On a Hyperbolic Solution to the Nonlinear Schrödinger Equation for a Square Well Potential Coupled to a Contact Impurity at the Delocalization Threshold

Méndez-Fragoso, Ricardo; Cabrera‐Trujillo, R.

doi:10.1016/bs.aiq.2015.03.007

Cited by 1 publication

(4 citation statements)

References 22 publications

(29 reference statements)

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“…(13) (solid line) for the case of β = 0, i.e., no contact impurity. The result agrees with our previous findings [10,11]. In the same figure, we show the analytical behavior of g when a contact impurity of strength β = 0.1 √ V 0 is present (blue dashed line).…”

Section: Discussion Of the Resultssupporting

confidence: 92%

“…In this case, g is not a free parameter, but it is related to the number of atoms that fill the potential cage. For the case of an attractive square potential, we have already reported the solutions to the matter wave profile and the scaling law that g must fulfill [10,11]. Now, we are interested in the situation when repulsive contact impurities are present inside the attractive confinement well.…”

Section: Analytic Solutionsmentioning

confidence: 99%

“…As the reader notices, these are the generalization of Eqs. (11) and (12). The above equations provide a set of 2(N + 1) equations that allows us to obtain the parameters m i and ϕ i .…”

Section: Square Well Potential With Two or More Delta Potentialsmentioning

confidence: 99%

“…We have started the study of such quantum matter confined systems by a square well impurity [10,11], such that the details of the relation of the number of particles to the nonlinear coupling constant in the nonlinear Schrödinger equations are left aside.…”

Section: Introductionmentioning

confidence: 99%

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Confinement of an ultra-cold-matter wave packet near the delocalization threshold by a waveguide bend with two or more contact impurities

Méndez-Fragoso

Cabrera‐Trujillo

2021

Eur. Phys. J. D

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The properties of confined quantum systems are of fundamental importance in the understanding of quantum behavior at extreme conditions. One of such quantum systems at extreme conditions is an ultracold quantum matter wave packet confined by a square well potential. The square well potential could be produced by a bend in a waveguide in an atom chip. Of further interest is the presence of contact impurities inside the bend produced by guide defects. In order to study such a system, its properties are well described by the nonlinear Schrödinger equation. In this work, we generalize our previous work (Méndez-Fragoso and Cabrera-Trujillo in Eur J Phys D 69:139, 2015) to study the ground state behavior of a quantum matter wave packet under confinement by a bend modeled by an attractive square well potential of strength V0 and width 2R in the presence of several contact impurities represented by delta potentials with strength β placed inside it at the threshold of delocalization, i.e., at the point where the well has trapped the maximum number of particles. We find that the maximum number of atoms held by the squared well potential only depends on the total strength of the contact impurities and not on their position. This implies that the maximum number of trapped particles is the same for one or more contact impurities as long as the combined strength is the same. For small R √ V0 values of the squared well potential, the number of particles trapped at the delocalization threshold is lower than when no contact impurities are present and decreases more as the contact impurity repulsive strength increases. This induces a threshold on the maximum number of particles trapped by an attractive squared well at 2RV0 = i βi. The matter wave packet profile shows the effect of the contact impurity as a wedge shape at the contact impurity position.

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Section: Discussion Of the Resultssupporting

confidence: 92%

Section: Analytic Solutionsmentioning

confidence: 99%

“…As the reader notices, these are the generalization of Eqs. (11) and (12). The above equations provide a set of 2(N + 1) equations that allows us to obtain the parameters m i and ϕ i .…”

Section: Square Well Potential With Two or More Delta Potentialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations