Universal two-body spectra of ultracold harmonically trapped atoms in two and three dimensions

Zinner, N. T.

doi:10.1088/1751-8113/45/20/205302

Cited by 24 publications

(19 citation statements)

References 91 publications

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“…This is very similar to what is seen in other confined systems such as short-range interacting two-body systems in a harmonic trap [56]. The latter show similar jumps as function of the ratio of the interaction and confinement energy scales and have been related to the Zeldovich rearrangement effect seen for particles in strong magnetic fields [57,58].…”

Section: Trimer Energy With Periodic Boundary Conditionssupporting

confidence: 84%

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

Yamashita

Bellotti

Frederico

et al. 2014

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

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The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic of great interest in different fields of physics. In this paper we study weakly bound states of non-relativistic two and three boson systems when passing continuously from a three (3D) to a two-dimensional (2D) regime within a 'squeezed dimension' model. We use periodic boundary conditions to derive a surprisingly simple form of the three-boson Schrödinger equation in momentum space that we solve numerically. Our results show a distinct dimensional crossover as three-boson states will either disappear into the continuum or merge with a 2D counterpart, and also a series of sharp transitions in the ratios of three-body and two-body energies from being purely 2D to purely 3D.

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Section: Trimer Energy With Periodic Boundary Conditionssupporting

confidence: 84%

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

Yamashita

Bellotti

Frederico

et al. 2014

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

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“…Another interesting direction in which the harmonic model can be used is for the study of higher-order terms in the interaction such as those coming from effectiverange corrections to the model of Busch et al [18,43]. Recent experiments have shown a potential need for such corrections in both two- [44] and three-dimensional cold atomic gas systems [45].…”

Section: Discussionmentioning

confidence: 99%

Many-particle systems in one dimension in the harmonic approximation

et al. 2012

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We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic approximation scheme at the level of the Hamiltonian. We investigate the scaling with particle number of the ground state energies for systems consisting of identical bosons or fermions. We then proceed to focus on bosonic systems and make a detailed comparison to known exact results in the absence of the parabolic external trap for three-body systems. We also consider the thermodynamics of the harmonic model which turns out to be similar for bosons and fermions due to the lack of degeneracy in one dimension.

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“…The lack of symmetry between primed and unprimed coordinates in (25) is deceiving. One can either use the definition (22) or the properties of 3 F 2 (· · · ; · ·; ·) to show that R(ν , µ , ν, µ) = R(ν, µ, ν , µ ).…”

Section: Symmetries and The Superselection Rulementioning

confidence: 99%

Symmetries of three harmonically trapped particles in one dimension

Harshman

2012

Phys. Rev. A

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This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible three-parameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in few-particle, few-well systems with ultracold atoms in optical traps.

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Universal two-body spectra of ultracold harmonically trapped atoms in two and three dimensions

Cited by 24 publications

References 91 publications

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

Many-particle systems in one dimension in the harmonic approximation

Symmetries of three harmonically trapped particles in one dimension

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