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Journal of Physics B Atomic Molecular and Optical Physics

Ultracold Rydberg atoms in a magneto-electric trap

Ulrich Schmidt, Igor Lesanovsky, Peter Schmelcher

Published Feb 19, 2007• 8 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/40/5/015

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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 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.
We investigate the impact of an external magnetic field on ultra-long-range and ultracold Rydberg molecules. The Born–Oppenheimer potential surfaces are analysed and discussed for different values of the magnetic field strength. The magnetic field provides an angular confinement turning a rotational degree of freedom into a vibrational one. We explore the vibrational dynamics and observe a pronounced transition in the level spacing from a linear splitting via an irregular regime to a 2D harmonic oscillator-like behaviour. Scaling arguments for the dependence of the potential energy surfaces on the field strengths are provided. The occurrence of a monotonic lowering of the magnitude of the electric dipole moment with increasing magnetic field strength is shown.
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 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 study electronically excited atoms exposed to a magnetic quadrupole field. In order to describe the electron dynamics, a one-body approach is employed. Due to the inhomogeneity of the field, the spatial and spin degrees of freedom become coupled in a unique way. The underlying unitary and anti-unitary symmetries are discussed in detail leading to remarkable features such as a two-fold degeneracy of any energy level. We analyse the energy level structure throughout a wide range of field gradients. An investigation of the electronic spin properties is performed by studying the spatially dependent spin-polarization which exhibits a rich nodal structure. We compute wavelengths and strengths for electromagnetic transitions and provide the selection rules. A discussion of the so-called ellipsoidal states which exhibit unique properties such as large mean orbital angular momenta and spatial compactness is provided. The property of magnetic field-induced permanent electric dipole moments is analysed in detail. Wherever reasonable, the results obtained for the quadrupole field are compared to the homogeneous field case.
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.