Effect of nonlinearity on the dynamics of a particle in field-induced systems

Datta, P.K.; Jayannavar, A. M.

doi:10.1103/physrevb.58.8170

Cited by 16 publications

(9 citation statements)

References 13 publications

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“…Travelling self-trapped states are consistent with the observation of soliton-like structures described in Ref. [30] and have also reported in another systems [17,42]. Results of Hadamard quantum gates (θ = π/4) suggest the velocity of the solitons-like formations decreasing as χ increases, in such way that, for sufficiently strong nonlinearities, a scenario of collisions with inelastic scattering comes up.…”

Section: Resultssupporting

confidence: 88%

Self-trapped quantum walks

Buarque

Dias

2020

Phys. Rev. A

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We study the existence and charaterization of self-trapping phenomena in discrete-time quantum walks. By considering a Kerr-like nonlinearity, we associate an acquisition of the intensity-dependent phase to the walker while it propagates on the lattice. Adjusting the nonlinear parameter (χ) and the quantum gates (θ), we will show the existence of different quantum walking regimes, including those with travelling soliton-like structures or localized by self-trapping. This latter scenario is absent for quantum gates close enough to Pauli-X. It appears for intermediate configurations and becomes predominant as quantum gates get closer to Pauli-Z. By using χ versus θ diagrams, we will show that the threshold between quantum walks with delocalized or localized regimes exhibit an unusual aspect, in which an increment on the nonlinear strength can induce the system from localized to a delocalized regime.

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Section: Resultssupporting

confidence: 88%

Self-trapped quantum walks

Buarque

Dias

2020

Phys. Rev. A

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“…As a result, the fraction of the excitation that can propagate is now effectively smaller, leading to smaller values of m 2 (t) as χ is increased. We note that a similar type of self-trapping phenomenon 17,18 was observed in various nonlinear lattices, 9,10,19,21,22,23,24,25 though in all these cases the value of χ * was much larger, i.e. χ * ∼ O(1).…”

Section: B Critical Nonlinearitysupporting

confidence: 71%

Wavepacket dynamics of the nonlinear Harper model

Kottos

2007

Phys. Rev. B

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The destruction of anomalous diffusion of the Harper model at criticality, due to weak nonlinearity $\chi$, is analyzed. It is shown that the second moment grows subdiffusively as $ \sim t^{\alpha}$ up to time $t^*\sim \chi^{\gamma}$. The exponents $\alpha$ and $\gamma$ reflect the multifractal properties of the spectra and the eigenfunctions of the linear model. For $t>t^*$, the anomalous diffusion law is recovered, although the evolving profile has a different shape than in the linear case. These results are applicable in wave propagation through nonlinear waveguide arrays and transport of Bose-Einstein condensates in optical lattices.Comment: 6 pages, 5 figures. Revised and published in Phys. Rev.

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“…For instance, for many atoms in a Bose-Einstein condensate, a mean field treatment leads to the Gross-Pitaevsky equation for nonlinear waves. The main effect of nonlinearity is to deteriorate Bloch oscillations, as recently studied experimentally [5] and theoretically [6][7][8].In contrast, we will explore the fate of Bloch oscillations for quantum interacting few-body systems. This is motivated by recent experimental advance [9] in monitoring and manipulating few bosons in optical lattices.…”

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confidence: 96%

mentioning

confidence: 99%

Interaction-induced fractional Bloch and tunneling oscillations

et al. 2010

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We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single-particle Bloch oscillations. For strong interaction the Bloch oscillation regime re-emerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength affects the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength, a particle will tunnel from the interacting cloud to a well-defined distant lattice location. Bloch oscillations [1] in dc biased lattices are due to wave interference and have been observed in a number of quite different physical systems: atomic oscillations in Bose-Einstein condensates (BECs) [2], light intensity oscillations in waveguide arrays [3], and acoustic waves in layered and elastic structures [4], among others.Quantum many-body interactions can alter the above outcome. A mean-field treatment makes the wave equations nonlinear and typically nonintegrable. For instance, for many atoms in a Bose-Einstein condensate, a mean-field treatment leads to the Gross-Pitaevsky equation for nonlinear waves. The main effect of nonlinearity is to deteriorate Bloch oscillations, as recently studied experimentally [5] and theoretically [6][7][8].In contrast, we explore the fate of Bloch oscillations for quantum interacting few-body systems. This exploration is motivated by a recent experimental advance [9] in monitoring and manipulating few bosons in optical lattices. Few-body quantum systems are expected to have finite eigenvalue spacings, consequent quasiperiodic temporal evolution, and phase coherence. In a recent report on interacting electron dynamics, spectral evidence for a Bloch frequency doubling was reported [10]. On the other hand, it was also recently argued that Bloch oscillations are effectively destroyed for few interacting bosons [11].In this Brief Report, we show that for strongly interacting bosons a coherent Bloch oscillation regime re-emerges. If the bosons are clustered into an interacting cloud at time t = 0, the period of Bloch oscillations will be a fraction of the period of the noninteracting case, scaling as the inverse number of interacting particles (Fig. 1). The amplitude (spatial extent) of these fractional Bloch oscillations decreases with increasing interaction strength. For specific values of the interaction, one of the particles leaves the interacting cloud and tunnel for a possibly distant and well-defined site of the lattice. For few particles, the dynamics is always quasiperiodic, and a decoherence similar to the case of a mean-field nonlinear equation [7] does not take place.We consider the Bose-Hubbard model with a dc field:whereb + j andb j are standard boson creation and annihilation operators at lattice site j , the hopping t 1 = 1, and U and E are the interaction and dc field strengths, respectively. To study the dynamics of...

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Effect of nonlinearity on the dynamics of a particle in field-induced systems

Cited by 16 publications

References 13 publications

Self-trapped quantum walks

Self-trapped quantum walks

Wavepacket dynamics of the nonlinear Harper model

Interaction-induced fractional Bloch and tunneling oscillations

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