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

arXiv:physics/0610194 · Physical Review Letters

Controlling Ultracold Rydberg Atoms in the Quantum Regime

Bernd Hezel, Igor Lesanovsky, Peter Schmelcher

Published Nov 29, 2006• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.97.223001

Related papers

Ultracold Rydberg atoms in a Ioffe-Pritchard trap

Bernd Hezel, Igor Lesanovsky, Peter Schmelcher

We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold Rydberg gas.

arXiv:0705.1299•Physical Review A•Nov 26, 2007•14 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

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

Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap

Bernd Hezel

Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap — Subject of this thesis is a theoretical investigation of the quantum properties of highly excited atoms in an inhomogeneous magnetic field configuration. It is demonstrated how the large size of the Rydberg atoms alters the coupling to strong magnetic gradients. We find that Rydberg atoms can be tightly trapped in long-lived electronic states. This confinement permits the creation of a one-dimensional Rydberg gas stabilized against auto-ionization by a dipolar repulsion between the atoms, which is generated imposing a homogeneous electric field. This strongly anisotropic interaction is also responsible for a well controllable equilibrium configuration of two Rydberg atoms in the trap whose distance can be changed by tuning the electric field.

•Jan 1, 2010•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

One-Dimensional Rydberg Gas in a Magnetoelectric Trap

Michael Mayle, Bernd Hezel, Igor Lesanovsky +1 more

We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the required linear density of Rydberg atoms.

arXiv:0704.2299•Physical Review Letters•Sep 14, 2007•19 citations
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 discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold Rydberg gas.
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 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.
Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap — Subject of this thesis is a theoretical investigation of the quantum properties of highly excited atoms in an inhomogeneous magnetic field configuration. It is demonstrated how the large size of the Rydberg atoms alters the coupling to strong magnetic gradients. We find that Rydberg atoms can be tightly trapped in long-lived electronic states. This confinement permits the creation of a one-dimensional Rydberg gas stabilized against auto-ionization by a dipolar repulsion between the atoms, which is generated imposing a homogeneous electric field. This strongly anisotropic interaction is also responsible for a well controllable equilibrium configuration of two Rydberg atoms in the trap whose distance can be changed by tuning the electric field.
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 study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the required linear density of Rydberg atoms.