Spectral functions and localization-landscape theory in speckle potentials

Pierre Pelletier; Dominique Delande; Vincent Josse; Alain Aspect; Svitlana Mayboroda; Douglas N. Arnold; Marcel Filoche

doi:10.1103/PhysRevA.105.023314

Spectral functions and localization-landscape theory in speckle potentials

Pierre Pelletier
, Dominique Delande
, Vincent Josse
, Alain Aspect
, Svitlana Mayboroda
, Douglas N. Arnold
, Marcel Filoche

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.

Original language	English (US)
Article number	023314
Journal	Physical Review A
Volume	105
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.105.023314
State	Published - Feb 2022

Bibliographical note

Funding Information:
This work was supported by grants to several of the authors from the Simons Foundation (Grants No. 601939, A.A.; No. 601937, D.N.A.; No. 601944, M.F.; No. 563916, S.M.) and, in part, by the DMS NSF No. 1839077. V.J. was supported by an “Investissements d'Avenir” grant from LabEx PALM (ANR-10-LABX-0039-PALM). A.A. acknowledges support through the Augustin Fresnel chair of the Institut d'Optique Graduate School, sponsored by Institut d'Optique and supported by Nokia Bell labs. He also acknowledges support from the iXcore-iXlife-IXblue foundation for research.

Publisher Copyright:
© 2022 American Physical Society.

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10.1103/PhysRevA.105.023314

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title = "Spectral functions and localization-landscape theory in speckle potentials",

abstract = "Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.",

author = "Pierre Pelletier and Dominique Delande and Vincent Josse and Alain Aspect and Svitlana Mayboroda and Arnold, \{Douglas N.\} and Marcel Filoche",

note = "Funding Information: This work was supported by grants to several of the authors from the Simons Foundation (Grants No. 601939, A.A.; No. 601937, D.N.A.; No. 601944, M.F.; No. 563916, S.M.) and, in part, by the DMS NSF No. 1839077. V.J. was supported by an “Investissements d'Avenir” grant from LabEx PALM (ANR-10-LABX-0039-PALM). A.A. acknowledges support through the Augustin Fresnel chair of the Institut d'Optique Graduate School, sponsored by Institut d'Optique and supported by Nokia Bell labs. He also acknowledges support from the iXcore-iXlife-IXblue foundation for research. Publisher Copyright: {\textcopyright} 2022 American Physical Society.",

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AU - Arnold, Douglas N.

AU - Filoche, Marcel

N1 - Funding Information: This work was supported by grants to several of the authors from the Simons Foundation (Grants No. 601939, A.A.; No. 601937, D.N.A.; No. 601944, M.F.; No. 563916, S.M.) and, in part, by the DMS NSF No. 1839077. V.J. was supported by an “Investissements d'Avenir” grant from LabEx PALM (ANR-10-LABX-0039-PALM). A.A. acknowledges support through the Augustin Fresnel chair of the Institut d'Optique Graduate School, sponsored by Institut d'Optique and supported by Nokia Bell labs. He also acknowledges support from the iXcore-iXlife-IXblue foundation for research. Publisher Copyright: © 2022 American Physical Society.

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N2 - Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.

AB - Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.

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Spectral functions and localization-landscape theory in speckle potentials

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