Analytical solutions for the dynamics of two trapped interacting ultracold atoms

Idziaszek, Zbigniew; Calarco, Tommaso

doi:10.1103/physreva.74.022712

Cited by 115 publications

(191 citation statements)

References 35 publications

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“…1) fall into two groups: those that are independent of the interaction strength (horizontal lines) and those that depend on . In all instances the energy of the triplet states is independent of , as found also for a single well 17 signifying the left and right wells and , the two spin projections). Such states approximate the highly entangled Bell states 10,18 .…”

supporting

confidence: 70%

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

2015

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"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analoguesimulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynmans' vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational microscopy solutions of the hamiltonian, uncovering the spectral evolution, wave function anatomy, and entanglement properties of the interacting fermions in the entire parameter range, including crossover from a SW to a DW confinement and a controllable energy imbalance between the wells. We demonstrate attractive pairing and formation of repulsive, highly-correlated, ultracold Wigner molecules, well-described in the natural orbital representation. The agreement with the measurements affirms the henceforth gained deep insights into ultracold molecules and opens access to the size-dependent evolution of nano-clustered and condensed-matter phases and ultracold-atoms quantum information.Key words: ultracold atoms, double-well nano-confinement, Wigner molecule, configuration interaction, entanglement, strong correlated matter *Corresponding Author: uzi.landman@physics.gatech.edu arXiv:1508.02308v3 2 Ingress to the origins of complex physical phenomena often requires experiments whereby theories are tested or suggested through artificial manipulations of physical circumstances. During the past decade, a cornucopia of new tools have emerged resulting from the discovery and advancement of methods for the preparation and trapping of ultracold atomic gases, controlled tuning of the interparticle interactions (via magnetic manipulation of the Feshbach resonance), and the creation of synthetic gauge fields through atom-light interactions in optical lattices of varied geometries and topologies 1,2 . The remarkable pristine nature of these systems, and the exquisite level of control that can be exercised over them, brought forth a realization of Richard Feynman's vision 3 for the construction of physical quantum simulators, capable of an exact simulation, of systems or situations that are computationally or analytically intractable. Indeed, in the past several years we witnessed a surge of realizations of such exact simulations addressing diverse fields (see reviews in refs.1 and 2), including in particular the behavior of strongly interacting fermions where computations are precluded because of the "fermion sign problem." 4 . These systems range from high-Tc superconductivity 1,2 , collosal magnetoresistance 5 and quantum Hall effects 2 to atomic frequency resonators 6 , interferometry 7,8 , matter wave gyroscopes 9 and the development of scalable quantum computers with neutral atoms 10,11 .Progress aiming at a "bottom-up" app...

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supporting

confidence: 70%

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

2015

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“….. Equation (46) permits to recover the results deduced by using the zero-range potential approach [18,[21][22][23].…”

Section: Quasi-2d Geometrymentioning

confidence: 98%

“…This issue has been already the subject to many theoretical studies [4,5,[18][19][20][21][22][23] where a zero-range potential approach was used and much more sophisticated multichannel studies have been performed in Refs. [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Ultracold-atom collisions in atomic waveguides: A two-channel analysis

Kristensen

Pricoupenko

2015

Phys. Rev. A

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Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound state properties.

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“…(29), in the case of the BA, we denote the mixed channel state |ψ m,BA η and using Eqs. (29) and (15), one obtains…”

Section: B Integral Equation Of the Three-body Problemmentioning

confidence: 99%

One-dimensional ultracold atomic gases: Impact of the effective range on integrability

Kristensen

Pricoupenko

2016

Phys. Rev. A

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Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions at the contact of three particles. This last feature permits us to solve a contradiction brought by the contact model which can lead to an opposite result concerning the integrability issue. For fermions, the vicinity of integrability is characterized by large deviations with respect to the predictions of the Bethe ansatz.

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Analytical solutions for the dynamics of two trapped interacting ultracold atoms

Cited by 115 publications

References 35 publications

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

Ultracold-atom collisions in atomic waveguides: A two-channel analysis

One-dimensional ultracold atomic gases: Impact of the effective range on integrability

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