Matter-wave analog of an optical random laser

Płodzień, Marcin; Sacha, Krzysztof

doi:10.1103/physreva.84.023624

Cited by 16 publications

(23 citation statements)

References 32 publications

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“…Diffraction effects are responsible for a finite correlation length of the speckle potentials. Interestingly, properties of such a disorder can be easily engineered that allows, e.g., for preparation of a matter-wave analog of an optical random laser [40].…”

Section: A Deformation Of a Dark Soliton: Expansion In Bogoliubov Modesmentioning

confidence: 99%

Dark soliton in a disorder potential

Mochol

Płodzień²,

Sacha³

2012

Phys. Rev. A

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We consider dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals good agreement even if the strength of the disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of a disorder. The Anderson localized soliton may decay due to quasi-particle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than condensate lifetime in a typical experiment.Comment: 10 pages, 3 figures, version accepted for publication in Phys. Rev.

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Section: A Deformation Of a Dark Soliton: Expansion In Bogoliubov Modesmentioning

confidence: 99%

Dark soliton in a disorder potential

Mochol

Płodzień²,

Sacha³

2012

Phys. Rev. A

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“…The structural disorder strength is σ Δ =0.21. The black continuous line represents the limit behaviour given by (47). energy of the system can be labelled with the quantum numbers (q, s) and take the form…”

Section: Radial Part Of the Schrödinger Equationmentioning

confidence: 99%

“…For strongly correlated disorder, these studies generally show that extended states and ballistic diffusion processes emerge. In the field of cold atoms, the use of correlated disorder to produce spectral shaping of the localisation length in 2D and 3D experiments was considered in [47,48]. More recently, the effects of short-range correlations were considered for a Bose gas confined on a 2D square lattice [49].…”

Section: Introductionmentioning

confidence: 99%

“…The value(46) corresponds to a critical energy q 245.which lies well within the first band and broadly agrees with the observed inflection point where the participation ratio for the Kronig-Penney model(8) starts to decline, see bottom panels offigure 7.Note that, for resonant states of the form(43), the IPR(36) takes the valueWe observe that strong resonances which confine the wavefunction to a single well do not occur for every disorder realisation, therefore (47) represents a lower bound for the average participation ratio. With the values of the parameters considered in numerical simulations, we can expect the parameter(47) to take values P 13 for q ranging from 15.6 to 17.5. This is consistent with the asymptotic value P 0.251 á ñ - of the average participation ratio obtained in numerical simulation at the top of the band.…”

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Localisation and transport in bidimensional random models with separable Hamiltonians

et al. 2019

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We consider two bidimensional random models characterised by the following features: (a) their Hamiltonians are separable in polar coordinates and (b)the random part of the potential depends either on the angular coordinate or on the radial one, but not on both. The disorder correspondingly localises the angular or the radial part of the eigenfunctions. We analyse the analogies and the differences which exist between the selected 2D models and their 1D counterparts. We show how the analogies allow one to use correlated disorder to design a localisation length with pre-defined energy dependence and to produce directional localisation of the wavefunctions in models with angular disorder. We also discuss the importance of finite-size and resonance effects in shaping the eigenfunctions of the model with angular disorder; for the model with disorder associated to the radial variable we show under what conditions the localisation length coincides with the expression valid in the 1D case.

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“…Interestingly, properties of a speckle potential can be easily modified. Especially, one can create a disorder where Anderson localization operates as a band-pass filter that allows for the realization of a matter-wave analog of an optical random laser [46,47].…”

Section: Impact Of Soliton Interactions On Anderson Localizationmentioning

confidence: 99%

Breakdown of Anderson localization of interacting quantum bright solitons in a disorder potential

Płodzień

Sacha

2012

Phys. Rev. A

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The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson localization phenomenon. Perturbation calculus shows that even very weak interactions modify localization properties of the system eigenstates. For stronger interactions (i.e., when the solitons are close to each other), the localization is totally broken. It implies that in order to experimentally observe the Anderson localization effects, a single bright soliton has to be prepared and excitation of soliton trains must be avoided.

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Matter-wave analog of an optical random laser

Cited by 16 publications

References 32 publications

Dark soliton in a disorder potential

Dark soliton in a disorder potential

Localisation and transport in bidimensional random models with separable Hamiltonians

Breakdown of Anderson localization of interacting quantum bright solitons in a disorder potential

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