Dimensional crossover in non-relativistic effective field theory

Beane, Silas R.; Jafry, Murtaza

doi:10.1088/1361-6455/aaf5fb

Cited by 8 publications

(9 citation statements)

References 21 publications

(49 reference statements)

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“…Recently, a similar relation between these two scattering lengths has been established in Ref. [72], by means of non relativistic effective field theory. The connection between the scattering lengths is achieved by imposing periodic boundary conditions along one direction and comparing the effective range expansion with the purely 1D one.…”

mentioning

confidence: 53%

“…The crossover to different dimensions has been investigated in various setups and several relations have been established for the scattering properties in different dimensions, e.g. between the scattering lengths [16][17][18][19][20][21][22]. These relations give rise to confinement induced resonances [16,[23][24][25][26], which provide further means to tune the interparticle interaction in lower dimensional settings.…”

Section: Introductionmentioning

confidence: 99%

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Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

Bougas,

Mistakidis,

Alshalan

et al. 2020

Preprint

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We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two and the one dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wavefunction, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions while for fixed anisotropy quenches towards the non-interacting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher-lying excited states.

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confidence: 53%

Section: Introductionmentioning

confidence: 99%

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

Bougas,

Mistakidis,

Alshalan

et al. 2020

Preprint

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“…In addition, more complex reactions considering the collision of diatomic molecules widens the scope of our investigation. Another perspective is the manipulation of the aspect ratio of the trap, changing the effective dimension in which the reaction takes place in a continuous way from three to two dimensions [97][98][99][100], therefore we hope that in the future not only the interaction can be tuned but also the effective dimension.…”

Section: Discussionmentioning

confidence: 99%

Cold atom-dimer reaction rates with $^4$He, $^{6,7}$Li and $^{23}$Na

Shalchi,

Yamashita,

Frederico

et al. 2020

Preprint

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Atom-dimer exchange and dissociation reaction rates are predicted for different combinations of two 4 He atoms and one of the alkaline species among 6 Li, 7 Li and 23 Na, by using three-body scattering formalism with short-range two-body interactions. Our study was concerned with lowenergy reaction rates in which the s−, p− and d− wave contributions are the relevant ones. The 4 He is chosen as one of the atoms in the binary mixture, in view of previous available investigations and laboratory accessibilities. Focusing on possible experimental cold-atom realizations with twoatomic mixtures, in which information on atom-dimer reaction rates can be extracted, we predict the occurrence of a dip in the elastic reaction rate for colliding energies smaller than 20 mK, when the dimer is the 4 He 23 Na molecule. We are also anticipating a zero in the elastic p−wave contribution for the 4 He + 4 He 7 Li and 4 He + 4 He 23 Na reaction processes. With weakly-bound molecules reacting with atoms at very low colliding energies, we interpret our results on the light of Efimov physics which supports model independence and robustness of our predictions. Specific sensitivities on the effective range were evidenced, highlighted by the particular inversion role of the p− and d−waves in the atom exchange and dissociation processes.

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“…The physical interpretation of the squeezing parameter in this procedure is a problem necessary to be addressed to connect properly to measurements. The same compactifying procedure along one or two directions has been employed to investigate the Smatrix for two-body scattering [10], and again the focus is on scattering under confining conditions. Another structure-related investigation has appeared in the literature, that is the superfluid phase transition temperature in the crossover from three to two dimensions [11].…”

Section: Introductionmentioning

confidence: 99%

Confinement of two-body systems and calculations in d dimensions

Garrido

Jensen

2019

Phys. Rev. Research

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A continuous transition for a system moving in a three-dimensional (3D) space to moving in a lower-dimensional space, 2D or 1D, can be made by means of an external squeezing potential. A squeeze along one direction gives rise to a 3D to 2D transition, whereas a simultaneous squeeze along two directions produces a 3D to 1D transition, without going through an intermediate 2D configuration. In the same way, for a system moving in a 2D space, a squeezing potential along one direction produces a 2D to 1D transition. In this work we investigate the equivalence between this kind of confinement procedure and calculations without an external field, but where the dimension d is taken as a parameter that changes continuously from d = 3 to d = 1. The practical case of an external harmonic oscillator squeezing potential acting on a two-body system is investigated in details. For the three transitions considered, 3D → 2D, 2D → 1D, and 3D → 1D, a universal connection between the harmonic oscillator parameter and the dimension d is found. This relation is well established for infinitely large 3D scattering lengths of the two-body potential for 3D → 2D and 3D → 1D transitions, and for infinitely large 2D scattering length for the 2D → 1D case. For finite scattering lengths size corrections must be applied. The traditional wave functions for external squeezing potentials are shown to be uniquely related with the wave functions for specific non-integer dimension parameters, d.

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Dimensional crossover in non-relativistic effective field theory

Cited by 8 publications

References 21 publications

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

Cold atom-dimer reaction rates with $^4$He, $^{6,7}$Li and $^{23}$Na

Confinement of two-body systems and calculations in d dimensions

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