Localization of Bose–Einstein Condensation by Disorder

Shams, Ali; Dubois, Jonathan; Glyde, H. R.

doi:10.1007/s10909-006-9227-3

Cited by 4 publications

(5 citation statements)

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“…For strong enough potential wells, we see localization of the condensate to islands and loss of superflow along the lattice. The localization of the condensate to islands that we see could be similar to that observed in disordered systems such as helium in porous media [37][38][39][40][41][42] because the localization in porous media is thought to be depletion mediated 41,42 rather than caused by disorder per se. Depletion can localize the condensate whenever there are sharp changes in the density profile and that can happen either in periodic or aperiodic ͑disor-dered͒ systems.…”

Section: Discussionsupporting

confidence: 75%

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Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Shams

Glyde

2009

Phys. Rev. B

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We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate ͑1͒ the impact of the periodic external potential on the spatial distribution of the condensate, and ͑2͒ the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells ͑tight binding͒ and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.

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Section: Discussionsupporting

confidence: 75%

“…The state with BEC localized to islands is often denoted as a Bose glass. In a recent paper, Shams et al 42 have shown through variational Monte Carlo ͑MC͒ simulation at 0 K that depletion-mediated localization is indeed a plausible effect in systems where there are regions of extremely high density.…”

Section: Introductionmentioning

confidence: 99%

Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Shams

Glyde

2009

Phys. Rev. B

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“…Вивчення термодинамiчних властивостей 4 He сьогоднi проводиться не тiльки для рiдкого [19,18,17] чи газоподiбного стану [20], багато робiт присвяченi i твердому стану [25,24,23,22,21]. Активно вивчається термодинамiка плiвок [28,26,27] та сумiшей [30,29], а також поведiнка 4 He в рiзних середовищах [33,32,31].…”

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Internal energy of the many-boson system with three- and four-particle direct correlations taken into account

Vakarchuk¹,

Hryhorchak²

2015

J. Phys. Stud.

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In this paper we calculate kinetic, potential and full energy with three-and four-particle direct correlations taken into account at wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, Journ. Phys. Stud. 3, 3005 (2009)]. In the low temperature limit the obtained expression for the full energy is equal to the wellknown expression for ground state energy in the approximation of "two sums over the wave vector". The results of this work can be applied for the numeric calculation of the heat capacity of liquid 4 He in order to check the theoretical and experimental results quantatively, especially in the λ-transition region. 1 Вступ Розрахунок внутрiшньої енергiї такої багатобозонної системи, як рiдкий 4 He має доволi давню iсторiю. Великою мiрою це пов'язано iз прагненням теоретично описати λ-подiбний хiд кривої теплоємностi в околi точки фазового переходу. Першi кроки були зробленi в напрямi наближеного обчислення енергiї основного стану i енергетичного спектру цiєї системи ще Боголюбовим [1] майже сiмдесят рокiв тому. Пiзнiше вiн разом iз Зубарєвим у роботi [2] знайшли хвильову функцiю основного стану, а також хвильовi функцiї нижнiх збуджених рiвнiв для слабонеiдеального бозе-газу з допомогою методу колективних змiнних. В границi зникаюче малої взаємодiї енергiя основного стану бозе-системи була вперше коректно знайдена в роботi [3]. Розрахунок проводився з використанням псевдотенцiалу.Дослiдження термодинамiчних функцiй основного стану рiдкого 4 He, зокрема внутрiшньої енергiї, в наближеннi вищому, нiж наближення Боголюбова, було проведено в рядi робiт [4,5,6,7]. Завдяки цим роботам було показано, що врахування три-та чотиричастинкових кореляцiй покращує значення для енергiї основного стану.Трохи згодом в роботах [8,9] з допомогою двочасових температурних функцiй Грiна були отриманi вирази для термодинамiчних функцiй рiдкого 4 He в широкотемпературному дiапазонi. В пiдходi колективних змiнних термодинамiчнi функцiї багатобозонної системи в широкотемпературнiй областi були знайденi в роботi [10]. Розрахунок проводився за допомогою уcереднення з матрицею густини взаємодiючих бозе-частинок в наближеннi парних кореляцiй. Узгодження з експериментальними даними отриманих результатiв для кiнетичної, потенцiальної та повної енергiї є досить добрим [11,12,13,14], однак неповним. Це великою мiрою пов'язано з тим, що для матрицi густини було взято лише наближення парних кореляцiї. Для бiльш точних результатiв потрiбно врахувати три-та чотиричастинковi кореляцiї. Як вiдомо [15,16], їх внесок в значення термодинамiчних функцiй може виявитися досить значним. Врахування внескiв три-i чотиричастинкових кореляцiй у внутрiшню енергiю багатобозонної системи i є предметом цiєї роботи. 1 arXiv:1506.03987v1 [cond-mat.quant-gas]

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“…The gapless modes that propagate along a physical boundary, while they are exponentially decaying away from the physical boundary, are gapless boundary modes or edge states. 12 Examples for the occurrence of surface excitations in bounded BECs comprise, for example, superfluid 4 He (helium II) confined in pores, 13 self-bound condensates at the low-density surface of superfluid helium 14 , as well as surface states of a BEC trapped in an external potential 15 , or surface states of other media with a defocusing nonlinearity. 16 They are of fundamental interest since they reveal the role of quantum effects on the excitation character (i.e., effects which are not existing on the classical level) in restricted geometries.…”

Section: Introductionmentioning

confidence: 99%

Exact surface-wave spectrum of a dilute quantum liquid

Pikhitsa

Fischer

2019

Phys. Rev. B

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We consider a dilute gas of bosons with repulsive contact interactions, described on the mean-field level by the Gross-Pitaevskiǐ equation, and bounded by an impenetrable "hard" wall (either rigid or flexible). We solve the Bogoliubov-de Gennes equations for excitations on top of the Bose-Einstein condensate analytically, by using matrix-valued hypergeometric functions. This leads to the exact spectrum of gapless Bogoliubov excitations localized near the boundary. The dispersion relation for the surface excitations represents for small wavenumbers k a ripplon mode with fractional power law dispersion for a flexible wall, and a phonon mode (linear dispersion) for a rigid wall. For both types of excitation we provide, for the first time, the exact dispersion relations of the dilute quantum liquid for all k along the surface, extending to k → ∞. The small wavelength excitations are shown to be bound to the surface with a maximal binding energy ∆ = 1 8 ( √ 17 − 3) 2 mc 2 0.158 mc 2 , which both types of excitation asymptotically approach, where m is mass of bosons and c bulk speed of sound. We demonstrate that this binding energy is close to the experimental value obtained for surface excitations of helium II confined in nanopores, reported in Phys. Rev. B 88, 014521 (2013). arXiv:1812.08002v2 [cond-mat.quant-gas]

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Localization of Bose–Einstein Condensation by Disorder

Cited by 4 publications

References 23 publications

Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Internal energy of the many-boson system with three- and four-particle direct correlations taken into account

Exact surface-wave spectrum of a dilute quantum liquid

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