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An experiment with cold atoms confined in an isotropic three-dimensional harmonic potential confirms the long-predicted non-damping oscillations of the breathing mode.

David Guéry-Odelin, Emmanuel Trizac

Published Jan 1, 2015• 0 citations
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Observation of a Persistent Non-Equilibrium State in an Extremely Isotropic Harmonic Potential

Daniel Lobser

Ludwig Boltzmann made tremendously important contributions to the problem of connecting macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end of the nineteenth century, Boltzmann was confronted with various strong objections to his work. For example, Boltzmann's atomistic explanations presuppose the reality of atoms, a notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique by Loschmidt that Boltzmann's H-theorem, put forth as a microscopic explanation for the Second Law of Thermodynamics, could hardly account for irreversible physics when the individual two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence of special cases of the Boltzmann equation in which time-varying distributions of atoms resist the imperative of equilibration, even in the presence of collisions. Boltzmann discussed such situations in a paper dedicated to responding to Loschmidt's critique [7, 4]. Perhaps Boltzmann's motivation was to enumerate special cases where his famous H value does not relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality. Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is an all-but universal result predicted by the Boltzmann equation.\nSuch improbable systems of atoms have only very recently been realized experimentally. Kinoshita et al. [36] experimentally confirmed that atoms constrained to move in a quasi one-dimensional potential, an atomistic Newtons cradle, exhibit vastly suppressed relaxation. Chevy et al. [15] observed long-lived breathe-mode oscillations in highly elongated but still 3D geometries. Perhaps one of the more interesting cases is the vanishing damping of the monopole breathe-mode oscillation in a spherically symmetric harmonic oscillator [29], where a cloud of atoms experiences undamped temperature oscillations, causing the cloud to expand and contract as if it were breathing. Until now, this phenomenon has been experimentally inaccessible due to the difficulty in generating isotropic harmonic confinement. This thesis discusses a new magnetic trap capable of producing spherical confinement and presents the first experimental realization of this historically significant oddity using a magnetically trapped gas of 87Rb atoms.

•Jan 1, 2015•4 citations

Breathing Mode of an Anharmonically Trapped One-Dimensional Bose Gas

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Journal of Low Temperature Physics•Jan 2, 2019•4 citations

Persistent breather and dynamical symmetry in a unitary Fermi gas

Dali Sun, Jing Min, Xiangchuan Yan +8 more

SO(2,1) dynamical symmetry makes a remarkable prediction that the breathing oscillation of a scale-invariant quantum gas in an isotropic harmonic trap is isentropic and can persist indefinitely. In two dimensions, this symmetry is broken due to quantum anomaly in the strongly interacting range, and consequently the lifetime of the breathing mode becomes finite. The persistent breather in a strongly interacting system has so far not been realized. Here, we experimentally achieve the long-lived breathing mode in a three-dimensional unitary Fermi gas, which is protected by the SO(2,1) symmetry. The nearly perfect SO(2,1) symmetry is realized by loading the ultracold Fermi gas in an isotropic trap and tuning the interatomic interaction to resonance. The breathing mode oscillates at twice the trapping frequency even for large excitation amplitudes. The ratio of damping rate to oscillation frequency is as small as 0.002, providing an interacting persistent breather. The oscillation frequency and damping rate are nearly constant for different atomic densities and temperatures, demonstrating the robustness of the SO(2,1) symmetry in three dimensions. The factors that lead to the residual damping have also been clarified. This work opens the way to study many-body nonequilibrium dynamics related to the dynamical symmetry.

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Phase space resonances in the quantum dynamics of cold atoms

Andrew G. Truscott, W. K. Hensinger, M. E. J. Friese +2 more

•Jan 1, 1999•0 citations

Collective motions of a quantum gas confined in a harmonic trap

Dae-Yup Song

Single-component quantum gas confined in a harmonic potential, but otherwise isolated, is considered. From the invariance of the system of the gas under a displacement-type transformation, it is shown that the center of mass oscillates along a classical trajectory of a harmonic oscillator. It is also shown that this harmonic motion of the center has, in fact, been implied by Kohn's theorem. If there is no interaction between the atoms of the gas, the system in a time-independent isotropic potential of frequency ${\ensuremath{\nu}}_{c}$ is invariant under a squeeze-type unitary transformation, which gives collective radial breathing motion of frequency $2{\ensuremath{\nu}}_{c}$ to the gas. The amplitudes of the oscillating and breathing motions from the exact invariances could be arbitrarily large. For a Fermi system, appearance of $2{\ensuremath{\nu}}_{c}$ mode of the large breathing motion indicates that there is no interaction between the atoms, except for a possible long-range interaction through the inverse-square-type potential.

arXiv:cond-mat/0609251•Physical Review A•Aug 23, 2005•3 citations

Breathing mode of a harmonically trapped two-dimensional Fermi gas

Chao Gao, Zhenhua Yu

Bulletin of the American Physical Society•Jun 5, 2013•0 citations
Ludwig Boltzmann made tremendously important contributions to the problem of connecting macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end of the nineteenth century, Boltzmann was confronted with various strong objections to his work. For example, Boltzmann's atomistic explanations presuppose the reality of atoms, a notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique by Loschmidt that Boltzmann's H-theorem, put forth as a microscopic explanation for the Second Law of Thermodynamics, could hardly account for irreversible physics when the individual two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence of special cases of the Boltzmann equation in which time-varying distributions of atoms resist the imperative of equilibration, even in the presence of collisions. Boltzmann discussed such situations in a paper dedicated to responding to Loschmidt's critique [7, 4]. Perhaps Boltzmann's motivation was to enumerate special cases where his famous H value does not relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality. Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is an all-but universal result predicted by the Boltzmann equation.\nSuch improbable systems of atoms have only very recently been realized experimentally. Kinoshita et al. [36] experimentally confirmed that atoms constrained to move in a quasi one-dimensional potential, an atomistic Newtons cradle, exhibit vastly suppressed relaxation. Chevy et al. [15] observed long-lived breathe-mode oscillations in highly elongated but still 3D geometries. Perhaps one of the more interesting cases is the vanishing damping of the monopole breathe-mode oscillation in a spherically symmetric harmonic oscillator [29], where a cloud of atoms experiences undamped temperature oscillations, causing the cloud to expand and contract as if it were breathing. Until now, this phenomenon has been experimentally inaccessible due to the difficulty in generating isotropic harmonic confinement. This thesis discusses a new magnetic trap capable of producing spherical confinement and presents the first experimental realization of this historically significant oddity using a magnetically trapped gas of 87Rb atoms.
SO(2,1) dynamical symmetry makes a remarkable prediction that the breathing oscillation of a scale-invariant quantum gas in an isotropic harmonic trap is isentropic and can persist indefinitely. In two dimensions, this symmetry is broken due to quantum anomaly in the strongly interacting range, and consequently the lifetime of the breathing mode becomes finite. The persistent breather in a strongly interacting system has so far not been realized. Here, we experimentally achieve the long-lived breathing mode in a three-dimensional unitary Fermi gas, which is protected by the SO(2,1) symmetry. The nearly perfect SO(2,1) symmetry is realized by loading the ultracold Fermi gas in an isotropic trap and tuning the interatomic interaction to resonance. The breathing mode oscillates at twice the trapping frequency even for large excitation amplitudes. The ratio of damping rate to oscillation frequency is as small as 0.002, providing an interacting persistent breather. The oscillation frequency and damping rate are nearly constant for different atomic densities and temperatures, demonstrating the robustness of the SO(2,1) symmetry in three dimensions. The factors that lead to the residual damping have also been clarified. This work opens the way to study many-body nonequilibrium dynamics related to the dynamical symmetry.
Single-component quantum gas confined in a harmonic potential, but otherwise isolated, is considered. From the invariance of the system of the gas under a displacement-type transformation, it is shown that the center of mass oscillates along a classical trajectory of a harmonic oscillator. It is also shown that this harmonic motion of the center has, in fact, been implied by Kohn's theorem. If there is no interaction between the atoms of the gas, the system in a time-independent isotropic potential of frequency ${\ensuremath{\nu}}_{c}$ is invariant under a squeeze-type unitary transformation, which gives collective radial breathing motion of frequency $2{\ensuremath{\nu}}_{c}$ to the gas. The amplitudes of the oscillating and breathing motions from the exact invariances could be arbitrarily large. For a Fermi system, appearance of $2{\ensuremath{\nu}}_{c}$ mode of the large breathing motion indicates that there is no interaction between the atoms, except for a possible long-range interaction through the inverse-square-type potential.