The Classical Limit of the Quantum Kepler Problem

Martín-Ruiz, A.; Bernal, Jorge; Frank, A.; Carbajal-Domínguez, Adrian

doi:10.4236/jmp.2013.46112

Cited by 18 publications

(21 citation statements)

References 16 publications

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“…To deal with numerical challenges discussed in appendix B, for Fig. 3 we have replaced the potential based on the Rydberg electron wave function V gR,n (R), by one based on the corresponding classical probability density (CPD) [33]:…”

Section: Classical Electron Distributionmentioning

confidence: 99%

Tracking Rydberg atoms with Bose-Einstein condensates

Tiwari

Wüster

2019

Phys. Rev. A

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We propose to track position and velocity of mobile Rydberg excited impurity atoms through the elastic interactions of the Rydberg electron with a host condensate. Tracks first occur in the condensate phase, but are then naturally converted to features in the condensate density or momentum distribution. The condensate thus acts analogous to the cloud or bubble chambers in the early days of elementary particle physics. The technique will be useful for exploring Rydberg-Rydberg scattering, rare inelastic processes involving the Rydberg impurities, coherence in Rydberg motion and forces exerted by the condensate on the impurities. Our simulations show that resolvable tracks can be generated within the immersed Rydberg life time and condensate heating is under control. Finally we demonstrate the utility of this Rydberg tracking technique to study ionizing Rydberg collisions or angular momentum changing interactions with the condensate.

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Section: Classical Electron Distributionmentioning

confidence: 99%

Tracking Rydberg atoms with Bose-Einstein condensates

Tiwari

Wüster

2019

Phys. Rev. A

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“…It has been found previously that a Rydberg impurity excited in the BEC causes atomloss and heating, increasing with the number of repeated excitations of a Rydberg impurity [9,30]. In two-dimensions, we have shown in Ref.…”

Section: Local Heating Of the Condensatementioning

confidence: 58%

“…Also the highly oscillatory character that is inherited from the radial part of the Rydberg wavefunction poses numerical challenges. This can be partly alleviated by replacing the Rydberg-electron wavefunction with a classical approximation [30], as discussed in [16]. To this end, we consider a third potential, referred to as "classical approximation of s-wave" (CASW), in which we replace (1) for ion at the origin by…”

Section: Electron-atom Scatteringmentioning

confidence: 99%

Dynamics of atoms within atoms

Tiwari,

Engel,

Wagner

et al. 2021

Preprint

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Recent experiments with Bose-Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross-Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same Rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron-atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics.

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“…In most cases, Equation (1) is very difficult to evaluate analytically. We briefly review an alternative procedure to compute the local averages appearing in Equation (1) [12,13]. Supported by the harmonic analysis criteria, we write the classical and quantum distributions as a Fourier expansion, ( ) (1) and (2) is that the Fourier coefficients have a similar behaviour for n large,…”

Section: General Proceduresmentioning

confidence: 99%

“…Finally calculating the inverse Fourier transform of the asymptotic Fourier coefficients we obtain, at least in a first approximation, the classical probability density. Analytical results for the simplest quantum systems were reported [12,13]. Now we focus on the general problem.…”

Section: General Proceduresmentioning

confidence: 99%

Macroscopic Quantum Behaviour of Periodic Quantum Systems

Martín-Ruiz¹,

Bernal²,

Carbajal-Domínguez³

2014

JMP

Self Cite

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In this paper we introduce a simple procedure for computing the macroscopic quantum behaviour of periodic quantum systems in the high energy regime. The macroscopic quantum coherence is ascribed to a one-particle state, not to a condensate of a many-particle system; and we are referring to a system of high energy but with few degrees of freedom. We show that, in the first order of approximation, the quantum probability distributions converge to its classical counterparts in a clear fashion, and that the interference effects are strongly suppressed. The harmonic oscillator provides a testing ground for these ideas and yields excellent results.

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The Classical Limit of the Quantum Kepler Problem

Cited by 18 publications

References 16 publications

Tracking Rydberg atoms with Bose-Einstein condensates

Tracking Rydberg atoms with Bose-Einstein condensates

Dynamics of atoms within atoms

Macroscopic Quantum Behaviour of Periodic Quantum Systems

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