Trap-induced shape resonances in an ultracold few-body system of an atom and static impurities

Sroczyńska, Marta; Wasak, Tomasz; Jachymski, Krzysztof; Calarco, Tommaso; Idziaszek, Zbigniew

doi:10.1103/physreva.98.012708

Cited by 13 publications

(14 citation statements)

References 42 publications

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“…In this work the authors use a Green's function approach to solve the problem of a singleparticle moving in an arbitrary trapping potential which has regularized delta scatterers superposed. The solution presented here will coincide with the one-dimensional solution of [29] after substitution of the Green's function for the infinite square well.…”

Section: Solution Of the Arbitrary Finite Kp Model 21 Modelmentioning

confidence: 72%

“…Let us also mention that a different approach to the single-particle problem was recently proposed by Sroczyńska et al [29]. In this work the authors use a Green's function approach to solve the problem of a singleparticle moving in an arbitrary trapping potential which has regularized delta scatterers superposed.…”

Section: Solution Of the Arbitrary Finite Kp Model 21 Modelmentioning

confidence: 99%

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Topological states in the Kronig–Penney model with arbitrary scattering potentials

Reshodko

Benseny

Romhányi³

et al. 2019

New J. Phys.

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We use an exact solution to the fundamental finite Kronig-Penney model with arbitrary positions and strengths of scattering sites to show that this iconic model can possess topologically nontrivial properties. By using free parameters of the system as extra dimensions we demonstrate the appearance of topologically protected edge states as well as the emergence of a Hofstadter butterfly-like quasimomentum spectrum, even in the case of small numbers of scattering sites. We investigate the behavior of the system in the weak and strong scattering regimes and observe drastically different shapes of the quasimomentum spectrum.

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Section: Solution Of the Arbitrary Finite Kp Model 21 Modelmentioning

confidence: 72%

Section: Solution Of the Arbitrary Finite Kp Model 21 Modelmentioning

confidence: 99%

Topological states in the Kronig–Penney model with arbitrary scattering potentials

Reshodko

Benseny

Romhányi³

et al. 2019

New J. Phys.

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show abstract

“…Precise information about the structure of states resulting from the interplay of strong interactions and confinement can nevertheless be very beneficial, as it allows to make use of the specific properties of the spectrum to increase the efficiency of state preparation and gate operation. One notable example are the so-called trap-induced resonances [38][39][40] resulting from the anticrossing between the molecular-like bound states and the spatially extended trap states.…”

Section: Introductionmentioning

confidence: 99%

Controlling the dynamics of ultracold polar molecules in optical tweezers

Sroczyńska,

Dawid,

Tomza

et al. 2021

Preprint

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Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the two-body states, with the potential for significant gate speedup employing trapinduced resonances.

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“…They have been proposed for quantum simulations [13][14][15], quantum computations [16][17][18], realization of new mesoscopic quantum states [19,20], probing quantum gases [21][22][23][24] or fundamental studies of low-energy collisions and molecular states [25][26][27][28][29][30][31][32][33][34][35][36]. By tuning the geometric arrangement of the impurities, it is possible to simulate various solid-state and molecular systems [37][38][39][40]. Several experiments have been focused on studying controlled chemical reactions at ultra-low temperatures in such systems [5,[41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…The regularized delta potential models only swave scattering at ultralow energies and depends only on a single parameter: the s-wave scattering length. Its zero-range character allows for analytical solution of the corresponding Schrödinger equation for arbitrary set of delta-like scatterers [40].…”

Section: Introductionmentioning

confidence: 99%

Bound states of an ultracold atom interacting with a set of stationary impurities

Sroczyńska,

Idziaszek

2020

Preprint

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In this manuscript we analyse properties of bound states of an atom interacting with a set of static impurities. We begin with the simplest system of a single atom interacting with two static impurities. We consider two types of atom-impurity interaction: (i) zero-range potential represented by regularized delta, (ii) more realistic polarization potential, representing long-range part of the atom-ion interaction. For the former we obtain analytical results for energies of bound states. For the latter we perform numerical calculations based on the application of finite element method. Then, we move to the case of a single atom interacting with one-dimensional (1D) infinite chain of static ions. Such a setup resembles Kronig-Penney model of a 1D crystalline solid, where energy spectrum exhibits band structure behaviour. For this system, we derive analytical results for the band structure of bound states assuming regularized delta interaction, and perform numerical calculations, considering polarization potential to model atom-impurity interaction. Both approaches agree quite well when separation between impurities is much larger than characteristic range of the interaction potential.

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Trap-induced shape resonances in an ultracold few-body system of an atom and static impurities

Cited by 13 publications

References 42 publications

Topological states in the Kronig–Penney model with arbitrary scattering potentials

Topological states in the Kronig–Penney model with arbitrary scattering potentials

Controlling the dynamics of ultracold polar molecules in optical tweezers

Bound states of an ultracold atom interacting with a set of stationary impurities

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