Quantum chaos in ultracold collisions of gas-phase erbium atoms

Frisch, Albert; Mark, Manfred J.; Aikawa, K.; Ferlaino, Francesca; Bohn, John L.; Makrides, Constantinos; Petrov, A. N.; Kotochigova, Svetlana

doi:10.1038/nature13137

Cited by 231 publications

(338 citation statements)

References 37 publications

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“…to cope with in real physical systems like, e.g., nuclei and molecules [38][39][40][41], so such a procedure is a requisite for their analysis [42,43]. It is applied to the spectra of irregular, fully connected microwave networks simulating quantum graphs with violated T invariance.…”

Section: Arxiv:160906073v1 [Nlincd] 20 Sep 2016mentioning

confidence: 99%

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

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We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels. Introduction.-In the last decades the concept of quantum chaos, that is, the understanding of the features of the classical dynamics in terms of the spectral properties of the corresponding quantum system, like nuclei, atoms, molecules, quantum wires and dots or other complex systems [1][2][3], has been elaborated extensively. It has been established by now that the spectral properties of generic quantum systems with classically regular dynamics agree with those of Poissonian random numbers [4] while they coincide with those of the eigenvalues of random matrices [6] from the Gaussian orthogonal ensemble (GOE) and the Gaussian unitary ensemble (GUE) for classically chaotic systems with and without timereversal (T ) invariance [5], respectively, in accordance with the Bohigas-Giannoni-Schmit (BGS) conjecture [7].A multitude of studies with focus on problems from the field of quantum chaos have been performed by now theoretically and numerically. However, there are nongeneric features in the spectra of real physical systems that are not yet fully understood. Such problems are best tackled experimentally with the help of model systems like microwave billiards [8,9] and microwave graphs [10,11]. In the experiments with microwave billiards the analogy between the scalar Helmholtz equation and the Schrödinger equation of the corresponding quantum billiard is exploited. Microwave graphs [10,11] simulate the spectral properties of quantum graphs [12][13][14], networks of onedimensional wires joined at vertices. They provide an extremely rich system for the experimental and the theoretical study of quantum systems, that exhibit a chaotic dynamics in the classical limit.The idea of quantum graphs was introduced by Linus Pauling to model organic molecules [15] and they are also used to simulate, e.g., quantum wires [16], optical waveguides [17] and mesoscopic quantum systems [18,19]. The validity of the BGS conjecture was proven rigourously for graphs with incommensurable bond lengths in Refs. [20,21]. Accordingly, the fluctuation properties in the spectra of classically chaotic quantum graphs with and without T invariance are expected

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Section: Arxiv:160906073v1 [Nlincd] 20 Sep 2016mentioning

confidence: 99%

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

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“…The systems we consider in this paper can also be probed by mapping out the momentum distributions. Some more recent proposals to probe chaotic dynamics involve both cold atoms, molecules and ions [34][35][36], and just a few months ago atoms with large magnetic dipole moments have shown experimental signs of chaotic behavior in their scattering dynamics [37].…”

Section: Introductionmentioning

confidence: 99%

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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We compute single-particle energy spectra for a one-body hamiltonian consisting of a twodimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

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“…Recently, level repulsion has been experimentally verified in disordered cyanine-dye-based molecular nanoaggregates [43]. In order to study the repulsion parameter β of spectral statistics, we fit the nearest neighbor spacing distribution to the phenomenological Brody distribution [44] which has been used succesfully for similar purposes in many areas related to localization in disordered systems or quantum chaos [45][46][47][48][49]:…”

Section: Results: Localization Spectral Statistics and Optical mentioning

confidence: 99%

Superradiance at the localization-delocalization crossover in tubular chlorosomes

et al. 2016

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We study the effect of disorder on spectral properties of tubular chlorosomes in green sulfur bacteria Cf. aurantiacus. Employing a Frenkel-exciton Hamiltonian with diagonal and off-diagonal disorder consistent with spectral and structural studies, we analyze excitonic localization and spectral statistics of the chlorosomes. A size-dependent localization-delocalization crossover is found to occur as a function of the excitonic energy. The crossover energy region coincides with the more optically active states with maximized superradiance, and is, consequently, more conducive for energy transfer.

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Quantum chaos in ultracold collisions of gas-phase erbium atoms

Cited by 231 publications

References 37 publications

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Superradiance at the localization-delocalization crossover in tubular chlorosomes

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