Collective oscillations of a trapped quantum gas in low dimensions

Rosi, Giulia De; Stringari, S.

doi:10.1103/physreva.92.053617

Cited by 29 publications

(40 citation statements)

References 70 publications

(122 reference statements)

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“…( ) c m 2 3 is the sound velocity for a pancake-shaped Bose gas [48]. For our coldest samples the measured damping rate for the superfluid phase is close to the damping predicted by equation (2).…”

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confidence: 79%

Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics

et al. 2016

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We report direct evidence of superfluidity in a quasi two-dimensional Bose gas by observing its dynamical response to a collective excitation, the scissors mode. Relying on a novel local average analysis, we are able to probe inhomogeneous clouds and reveal their local dynamics. We identify in this way the superfluid and thermal phases inside the gas and locate the boundary at which the Berezinskii-Kosterlitz-Thouless crossover occurs. This new analysis also allows to evidence the coupling of the two fluids which induces at finite temperatures damping rates larger than the usual Landau damping.

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confidence: 79%

Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics

et al. 2016

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“…All of the large N clouds have high peak densities and thus approach the strongly interacting regime in the 3D limit where behavior similar to a unitary gas can be expected. The largest cloud for z /a 3D ≈ +0.5 shows a possible deviation towards the bosonic molecule result ω B /ω r = 10/3 [39].…”

Section: Arxiv:180405102v1 [Cond-matquant-gas] 13 Apr 2018mentioning

confidence: 81%

“…Equations of state of this form permit simple solutions to the hydrodynamic equations, valid for both superfluids and normal phase gases in the collisional regime. For the 2D breathing mode one obtains ω B = √ 2q ω r [38,39]. Of relevance here are the strict 2D limit, where ω z µ and q → 2 (ignoring the small anomalous upshift), and the oblate 3D limit, where µ ω z ω B .…”

Section: Arxiv:180405102v1 [Cond-matquant-gas] 13 Apr 2018mentioning

confidence: 95%

“…In this limit, one can use the LDA, µ(x, y, z) = µ(x, y, 0) − V (z), to integrate over z and recover an effective 2D equation of state for the collective oscillation. For a Fermi gas in the unitarity limit (a 3D → ∞) one obtains q = 3/2 and ω B = √ 3 ω r [39,41]. Thus, the crossover from a thermodynamically 2D to 3D Fermi gas with resonant interactions should be marked by a change in ω B /ω r from ∼ 2 to √ 3 [40].…”

Section: Arxiv:180405102v1 [Cond-matquant-gas] 13 Apr 2018mentioning

confidence: 99%

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Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases

et al. 2018

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We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole or breathing mode as a function of dimensionality in Fermi gases with tunable interactions. The frequency of this mode is set by the adiabatic compressibility and probes the thermodynamic equation of state. In 2D, a dynamical scaling symmetry for atoms interacting via a δ-potential predicts the breathing mode to occur at exactly twice the harmonic confinement frequency. However, a renormalized quantum treatment introduces a new length scale which breaks this classical scale invariance resulting in a so-called quantum anomaly. Our measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths indicating the breakdown of a δ-potential model for atomic interactions. As the dimensionality is tuned from 2D to 3D we see the breathing oscillation frequency evolve smoothly towards the 3D limit.Two-dimensional (2D) materials exhibit many novel physical properties [1-4], but strong correlations and imperfections mean these are often difficult to understand theoretically. Quantum gases of neutral atoms may help address such fundamental challenges [5,6], as well as new phenomena, not readily accessible in other systems. One scenario, generally encountered in quantum field theories, is anomalous symmetry breaking. Specifically, a quantum anomaly occurs when a symmetry, present in a classical theory, is broken in the corresponding (renormalized) quantum theory. A paradigmatic example relevant to atomic collisions in ultracold alkali gases is the 2D δ-potential [7,8], where an additional length scale associated with the interactions is required to remove divergences in the elementary theory.Anomalous symmetry breaking has been considered in the context of 2D harmonically confined Bose [9] and Fermi gases [10][11][12] where interactions can be enhanced near a Feshbach resonance. In both cases, the anomaly leads to an increase in the frequency of the radial monopole mode, or breathing oscillation, above the value set by the scaling symmetry of the classical theory [13]. Previous experiments have studied the radial breathing mode in 2D Bose [14,15] and Fermi gases [16], although the anomalous upshift has not yet been observed. More broadly, the breathing mode is a sensitive probe of the adiabatic compressibility and hence the thermodynamic equation of state [17,18] of the gas being studied.In this Letter, we present measurements of the radial breathing mode frequency ω B for highly oblate Fermi gases as a function of the interaction strength and dimensionality. The dimensionality of a harmonically trapped gas can be tuned by varying the chemical potential µ relative to the confinement energies ω i , (i = x, y, z) in each dimension. When ω z µ, k B T ω x,y , where k B is Boltzmann's constant and T is the temperature, motion in the transverse (z) dimension can be frozen...

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“…3 ω R (≈ 1.73 ω R ) for a 3D Fermi gas confined to a "pancake" trap in the unitary limit [40]. Explicit breaking of scale invariance by the presence of the third dimension has been studied before both experimentally [41] and theoretically [41,42].…”

Section: Bcs Becmentioning

confidence: 99%

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

et al. 2018

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The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.Symmetries are an indispensable ingredient to any attempt of formulating a fundamental theory of nature. Yet, it is not allways true that one can make accurate predictions about the behaviour of some complex system based on the symmetries of its Hamiltonian alone. The fundamental reason behind this is the concept of symmetry breaking [1]. Symmetry violations often have drastic effects on the state of the system, for example when some metal breaks rotational invariance and becomes ferromagnetic. There are three different mechanisms through which a given system may violate some of the symmetries of its Hamiltonian: explicit, spontaneous and anomalous symmetry breaking [2].Quantum anomalies are violations of an exact symmetry of a classical action in the corresponding quantized theory [3]. They may occur when a cut-off has to be introduced to regularize divergent terms. This regulator may explicitly break some symmetry of the theory. If this symmetry is not restored even after the cut-off is removed at the end of the renormalization procedure, the symmetry is broken anomalously.Quantum anomalies are ubiquitous in quantum field theories and provide, important constraints on physical gauge theories like the standard model [4, 5] or on string theories [6, 7]. Whereas the formalisms of explicit and spontaneous symmetry breaking are frequently applied across many fields in physics [8][9][10], anomalous symmetry breaking is typically associated only with high energy physics. One exception was found in molecular physics [11,12] and here we report an observation of a quantum anomaly in the field of cold atom physics.A particular class of anomalies, called conformal anomalies, break the scale invariance of a theory, that is invariance of the Hamiltonian under r → λr. The most prominent examples are found in field theories like QED or QCD where the renormalized coupling constants depend on the energy scale and thus break scale invariance explicitly. In ordinary quantum mechanics the 1/r 2 -and the δ 2 -potential in 2D are well-known examples of conformal anomalies [13,14].Notably, the δ 2 -potential is used to model contact in-teractions in cold atom gases in two-dimensions as V int ∝ g 0 δ 2 (r i − r j ). Including the kinetic...

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Collective oscillations of a trapped quantum gas in low dimensions

Cited by 29 publications

References 70 publications

Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics

Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics

Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

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