Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Resonant quantum dynamics of neutral spin-1 particles in a magnetic guide

Johannes Bill, Martin-Isbjörn Trappe, Igor Lesanovsky, Peter Schmelcher

Published May 11, 2006• 8 citations
Publisher

Abstract

We investigate the resonant quantum motion of spin-1 particles in a magnetic guide. A symmetry analysis is undertaken in order to reveal the complex symmetry properties of the system which lead to a twofold degeneracy in the energy-level spectrum. Lifetimes and energies of the resonance states are computed by employing the complex scaling method. By analyzing several hundreds of resonances we are able to make conclusions about the global properties of the resonance spectrum. The effect of an Ioffe field which is applied parallel to the guide is also discussed. We observe a global increase of the lifetimes with increasing Ioffe-field strength. For certain parameter regimes we find the ground-state resonance to exhibit a longer lifetime than the energetically neighbored excited states. The latter could have interesting implications on the time evolution of trapped ultracold atomic ensembles. Applications of our results to calculate the resonance energies andlifetimes of the trapped alkali-metal atoms $^{7}\mathrm{Li}$ and $^{87}\mathrm{Rb}$ are outlined.

DOI
10.1103/physreva.73.053609

Related papers

Spectral properties and lifetimes of neutral spin- 12 fermions in a magnetic guide

Igor Lesanovsky, Peter Schmelcher

We investigate the resonant motion of neutral spin-$\frac{1}{2}$-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schr\"odinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the $^{6}\mathrm{Li}$ atom in the $F=\frac{1}{2}$ hyperfine ground state.

arXiv:physics/0411079•Physical Review A•Dec 7, 2004•11 citations

Spectral properties and lifetimes of neutral fermions and bosons in a magnetic quadrupole trap

Igor Lesanovsky, Peter Schmelcher

We investigate the motion of neutral fermions and bosons in a three-dimensional magnetic quadrupole trap. Inspecting the underlying Hamiltonian a variety of symmetries is revealed which give rise to degeneracies of the resonance energies. Our numerical approach which involves the eigenvalue problem resulting from a Sturmian basis set together with the complex scaling method enables us to calculate several hundred resonance states. The distributions of the energies and decay widths of the resonances are analyzed for both spin-$\frac{1}{2}$ fermions and spin-1 bosons. We also investigate under what conditions quasibound states with long lifetimes can be achieved. An effective scalar Schr\"odinger equation describing such states is derived. The results are applied to the cases of the alkali-metal atoms $^{87}\mathrm{Rb}$ and $^{6}\mathrm{Li}$ trapped in a hyperfine ground state.

Physical Review A•Mar 23, 2005•13 citations

Rydberg atoms in a magnetic guide

Igor Lesanovsky, Jörg Schmiedmayer, Peter Schmelcher

We investigate electronically excited atoms in a magnetic guide. It turns out that the Hamiltonian describing this system possesses a wealth of both unitary as well as antiunitary symmetries that constitute an uncommon extensive symmetry group. One consequence is the twofold degeneracy of any energy level. The spectral properties are investigated for a wide range of field gradients and the spatial distributions of the spin polarization are analyzed. Wavelengths, oscillator strengths, and selection rules are provided for the corresponding electromagnetic transitions. The effects due to an additional homogeneous bias field constituting a Ioffe-Pritchard trap are explored equally.

arXiv:physics/0408040•Physical Review A•Oct 18, 2004•18 citations

Quantum dynamics of ultracold atoms in inhomogeneous magnetic fields : from ground state atoms to Rydberg atoms

Igor Lesanovsky

Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in the presence of external inhomogeneous magnetic fields. We discuss the behavior of ground state atoms inside typical magnetic field configurations. Such atoms can be approximately treated as neutral point-like particles which carry a certain spin. In particular we analyze the resonance spectrum and the density of states of both fermionic and bosonic atoms. We point out the existence of so-called quasi-bound states whose wave functions can be approximately calculated analytically. Moreover, we focus on studying quantum mechanical states of ultracold but electronically highly excited atoms - so-called Rydberg atoms - inside magnetic traps. In a first step we explore their internal dynamics by employing a fixed-nucleus approximation. The latter assumes the atomic nucleus to be fixed in the magnetic field minimum. Within this framework we analyze spectral properties as well as properties of the electronic spin and calculate electromagnetic transitions. Finally we present an adiabatic approach which allows for a thorough description of the coupled center of mass and electronic dynamics. We highlight ways to magnetically trap highly excited atoms and present novel quantum states in which the center of mass and the electronic wave function are equal in size. This finding shows that Rydberg atoms even in inhomogeneous fields with moderate gradients cannot be considered point-like.

•Jan 1, 2006•0 citations

Scattering resonances of ultracold atoms in confined geometries

Shahpoor Saeidian

Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a quadrupole magnetic field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confienment. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit.

•Jan 1, 2008•0 citations

Lifetime of magnetically trapped ultracold atomic deuterium gas

J. M. V. A. Koelman, Henk T. C. Stoof, BOUDEWIJN J. VERHAAR +1 more

We have calculated the magnetic dipolar spin-relaxation rates of magnetically trapped doubly-spin-polarized atomic deuterium gas. The results are expressed in a simple closed formula describing the dipolar-relaxation-limited stability in the Boltzmann ($T\ensuremath{\gg}{T}_{F}$), the degeneracy ($T\ensuremath{\ll}{T}_{F}$), and the crossover ($T\ensuremath{\simeq}{T}_{F}$) regimes. In the degeneracy regime we typically find lifetimes of some hours. We also discuss the dipolar decay of magnetically trapped spin-polarized fermionic alkali-metal atoms.

Physical review. B, Condensed matter•Nov 1, 1988•13 citations
We investigate the resonant quantum motion of spin-1 particles in a magnetic guide. A symmetry analysis is undertaken in order to reveal the complex symmetry properties of the system which lead to a twofold degeneracy in the energy-level spectrum. Lifetimes and energies of the resonance states are computed by employing the complex scaling method. By analyzing several hundreds of resonances we are able to make conclusions about the global properties of the resonance spectrum. The effect of an Ioffe field which is applied parallel to the guide is also discussed. We observe a global increase of the lifetimes with increasing Ioffe-field strength. For certain parameter regimes we find the ground-state resonance to exhibit a longer lifetime than the energetically neighbored excited states. The latter could have interesting implications on the time evolution of trapped ultracold atomic ensembles. Applications of our results to calculate the resonance energies andlifetimes of the trapped alkali-metal atoms 7Li^{7}\mathrm{Li}7Li and 87Rb^{87}\mathrm{Rb}87Rb are outlined.
We investigate the resonant motion of neutral spin-12\frac{1}{2}21​-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schr\"odinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the 6Li^{6}\mathrm{Li}6Li atom in the F=12F=\frac{1}{2}F=21​ hyperfine ground state.
We investigate the motion of neutral fermions and bosons in a three-dimensional magnetic quadrupole trap. Inspecting the underlying Hamiltonian a variety of symmetries is revealed which give rise to degeneracies of the resonance energies. Our numerical approach which involves the eigenvalue problem resulting from a Sturmian basis set together with the complex scaling method enables us to calculate several hundred resonance states. The distributions of the energies and decay widths of the resonances are analyzed for both spin-12\frac{1}{2}21​ fermions and spin-1 bosons. We also investigate under what conditions quasibound states with long lifetimes can be achieved. An effective scalar Schr\"odinger equation describing such states is derived. The results are applied to the cases of the alkali-metal atoms 87Rb^{87}\mathrm{Rb}87Rb and 6Li^{6}\mathrm{Li}6Li trapped in a hyperfine ground state.
We investigate electronically excited atoms in a magnetic guide. It turns out that the Hamiltonian describing this system possesses a wealth of both unitary as well as antiunitary symmetries that constitute an uncommon extensive symmetry group. One consequence is the twofold degeneracy of any energy level. The spectral properties are investigated for a wide range of field gradients and the spatial distributions of the spin polarization are analyzed. Wavelengths, oscillator strengths, and selection rules are provided for the corresponding electromagnetic transitions. The effects due to an additional homogeneous bias field constituting a Ioffe-Pritchard trap are explored equally.
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in the presence of external inhomogeneous magnetic fields. We discuss the behavior of ground state atoms inside typical magnetic field configurations. Such atoms can be approximately treated as neutral point-like particles which carry a certain spin. In particular we analyze the resonance spectrum and the density of states of both fermionic and bosonic atoms. We point out the existence of so-called quasi-bound states whose wave functions can be approximately calculated analytically. Moreover, we focus on studying quantum mechanical states of ultracold but electronically highly excited atoms - so-called Rydberg atoms - inside magnetic traps. In a first step we explore their internal dynamics by employing a fixed-nucleus approximation. The latter assumes the atomic nucleus to be fixed in the magnetic field minimum. Within this framework we analyze spectral properties as well as properties of the electronic spin and calculate electromagnetic transitions. Finally we present an adiabatic approach which allows for a thorough description of the coupled center of mass and electronic dynamics. We highlight ways to magnetically trap highly excited atoms and present novel quantum states in which the center of mass and the electronic wave function are equal in size. This finding shows that Rydberg atoms even in inhomogeneous fields with moderate gradients cannot be considered point-like.
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a quadrupole magnetic field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confienment. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit.
We have calculated the magnetic dipolar spin-relaxation rates of magnetically trapped doubly-spin-polarized atomic deuterium gas. The results are expressed in a simple closed formula describing the dipolar-relaxation-limited stability in the Boltzmann ($T\ensuremath{\gg}{T}_{F}$), the degeneracy ($T\ensuremath{\ll}{T}_{F}$), and the crossover ($T\ensuremath{\simeq}{T}_{F}$) regimes. In the degeneracy regime we typically find lifetimes of some hours. We also discuss the dipolar decay of magnetically trapped spin-polarized fermionic alkali-metal atoms.