Precision Measurements of Collective Oscillations in the BEC-BCS Crossover

Altmeyer, A.; Riedl, Stefan; Kohstall, Christoph; Wright, Matthew; Geursen, R.; Bartenstein, M.; Chin, Cheng; Denschlag, Johannes Hecker; Grimm, Rudolf

doi:10.1103/physrevlett.98.040401

Cited by 229 publications

(271 citation statements)

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“…Our observations validate Fixed-Node Monte-Carlo simulations in the entire BEC-BCS crossover [65,66,67], and are in agreement with the Lee-Huang-Yang corrections to mean-eld for low-density bosonic and fermionic super uids. These exact results, obtained 60 years ago [76,77,78], had only been indirectly observed up to now [64,79].…”

Section: Chapter 5: Ground State Of An Attractive Fermi Gas: Phase DImentioning

confidence: 93%

“…This makes the comparison indirect, and tends to hide possibly small di erences between theories. Discriminating between a mean-eld BCS theory of the BEC-BCS crossover and advanced Monte-Carlo calculations [65,66,67] thus required to reach an excellent accuracy in the measurement of collective mode frequencies [64]. Finally, the trap averaging smears sharp features in the equation of state, and the super uid/normal phase transition is almost invisible in [63].…”

Section: Previous Thermodynamic Studiesmentioning

confidence: 99%

“…The rst kind of approaches is based on the determination of an equation of state of the entire trapped gas, through the measurement of the gas energy using the virial theorem [62,63], or the study of collective modes [64]. Since local properties are not probed, the comparison with theoretical results on homogeneous gases is indirect and requires an integration of the latter over the trap.…”

Section: Measuring the Equation Of State Of A Homogeneous Ultracold Gasmentioning

confidence: 99%

“…[62]) and at Duke University (black dots, from [63]). (b) Radial breathing mode frequency ω, normalized to the radial trapping frequency ω r , as a function of interaction strength 1/k F a (from [64]). …”

Section: Equation Of State Of a Trapped Fermi Gas With Resonant Intermentioning

confidence: 99%

“…For example, an equation of state of a trapped Fermi gas with resonant interactions was obtained in [62,63], relating the total energy to the total entropy. In [64] was performed a precision measurement of the frequency of collective modes of a trapped gas in the BEC-BCS crossover. In both cases the comparison with theory requires to integrate theoretical equations of state over the trap.…”

Section: Previous Thermodynamic Studiesmentioning

confidence: 99%

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Thermodynamics of Ultracold Fermi Gases

Nascimbène

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Chevy

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Latin America Optics and Photonics Conference

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Section: Chapter 5: Ground State Of An Attractive Fermi Gas: Phase DImentioning

confidence: 93%

Section: Previous Thermodynamic Studiesmentioning

confidence: 99%

Section: Measuring the Equation Of State Of A Homogeneous Ultracold Gasmentioning

confidence: 99%

Section: Equation Of State Of a Trapped Fermi Gas With Resonant Intermentioning

confidence: 99%

Section: Previous Thermodynamic Studiesmentioning

confidence: 99%

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Thermodynamics of Ultracold Fermi Gases

Nascimbène

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Latin America Optics and Photonics Conference

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Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Abraham

Bönitz

2014

Contrib. Plasma Phys.

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Particles spatially confined in trapping potentials have attracted increasing interest over the recent decade. Of particular importance are systems of charged particles, such as non-neutral plasmas, nanoplasmas, electrons in metal clusters, electrons in quantum-confined semiconductor structures ("artificial atoms"), electrons on the surface of liquid helium, ions in traps or highly charged particles (grains) in dusty plasmas. A second example of recent interest are systems with other kinds of pair interactions, including dipole interaction, which is important for excitons in quantum wells or ultracold Fermi and Bose gases in traps and optical lattices.Trapped systems are fundamentally different from macroscopic systems since they are dominated by strong spatial inhomogeneity and finite size effects (the properties depend on the exact particle number). Furthermore, by changing the strength of the confinement potential, the many-particle state of the system can be externally controlled-from weak coupling (gas-like) to strong coupling (crystal-like). While trapped classical particles are meanwhile well understood and accessible to first-principle computer simulations, their quantum counterparts still pose big challenges, both for experiment and theory. Therefore, collective properties that can be easily measured or computed and allow to diagnose the many-particle state of the system are of prime importance. It has been found that the quantum breathing mode (monopole oscillation) is one of the most important such properties. In recent years a number of theoretical studies has demonstrated that the quantum breathing mode is ideally suited to measure the coupling strength (the degree of nonideality) of a trapped system, its kinetic and interaction energy and other key observables. This give rise to a novel kind of "spectroscopy" of trapped systems.In this review these developments are summarized. The quantum breathing mode is studied for trapped fermions and bosons with Coulomb and dipole interaction, respectively. A systematic description of collective oscillations and especially the breathing mode is provided. Making use of time-dependent perturbation theory, it is shown how the corresponding breathing frequencies are connected to the properties of the initial equilibrium system. This gives rise to the application of the quantum mechanical sum rules. It is demonstrated how an improved version of the conventional sum rule formulas is suitable for an accurate description of the breathing mode in small systems. Finally, the dependence of the breathing mode on the particle number N is analyzed and the limit of large N is studied for one-dimensional and two-dimensional systems.

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Functional Renormalization and Ultracold Quantum Gases

Floerchinger¹

2010

Springer Theses

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Functional renormalization and ultracold quantum gases AbstractThe method of functional renormalization is applied to the theoretical investigation of ultracold quantum gases. Flow equations are derived for a Bose gas with approximately pointlike interaction, for a Fermi gas with two (hyperfine) spin components in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and for a Fermi gas with three components. The solution of the flow equations determine the properties of these systems both in the few-body regime and in thermal equilibrium.For the Bose gas this covers the quantum phase diagram, the condensate and superfluid fraction, the critical temperature, the correlation length, the specific heat or sound propagation. The properties are discussed both for three and two spatial dimensions. The discussion of the Fermi gas in the BCS-BEC crossover concentrates on the effect of particle-hole fluctuations but addresses the complete phase diagram. For the three component fermions, the flow equations in the few-body regime show a limit-cycle scaling and the Efimov tower of three-body bound states. Applied to the case of Lithium they explain recently observed three-body loss features. Extending the calculations by continuity to nonzero density, it is found that a new trion phase separates a BCS and a BEC phase for three component fermions close to a common resonance.More formal is the derivation of a new exact flow equation for scale dependent composite operators. This equation allows for example a better treatment of bound states.iii

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Precision Measurements of Collective Oscillations in the BEC-BCS Crossover

Cited by 229 publications

References 38 publications

Thermodynamics of Ultracold Fermi Gases

Thermodynamics of Ultracold Fermi Gases

Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Functional Renormalization and Ultracold Quantum Gases

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