Coupled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ℓ</mml:mi></mml:math>-wave confinement-induced resonances in cylindrically symmetric waveguides

Giannakeas, P.; Diakonos, F. K.; Schmelcher, Peter

doi:10.1103/physreva.86.042703

Cited by 42 publications

(80 citation statements)

References 52 publications

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“…Recent experimental advances allowed to explore the corresponding physics of CIRs in quasi-one-and quasi-two-dimensional (quasi-1D and quasi-2D) waveguide geometries [11][12][13][14][15] or in mixed dimensional scattering processes [16]. Complementing the experimental studies, substantial theoretical efforts exhibit a kaleidoscope of confinement-induced processes, such as dual [17] and higher partial wave CIRs [18,19], multichannel [20][21][22][23] or anharmonic CIRs [24][25][26] and CIR molecule formation [27] or dipolar CIRs [28][29][30]. Further studies on CIR effects focus on the impact of various confining geometries, such as quasi-2D either harmonic [31,32] or square well [33], and lattice potentials [34][35][36], or collisions in mixed dimensions [37].…”

Section: Introductionmentioning

confidence: 99%

“…The atoms are allowed to perform collisions with higher partial waves where we take into account that the total colliding energy is well above the threshold of the ground state of the transversal confinement. The theoretical conceptualization of the corresponding resonant phenomena is based on a fully analytical and non-perturbative framework of the K-matrix approach [19,28] including appropriate interatomic interactions with e.g. a van der Waals tail.…”

Section: Introductionmentioning

confidence: 99%

“…We remark, that Eq. (5) holds for arbitrary partial waves ℓ and ℓ ′ , under the assumption that either both are even or odd and at all energies within the continuum between the ground-and first excited channel, where the main difference to the K-Matrix derived in [19] is, that the K-Matrix there only holds as long as a ⊥ q 0 ≪ 1. In particular we also note, that in the case of ∆ ℓ ′ = 0, namely the single partial wave approximation, the formula reduces to…”

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confidence: 99%

“…(2) interrelates the wave functions of the asymptotic and the inner region. Consequently, the corresponding K matrices are connected according to the relation 18,19,28,33], where the K 3D -Matrix is a diagonal matrix in the ℓ-wave representation with entries given by the tangent of the phase shifts.…”

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confidence: 99%

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Energy-dependentℓ-wave confinement-induced resonances

2014

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The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIR) which are attributed to different angular momentum states ℓ and we explicitly show that in alkaline collisions only four universal ℓ-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of ℓ-wave CIRs is studied. In particular we show that all the ℓ-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized K-matrix theory and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Energy-dependentℓ-wave confinement-induced resonances

2014

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“…Furthermore, the LFT theory gives a compact description of a variety of physical processes such as dielectronic recombination [12], negative-ion photodetachment in magnetic [13] or electric fields [14][15][16] or under generic external confinement [17], or ultracold atomic and/or * pgiannak@purdue.edu † chgreene@purdue.edu ‡ robichf@purdue.edu dipolar collisions in the presence of external trapping potentials [18][19][20][21]. In molecular applications frame transformation theory has been decisive in describing the rich rovibrational Rydberg spectra of diatomic molecules [22], and the dissociative recombination of H + 3 [23,24].…”

Section: Introductionmentioning

confidence: 99%

Generalized local-frame-transformation theory for excited species in external fields

2016

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A rigorous theoretical framework is developed for a generalized local frame transformation theory (GLFT). The GLFT is applicable to the following systems: to Rydberg atoms or molecules in an electric field, or to negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local frame transformation theory developed initially by Fano and Harmin. This revised GLFT theory yields non-trivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semi-analytical GLFT Stark spectra with ab initio numerical simulations yields errors in the range of a few tens of MHz, an improvement over the original FanoHarmin theory whose errors are 10-100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.

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Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling

2018

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The nonequilibrium ultracold bosonic quantum dynamics in finite optical lattices of unit filling following a linear interaction quench from a superfluid to a Mott insulator state and vice versa is investigated. The resulting dynamical response consists of various inter and intraband tunneling modes. We find that the competition between the quench rate and the interparticle repulsion leads to a resonant dynamical response, at moderate ramp times, being related to avoided crossings in the many-body eigenspectrum with varying interaction strength. Crossing the regime of weak to strong interactions several transport pathways are excited. The higher-band excitation dynamics is shown to obey an exponential decay possessing two distinct time scales with varying ramp time. Studying the crossover from shallow to deep lattices we find that for a diabatic quench the excited band fraction decreases, while approaching the adiabatic limit it exhibits a non-linear behavior for increasing height of the potential barrier. The inverse ramping process from strong to weak interactions leads to a melting of the Mott insulator and possesses negligible higher-band excitations which follow an exponential decay for decreasing quench rate. Finally, independently of the direction that the phase boundary is crossed, we observe a significant enhancement of the excited to higher-band fraction for increasing system size.

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Coupledℓ-wave confinement-induced resonances in cylindrically symmetric waveguides

Cited by 42 publications

References 52 publications

Energy-dependentℓ-wave confinement-induced resonances

Energy-dependentℓ-wave confinement-induced resonances

Generalized local-frame-transformation theory for excited species in external fields

Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling

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