Hydrodynamic collective modes for cold trapped gases

Boettcher, Igor; Floerchinger, Stefan; Wetterich, C.

doi:10.1088/0953-4075/44/23/235301

Cited by 6 publications

(5 citation statements)

References 75 publications

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“…(42) is indeed a solution of the TF hydrodynamic equations with a mode spectrum which is independent of the explicit form of the local energy density ε loc [n]. This conclusion was arrived at earlier using a different approach [30,31]. A similar result was also found for a two-component Fermi gas interacting via an s-wave contact interaction by Amoruso et al [32].…”

Section: A Nodeless Excitationssupporting

confidence: 66%

Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

2014

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The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, twodimensional dipolar Fermi gas are examined within the Thomas-Fermi von Weizsäcker hydrodynamic theory. We focus on repulsive interactions, and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are independent of the interactions in the large particle limit. We argue quite generally that it is the local character of the two-dimensional energy density which is responsible for the insensitivity of surface excitations to the dipolar interaction strength, and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.

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Section: A Nodeless Excitationssupporting

confidence: 66%

Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

2014

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“…To resolve this mode spectrum, one may actually restrict to phenomenological collective mode spectra such as in Refs. [74][75][76]. Complementary approaches to obtain the scattering properties inside a medium from the vacuum T-matrix, however for a true 2D system, have been successfully applied, for instance, to the Fermi polaron problem [77].…”

Section: Discussionmentioning

confidence: 99%

Dimensional crossover of nonrelativistic bosons

2016

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We investigate how confining a transverse spatial dimension influences the few-and many-body properties of non-relativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold atom experiments. Using Functional Renormalization Group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the 3D and 2D s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during the renormalization group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold atom experiments.

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“…These energies match collective superfluid modes of harmonically trapped 2D Bose gases [28] [53]. In fact, spin waves θ are related to the superfluid velocity by means of v s = M (∇θ), i.e., they describe the same physical excitations [29][30][31].…”

mentioning

confidence: 84%

“…[12]. It should be possible to apply the method to other dimensions and polytropic equations of state, just as it is the case for superfluid hydrodynamic modes [28,45,46]. We proposed an LCA prescription which can be further developed by considering these other mode spectra.…”

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confidence: 99%

Quasi-long-range order in trapped two-dimensional Bose gases

Boettcher

Holzmann

2016

Phys. Rev. A

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We study the fate of algebraic decay of correlations in a harmonically trapped two-dimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where power-law correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the one-body density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the Thomas-Fermi radius. We establish that the trap-averaged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems.PACS numbers: 05.70. Jk, 64.60.an, With the achievement of quantum degeneracy in ultracold atom gases a new experimental platform for studying fundamental questions related to phase transitions and critical phenomena has appeared. In particular, correlation functions can be measured through interference and time-of-flight techniques [1][2][3][4][5][6][7]. A crucial aspect of the experiments, however, consists in the absence of translation invariance due to the presence of the external trapping potential. Consequently, correlations between points r and r are not uniquely determined by the value of r − r . This effect should be unimportant for short-range correlations, and, in fact, thermodynamic properties of ultracold gases are often very well-captured by a local density approximation. The situation changes drastically for a system at a critical point, where the correlation length diverges and thus competes with the inhomogeneity of the trapping potential.Whereas the experimental preparation of critical systems typically requires a highly fine-tuned setup, they are rather effortlessly realized in two-dimensional (2D) systems whose low-energy excitations can be mapped onto an XY model. Examples apart from 2D ultracold quantum gases [8][9][10][11][12] are given by thin Helium films [13], layered magnets [14,15], and 2D excitonpolariton condensates [16]. To quantify correlations in these systems we introduce the one-body density matrix ρ(r, r ) = Φ † (r)Φ(r ) , whereΦ † (r) is the creation operator for a particle at point r. For the spatially homogeneous case we then have ρ hom (r, r ) = f (|r − r |) with some function f (r) due to translation and rotation invariance. The Mermin-Wagner-Hohenberg theorem [17,18] forbids long-range order at any finite temperature such that lim r→∞ f (r) = 0. However, in the XY model an ordered low-temperature phase with inf...

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Hydrodynamic collective modes for cold trapped gases

Cited by 6 publications

References 75 publications

Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

Dimensional crossover of nonrelativistic bosons

Quasi-long-range order in trapped two-dimensional Bose gases

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