Breathing mode of two-dimensional atomic Fermi gases in harmonic traps

Gao, Chao; Yu, Zhenhua

doi:10.1103/physreva.86.043609

Cited by 49 publications

(59 citation statements)

References 27 publications

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“…Therefore, it can serve as a tool to detect the emergent scale invariance, similar as the anisotropic expansion now serving as a tool to probe the emergent hydrodynamics behavior. It can be used in future studies of dynamics in the quantum critical regime [35][36][37][38][39] and to calibrate scale symmetry anomaly in a two-dimensional quantum gases [40][41][42][43].…”

Section: Fig 1: (A-b)mentioning

confidence: 99%

Observation of the Efimovian expansion in scale-invariant Fermi gases

Deng

Shi

Diao

et al. 2016

Science

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Scale invariance emerges and plays an important role in strongly correlated many-body systems such as critical regimes nearby phase transitions and the unitary Fermi gases. Discrete scaling symmetry also manifests itself in quantum few-body systems such as the Efimov effect. Here we report both theoretical predication and experimental observation of a novel type expansion dynamics for scale invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time t, surprisingly, the expansion of cloud size exhibits a sequence of plateaus. Remarkably, the locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor and the entire expansion dynamics is governed by a log-periodic function. This striking expansion of quantum Fermi gases shares similar scaling laws and same mathematical description as the Efimov effect. Our work demonstrates the first expansion dynamics of a quantum many-body system with the temporal discrete scaling symmetry, which reveals the underlying spatial continuous scaling symmetry of the many-body system.Interaction between dilute ultracold atoms is described by the s-wave scattering length. For a spin-1/2 Fermi gas, when the scattering length diverges at a Feshbach resonance, there is no length scale other than the interparticle spacing in this many-body system, and therefore the system, known as the unitary Fermi gas, becomes scale invariant. The spatial scale invariance leads to universal thermodynamics and transport properties as revealed by many experiments [1][2][3][4][5][6][7][8][9][10][11][12][13]. On the other hand, in a boson system with an infinite scattering length, threebody bound state can form, where an extra length scale of the three-body parameter sets a short-range boundary condition for all three bosons being very close. It turns the continuous scaling symmetry into a discrete scaling symmetry, and gives rise to infinite number of three-body bound states whose energies obey a geometric scaling symmetry. This is well known as the Efimov effect [14,15], which has been observed in quite a few cold atom experiments [16][17][18][19][20][21][22][23][24], and recent experiments have also confirmed the geometric scaling of the energy spectrum [25][26][27][28]. Both the continuous and the discrete scaling symmetry are interesting emergent phenomena in a strongly interacting system. For a harmonic trapped gas, the expansion dynamics offers great insight to the property of the gas. Well known example is the anisotropic expansion that proves hydrodynamics behavior due to the Bose condensation [29,30] or strong interactions of Fermi gas [31]. Other examples are, for instance, slowing down of expansion in a disorder potential provides evidence for localization behaviors [32,33] and expansion in the presence of optical lattice reveals correlation effects [34]. In this work, we ask a question that, considering a scale invariant quantum gas hold by a harmonic trap, when the trap is gradually opened...

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Section: Fig 1: (A-b)mentioning

confidence: 99%

Observation of the Efimovian expansion in scale-invariant Fermi gases

Deng

Shi

Diao

et al. 2016

Science

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“…Thus, by Eq. (16), in this case the mean square of the cloud size R 2 (t) obeys the same formula as Eq. (8) It is worth mentioning that although the above mathematical treatment for the super Efimovian expansion of the unitary Fermi gas in an anisotropic trap is to some degrees similar to that for the Efimovian expansion [15], the difficulty in the experimental implementation could be quite different.…”

Section: Fig 2: (A)mentioning

confidence: 92%

“…Ψ({r i }, t) = (t log t/t * ) −3N/4 e iθ({ri},t) Φ({q i }, τ ), (16) with q i = (u i , v i , w i ) the scaled coordinates, and the phase function…”

Section: Fig 2: (A)mentioning

confidence: 99%

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Dynamic super Efimov effect

Shi

Zhai

et al. 2017

Phys. Rev. A

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Super Efimov effect is a recently proposed three-body effect characterized by a double-exponential scaling, which has not been observed experimentally yet. Here, we present the general dynamic equations determining the cloud size of a scale invariant quantum gas in a time dependent harmonic trap. We show that a double-log periodicity as the hallmark of the super Efimov effect emerges when the trap frequency is decreased with a specially designed time-dependence. We also demonstrate that this dynamic super Efimov effect can be realized with realistic choices of parameters in current experiments.In 1970, V. Efimov proposed a remarkable phenomenon which is now known as "the Efimov effect" [1]. He showed that, for three identical bosons in the three dimensions, when the pairwise interaction between the bosons is short-ranged and in the vicinity of an swave scattering resonance, there are an infinite number of three-body bound states, whose binding energies E n obey a discrete geometric scaling withwheres 0 1.006 is a universal constant [1, 2]. The Efimov effect attracts great interests both from the nuclear physics and the cold atom physics communities. In 2005, the first evidence of the Efimov effect was observed in a ultracold Cs gas [3], and later on more details of the effect were revealed in a series of experiments [4][5][6]. Recently, the Efimov effect has also been detected in the nuclear physics systems [7]. What lies at the heart of the Efimov effect is the geometric scaling behavior. However, ifs 0 is small, the exponential dependence makes the geometric scaling difficult to observe, since the next bound state would be very shallow in energy and very large in size. Fortunately, thes 0 parameter can be tuned by the atomic mass ratio in an unequal mass atomic mixture, and it becomes larger for larger mass ratio. Therefore, recently the geometric scaling has been observed in the Li and Cs mixture [8,9]. In 2013, a profound new theoretical development is put forward by Nishida, Moroz and Son [10]. They showed that, for three identical fermions confined in two dimensions, when the pairwise interaction is at the vicinity of a p-wave resonance, the fermions can also form an infinite number of three-body bound states [10], called super Efimov states, since the binding energies follow a fascinating double exponential scaling where the hyper-radius ρ quantifies the linear size of the super Efimov bound states, and ρ * is another parameter. From the effective potential Eq. (3), it becomes clear that the double exponential scaling of the binding energies corresponds to a double-log periodicity of the bound state wave-functions in space [13,14]. In a recent separate development, a dynamic Efimov effect for a scale invariant many-body quantum gas has been proposed [15], in which we considered the situation that the trap frequency ω(t) decreases as 1/( √ λt) with time t. We have shown that the expanding cloud size as a function of time bears the same geometric scaling behavior as the three-body Efimov effect. This aliken...

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“…However, the true inter-atomic interactions break the scaling invariance, and this leads to the frequency shift of breathing modes. In two-component Fermi gas with s-wave interactions, one finds that this shift is related to the contact of the system [38,39], and in particular, at unitarity, the scaling invariance is regained [40]. However, quite differently for a single component Fermi gas with p-wave interaction in two dimensions, the scaling invariance is also broken even at resonance when a → ∞ due to the existence of the contact C R .…”

Section: Breathing Mode and Contactsmentioning

confidence: 95%

Strongly interacting p -wave Fermi gas in two dimensions: Universal relations and breathing mode

Zhang

2017

Phys. Rev. A

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The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact has been extended to higher partial waves, in particular, the p-wave contacts have been experimentally probed in recent experiment. So far discussions on p-wave contacts have been limited to three-dimensions. In this paper, we generalize the p-wave contacts to two-dimensions and derive a series of universal relations, including the adiabatic relations, high momentum distribution, virial theorem and pressure relation. At high temperature and low density limit, we calculated the pwave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing mode frequency and the p-wave contacts are given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three and two dimensional Fermi gas and discuss possible experimental realization of two dimensional Fermi gas with p-wave interactions.

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Breathing mode of two-dimensional atomic Fermi gases in harmonic traps

Cited by 49 publications

References 27 publications

Observation of the Efimovian expansion in scale-invariant Fermi gases

Observation of the Efimovian expansion in scale-invariant Fermi gases

Dynamic super Efimov effect

Strongly interacting p -wave Fermi gas in two dimensions: Universal relations and breathing mode

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