Nondecaying Bloch modes of a dissipative lattice

Shchesnovich, V. S.

doi:10.1209/0295-5075/99/60005

Cited by 3 publications

(10 citation statements)

References 20 publications

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“…As was discussed before [11], besides application to the propagation of light in photonic crystals, our results can have applications in other branches of physics as, for instance, in the field of cold atoms and Bose-Einstein condensates in the spatially periodic traps created with laser beams, where externally controlled removal of atoms serves as dissipation (see, for instance, Refs. [15,16], the removal of atoms can be done by a set of ordered electron beams with the use of the electron microscopy technique of Refs.…”

Section: Introductionmentioning

confidence: 83%

“…Let us present the numerical results on the band structure of the dissipative lattice in Eq. (11). Fig.…”

Section: The Bloch Modes In the Case Of A Periodic Array Of Finite-wi...mentioning

confidence: 99%

“…where the narrow-width approximation requires that σ ≪ 2π (previously it was established that the nondecaying modes appear in this limit [11]). Our purpose is to find out properties of the nondecaying spatial structures governed by Eqs.…”

Section: Bloch Waves and Bloch Bands For A Dissipative Latticementioning

confidence: 99%

“…where the narrow-width approximation requires that σ ≪ 2π (previously it was established that the nondecaying modes appear in this limit [11]).…”

Section: Bloch Waves and Bloch Bands For A Dissipative Latticementioning

confidence: 99%

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Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations

Fernández¹,

Shchesnovich²

2014

J. Phys. A: Math. Theor.

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We demonstrate the existence of extremely weakly decaying linear and nonlinear modes (i.e. modes immune to dissipation) in the one-dimensional periodic array of identical spatially localized dissipations, where the dissipation width is much smaller than the period of the array. We consider wave propagation governed by the one-dimensional Schrödinger equation in the array of identical Gaussian-shaped dissipations with three parameters, the integral dissipation strength Γ 0 , the width σ and the array period d. In the linear case, setting σ → 0, while keeping Γ 0 fixed, we get an array of zero-width dissipations given by the Dirac delta-functions, i.e. the complex Kroning-Penney model, where an infinite number of nondecaying modes appear with the Bloch index being either at the center, k = 0, or at the boundary, k = π/d, of an analog of the Brillouin zone. By using numerical simulations we confirm that the weakly decaying modes persist for σ such that σ/d ≪ 1 and have the same Bloch index. The nondecaying modes persist also if a real-valued periodic potential is added to the spatially periodic array of dissipations, with the period of the dissipative array being multiple of that of the periodic potential. We also consider evolution of the soliton-shaped pulses in the nonlinear Schrödinger equation with the spatially periodic dissipative lattice and find that when the pulse width is much larger than the lattice period and its wave number k is either at the center, k = 2π/d, or at the boundary, k = π/d, a significant fraction of the pulse escapes the dissipation forming a stationary nonlinear mode with the soliton shaped envelope and the Fourier spectrum consisting of two peaks centered at k and −k.

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Section: Introductionmentioning

confidence: 83%

“…Let us present the numerical results on the band structure of the dissipative lattice in Eq. (11). Fig.…”

Section: The Bloch Modes In the Case Of A Periodic Array Of Finite-wi...mentioning

confidence: 99%

Section: Bloch Waves and Bloch Bands For A Dissipative Latticementioning

confidence: 99%

“…where the narrow-width approximation requires that σ ≪ 2π (previously it was established that the nondecaying modes appear in this limit [11]).…”

Section: Bloch Waves and Bloch Bands For A Dissipative Latticementioning

confidence: 99%

See 2 more Smart Citations

Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations

Fernández¹,

Shchesnovich²

2014

J. Phys. A: Math. Theor.

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“…Localized single-particle losses ( L = √ γ α ) are another case in which dissipative processes can help to the dynamical control of the quantum system. This fundamental dissipation process has attracted a lot of theoretical attention [32,52,53,[55][56][57][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83], not only because of its simplicity, but also due to the interesting phenomena that one can study. For example, as it was shown in [32,55,56,73] this dissipation mechanism can create attractive fixed points in the classical phase space of the system.…”

Section: The Bose-hubbard Modelmentioning

confidence: 99%

The dissipative Bose-Hubbard model

Kordas

Witthaut

Buonsante

et al. 2015

Eur. Phys. J. Spec. Top.

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Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counterintuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

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Stationary vortex flows and macroscopic Zeno effect in Bose-Einstein condensates with localized dissipation

Zezyulin¹

2014

Preprint

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We theoretically demonstrate a possibility to observe the macroscopic Zeno effect in an effectively two-dimensional (pancake-shaped) repulsive Bose-Einstein condensate subjected to a strong narrow dissipation. We show that the dissipation can generate stable stationary nonlinear flows which bear either zero or non-zero topological charge (vorticity). The superfluid flows towards the dissipative defect compensate the atomic losses. The macroscopic Zeno effect manifests itself in a nonmonotonous dependence of the inward current density on the strength of the dissipation.

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Nondecaying Bloch modes of a dissipative lattice

Cited by 3 publications

References 20 publications

Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations

Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations

The dissipative Bose-Hubbard model

Stationary vortex flows and macroscopic Zeno effect in Bose-Einstein condensates with localized dissipation

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