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

Quantum states of ultracold electronically excited atoms in a magnetic quadrupole trap

Igor Lesanovsky, Peter Schmelcher

Published Nov 17, 2005• 7 citations
Publisher

Abstract

In this work we present an investigation on the quantum dynamics of ultracold electronically excited atoms exposed to an external magnetic quadrupole field. We present a general Hamiltonian which describes the quantum dynamics of an atom in an arbitrary linear magnetic field. This makes our approach applicable to a wide range of atoms and magnetic field configurations. The system is solved by incorporating an adiabatic separation of the electronic and center-of-mass dynamics. We provide the adiabatic energy surfaces and discuss under which conditions trapped center-of-mass states can be achieved. We present energies and wave functions of the corresponding quantum states. By analyzing the properties of the combined center-of-mass and electronic quantum states we demonstrate that the extension of the electronic wave function can exceed that of the center-of-mass motion. Therefore such atoms cannot be considered as being pointlike. A discussion of electromagnetic transitions is also provided.

DOI
10.1103/physreva.72.053410

Related papers

Magnetic Trapping of Ultracold Rydberg Atoms

Igor Lesanovsky, Peter Schmelcher

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.

Physical Review Letters•Jul 26, 2005•33 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

Ultracold Rydberg atoms in a magneto-electric trap

Ulrich Schmidt, Igor Lesanovsky, Peter Schmelcher

We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schrödinger equation is solved by an adiabatic separation focusing on a fixed n -manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusp-like behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 19, 2007•8 citations

Magnetic trapping of ultracold Rydberg atoms in low angular momentum states

Michael Mayle, Igor Lesanovsky, Peter Schmelcher

We theoretically investigate the quantum properties of $nS$, $nP$, and $nD$ Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to pointlike particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schr\"odinger equation. In addition to the electronic properties, the center-of-mass dynamics of trapped Rydberg atoms is studied. In particular, we analyze the influence of a short-time Rydberg excitation, as required by certain quantum-information protocols, on the center-of-mass dynamics of trapped ground-state atoms. A corresponding heating rate is derived and the implications for the purity of the density matrix of an encoded qubit are investigated.

arXiv:0906.0946•Physical Review A•Nov 12, 2009•17 citations

Controlling Ultracold Rydberg Atoms in the Quantum Regime

Bernd Hezel, Igor Lesanovsky, Peter Schmelcher

We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived, and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schrödinger equation of the system within a given n manifold and show that for a sufficiently large Ioffe field strength the 2n;{2}-dimensional system of coupled Schrödinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center of mass and electronic states is undertaken. In particular, we discuss the situation of tight center of mass confinement outlining the procedure to generate a low-dimensional ultracold Rydberg gas.

arXiv:physics/0610194•Physical Review Letters•Nov 29, 2006•24 citations

Electronic structure of atoms in magnetic quadrupole traps

Igor Lesanovsky, Jörg Schmiedmayer, Peter Schmelcher

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin spatial as well as generalized time-reversal symmetries are established and shown to lead to a twofold degeneracy of the electronic states in the presence of the field. Low lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and, in particular, the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.

arXiv:physics/0402109•Physical Review A•May 12, 2004•14 citations
In this work we present an investigation on the quantum dynamics of ultracold electronically excited atoms exposed to an external magnetic quadrupole field. We present a general Hamiltonian which describes the quantum dynamics of an atom in an arbitrary linear magnetic field. This makes our approach applicable to a wide range of atoms and magnetic field configurations. The system is solved by incorporating an adiabatic separation of the electronic and center-of-mass dynamics. We provide the adiabatic energy surfaces and discuss under which conditions trapped center-of-mass states can be achieved. We present energies and wave functions of the corresponding quantum states. By analyzing the properties of the combined center-of-mass and electronic quantum states we demonstrate that the extension of the electronic wave function can exceed that of the center-of-mass motion. Therefore such atoms cannot be considered as being pointlike. A discussion of electromagnetic transitions is also provided.
We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.
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.
We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schrödinger equation is solved by an adiabatic separation focusing on a fixed n -manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusp-like behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.
We theoretically investigate the quantum properties of nSnSnS, nPnPnP, and nDnDnD Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to pointlike particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schr\"odinger equation. In addition to the electronic properties, the center-of-mass dynamics of trapped Rydberg atoms is studied. In particular, we analyze the influence of a short-time Rydberg excitation, as required by certain quantum-information protocols, on the center-of-mass dynamics of trapped ground-state atoms. A corresponding heating rate is derived and the implications for the purity of the density matrix of an encoded qubit are investigated.
We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived, and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schrödinger equation of the system within a given n manifold and show that for a sufficiently large Ioffe field strength the 2n;{2}-dimensional system of coupled Schrödinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center of mass and electronic states is undertaken. In particular, we discuss the situation of tight center of mass confinement outlining the procedure to generate a low-dimensional ultracold Rydberg gas.
We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin spatial as well as generalized time-reversal symmetries are established and shown to lead to a twofold degeneracy of the electronic states in the presence of the field. Low lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and, in particular, the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.