discuss the linear spectrum of such a system and show if the location of the $δ$ functions is slightly asymmetric, then the system can be driven through a series of exceptional points by the change of the gain-and-loss coefficient. In the nonlinear case, the system admits solutions with spatially constant and periodic densities which are presented in the exact analytical form. These solutions are supported by the current directed from the gain potential towards the absorbing potential. The system also admits currentless solutions. Stability and bifurcations of nonlinear solutions are also described.

nlin.PS↗

arXiv2016

Modes and exceptional points in waveguides with impedance boundary conditions

A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the dielectric, and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points, for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.

physics.optics↗

arXiv2016

Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and ${\cal PT}$ symmetry

We consider nonlinear modes of the nonlinear Schrödinger equation with a nonlocal nonlinearity and an additional PT-symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their linear stability in the limit of small nonlinearity. It is demonstrated that either PT symmetry or the nonlocality can be used to manage the stability of the small-amplitude nonlinear modes. The stability properties are also found to depend on the particular shape of the nonlocal kernel. Additional numerical simulations show that the stability results remain valid not only for the infinitesimally small nonlinear modes, but also for the modes of finite amplitude

nlin.PS↗

arXiv2016

Jamming anomaly in $\mathcal{PT}$-symmetric systems

The Schrödinger equation with a $\mathcal{PT}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $γ$, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger $γ$, where the increase of the amplitude produces a drop of the flux across the gain-loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.

physics.optics↗

arXiv2016

Nonlinear waves in $\cal PT$-symmetric systems

Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\cal PT$-symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of $\cal PT$ symmetry are pointed out.

nlin.PS↗