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arXiv:1402.6685 · Physical Review A

Energy-dependent ℓ -wave confinement-induced resonances

Benjamin Heß, Panagiotis Giannakeas, Peter Schmelcher

Published May 29, 2014• 15 citations
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Abstract

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 (CIRs) which are attributed to different angular momentum states $\ensuremath{\ell}$, and we explicitly show that in alkaline collisions only four universal $\ensuremath{\ell}$-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of $\ensuremath{\ell}$-wave CIRs is studied. In particular we show that all the $\ensuremath{\ell}$-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.

DOI
10.1103/physreva.89.052716

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Physical Review A•Nov 13, 2007•43 citations
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 (CIRs) which are attributed to different angular momentum states \ensuremathℓ\ensuremath{\ell}\ensuremathℓ, and we explicitly show that in alkaline collisions only four universal \ensuremathℓ\ensuremath{\ell}\ensuremathℓ-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of \ensuremathℓ\ensuremath{\ell}\ensuremathℓ-wave CIRs is studied. In particular we show that all the \ensuremathℓ\ensuremath{\ell}\ensuremathℓ-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 KKK-matrix theory, and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.
We perform an analytical investigation in the framework of generalized KKK-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for ddd waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.
We observe d-wave confinement-induced resonances (CIRs) of bosonic scattering in tightly confining harmonic waveguides. It is shown that the d-wave CIR emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave CIR is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave CIRs. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics. PACS numbers: 03.75.Be, 34.10.+x, 34.50.-s
We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\ensuremath{\omega}$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.
We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\ensuremath{\alpha}$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\ensuremath{\beta}$) is localized by a 3D harmonic trap. We show that in such a system if atom $\ensuremath{\alpha}$ is much heavier than $\ensuremath{\beta}$, confinement-induced resonance (CIR) can appear when the 3D sss-wave scattering length as{a}_{s}as​ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either as>0{a}_{s}>0as​>0 or as<0{a}_{s}<0as​<0. This is quite different from the usual CIRs which occur only when as{a}_{s}as​ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough to serve as a tool for the control of effective interatomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of strongly interacting systems with ultracold atoms with weak 3D background interaction (i.e., small as{a}_{s}as​), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.
In this thesis ultracold atom-atom and dipole-dipole collisions in the presence of a transversally harmonic waveguide are studied. A non- perturbative theoretical framework for multichannel collisions within quasi-onedimensional geometries is developed. This treatment is based on K-matrix formalism where we included higher angular momentum states and their direct couplings. Within this framework we investigate atomic collisions with higher partial wave interactions, where the effect of -wave confinementinduced resonances is observed. This provides us with a richer resonance structure, which may attribute new properties to ultracold gases, i.e. manybody systems. Similarly, for dipolar collisions in the presence of a harmonic waveguide we observed sequences of dipolar confinement-induced resonances, which are attributed to different -wave states. Moreover, we unravel the impact of the anisotropy of the dipolar interactions on confinement-induced resonances. In both systems our study provides us with analytically derived resonance conditions going beyond previous studies, since our framework avoids the limitations of pseudopotential theory. The obtained analytical results for both systems are in excellent agreement with the corresponding exact numerical simulations. In dieser Arbeit werden binare Kollisionen ultrakalter unpolarer sowie ultrakalter dipolarer Atome in quasi-eindimensionalen Wellenleitern mit harmonischen Fallenpotential in den transversalen Richtungen studiert. Hierzu wurde ein nicht-perturbativer Formalismus fur die Behandlung von Vielkanal-Kollisionen in quasi-eindimensionalen Fallengeometrien entwickelt. Dieser Zugang basiert auf dem K-Matrix Formalismus, wobei auch hohere Drehimpulseigenzustande und deren direkte Kopplung berucksichtigt werden. Mit Hilfe dieses Formalismus wurden binare Kollisionen zwischen ultrakalten unpolaren Atomen unter Berucksichtigung hoherer Partialwellen studiert. Hierbei wurde das Phanomen der l-Wellen “confinement-induced resonances“ beobachtet, welches zu einer - verglichen mit reinen s- Wellen confinement-induced resonances - reichhaltigeren Resonanzstruktur fuhrt. In analoger Weise wurden fur binare Kollisionen ultrakalter Dipole in harmonischen Wellenleitern eine Reihe von dipolaren confinement-induced resonances gefunden, welche verschiedenen l-Wellen Zustanden zugeordnet werden konnen. Daruber hinaus wurde die Auswirkung der Anisotropie der dipolaren Wechselwirkung auf confinement-induced resonances charakterisiert. Unser theoretischer Zugang zu den beiden obigen Systemen geht weit uber die bisherigen Studien hinaus, da die Restriktionen, die mit der sonst ublichen Pseudopotential-Theorie einhergehen, vermieden werden. Insbesondere erlaubt uns der Zugang, analytisch die Resonanzbedingungen herzuleiten. Die analytischen Resultate fur beide Systeme stehen in exzellenter Ubereinstimmung mit den korrespondierenden exakten numerischen Simulationen.
A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances (CIRs) for ultracold collisions of identical particles, sss-wave CIRs for bosons and ppp-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass (c.m.) and relative motions in the case of distinguishable atoms. The latter includes, in particular, sss- and ppp-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered [J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 (2006)] dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong sss- and ppp-wave scattering.