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

Yamashita, M. T.; Bellotti, F. F.; Frederico, T.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

doi:10.1088/0953-4075/48/2/025302

Cited by 29 publications

(26 citation statements)

References 65 publications

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“…The route to determining the scattering properties of two particles in a box potential via the T-matrix has also been explored in Ref. [62] and Eqs. (40) and (55) agree with the results therein for L = 2πR.…”

Section: B T-matrixmentioning

confidence: 99%

Dimensional crossover of nonrelativistic bosons

2016

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We investigate how confining a transverse spatial dimension influences the few-and many-body properties of non-relativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold atom experiments. Using Functional Renormalization Group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the 3D and 2D s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during the renormalization group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold atom experiments.

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Section: B T-matrixmentioning

confidence: 99%

Dimensional crossover of nonrelativistic bosons

2016

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“…Another interesting direction for future investigations would be to study how the presence of the Fermi sea would affect the momentum distribution of the three-body systems by calculating the measurable two-and three-body contacts through an extension of the techniques described in [51]. Another interesting point is the understanding of how the signature of the Efimov effect in 3D three-body systems under the influence of a Fermi sea [52] would disappear and connect to the result presented here through a change in dimensionality, similarly to what was done for three-identical bosons in [53,54].…”

Section: Discussion and Outlookmentioning

confidence: 62%

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

et al. 2016

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We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum k F , leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two-and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two-and three-body systems, the correction to the point at which the three-body states cease to exist is small.

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“…Finally, it should be mentioned that the EFT methods used here to obtain the relations among all effective range parameters for the case of toroidal compactification can also be fruitfully applied to the case of compactification achieved via the presence of atomic traps, which effectively confine the particles using harmonic potentials [8]. In addition, the consideration of three-and four-body systems as dimensionality is altered [7,8] is also a straightforward extention of EFT methods, although the analysis is significantly more involved than in the two-body sector.…”

Section: Resultsmentioning

confidence: 99%

“…One consequence of this symmetry is that the bound state in the system has zero energy (as there is no scale). The exact phase shift in the presence of the boundary is then given by [7] cot δ(p) = 2 π ln 2 sin L z p 2 , (4.12)…”

Section: = 4 To D =mentioning

confidence: 99%

“…Recent investigations of the phase diagram of Bose gases as the number of spatial dimensions is continuously varied have made use of relations among the scattering lengths in various dimensions [2][3][4][5][6]. In addition, there has been interest in investigating the three-body system and the Efimov effect as spatial dimensions are varied [7,8]. In cold-atom experiments, confinement of a dimension is typically achieved using trapping potentials.…”

Section: Introductionmentioning

confidence: 99%

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Dimensional crossover in non-relativistic effective field theory

Beane

Jafry

2019

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

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Isotropic scattering in various spatial dimensions is considered for arbitrary finiterange potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire, and from a plane to a wire, are considered by matching S-matrix elements. The problem is greatly simplified by regulating the ultraviolet divergences using dimensional regularization with minimal subtraction. General relations among (all) effective-range parameters in the various dimensions are derived, and the dependence of bound states on changing dimensionality are considered. Generally, it is found that compactification binds the two-body system, even if the uncompactified system is unbound. For instance, compactification from a box to a plane gives rise to a bound state with binding momentum given by ln 1 2 3 + √ 5 in units of the inverse compactification length. This binding momentum is universal in the sense that it does not depend on the two-body interaction in the box. When the two-body system in the box is at unitarity, the Smatrices of the compactified two-body system on the plane and on the wire are given exactly as universal functions of the compactification length.

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

Cited by 29 publications

References 65 publications

Dimensional crossover of nonrelativistic bosons

Dimensional crossover of nonrelativistic bosons

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

Dimensional crossover in non-relativistic effective field theory

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