Symmetry breaking in crossed magnetic and electric fields
C. Neumann, R. Ubert, S. Freund, E. Floethmann, B. Sheehy, K. H. Welge, M. R. Haggerty, J. B. Delos
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4 page REVTeX file including 5 postscript files (using psfig) Accepted for publication in Physical Review Letters. Difference from earlier preprint: we have discovered the cause of the earlier apparent discrepancy between experiment and theory and now achieve excellent agreement
We present the first observations of cylindrical symmetry breaking in highly excited diamagnetic hydrogen with a small crossed electric field, and we give a semiclassical interpretation of this effect. As the small perpendicular electric field is added, the recurrence strengths of closed orbits decrease smoothly to a minimum, and revive again. This phenomenon, caused by interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.
A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori and thereby allows one to characterize the periodic orbits by a set of winding numbers. With this knowledge, we construct the action variables as functions of the frequency ratios and carry out a semiclassical torus quantization. The semiclassical energy levels thus obtained agree well with exact quantum calculations.
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform s…
Multi-electron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode stability analysis is performed. A classification of the various modes, which are dominated either by the magnetic or Coulomb interactions, is provided. A six-dimensional wave-packet dynamical study, based on the MCTDH approach, is accomplished for the two-electron resonances, yielding in particular lifetimes of more than 0.1 $μ$s for strong elect…
Multi-electron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode and stability analysis are performed. A classification of the various modes, which are dominated by the magnetic field or the Coulomb interactions, is provided. Based on the MCTDH approach, we carry out a six-dimensional wave-packet dynamical study for the two-electron resonances, yielding in particular lifetimes of more than 0.1 $μ$s for strong e…
In the combination of crossed electric and magnetic fields and the Coulomb field of the atomic nucleus the spectrum of the Rydberg electron in the vicinity of the Stark saddle-point are investigated at a quantum mechanical level. The results expose a quantum anomaly dissociation: quasibound states near and above the saddle-point ionization limit predicted at the semi-classical level disappear at a quantum mechanical level.
Paramagnetic, dipolar Hund's case-a radicals are considered in the presence of arbitrary, non-collinear combinations of electric and magnetic fields. The field-dependent part of the Hamiltonian is found to be exactly diagonalizable, and described by quantum numbers given by the projection of the molecule's total angular momentum along a space-fixed axis that is determined by both the fields and the electric and magnetic dipole moments of the molecule. In cases of strong fields, this procedure identifies a set of quantum numbers for the molecule in crossed fields. We dub this set a "Hund's case…
Helium atoms have been prepared in the circular $|n=55,\ell=54,m_{\ell}=+54\rangle$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially travelling in pulsed supersonic beams, were photoexcited from the metastable $1s2s\,^3S_1$ level to the outermost, $m_{\ell}=0$ Rydberg-Stark state with $n=55$ in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with $m_{\ell}=+54$ defined with respect to the magnetic fie…
It was earlier reported [PRL 78 199, (1997)] that long-lived excited states of positronium can be formed in crossed electric and magnetic fields at laboratory field strengths. Unlike the lower-lying states that are localized in the magnetically distorted Coulomb well, these long-lived states which can possess a lifetime up to many years are localized in an outer potential well that is formed for certain values of the pseudomomentum and magnetic field. The present work extends the original analysis and studies the dependence of the spectrum as a function of field strength and pseudomomentum ove…
We show the existence of ultra-long-range giant dipole molecules formed by a neutral alkali ground state atom that is bound to the decentered electronic wave function of a giant dipole atom. The adiabatic potential surfaces emerging from the interaction of the ground state atom with the giant dipole electron posses a rich topology depending on the degree of electronic excitation. Binding energies and the vibrational motion in the energetically lowest surfaces are analyzed by means of perturbation theory and exact diagonalization techniques. The resulting molecules are truly giant with internuc…
We present a detailed quantum mechanical treatment of the photodetachment of H$^{-}$ by a short laser pulse in the presence of crossed static electric and magnetic fields. An exact analytic formula is presented for the final state electron wave function (describing an electron in both static electric and magnetic fields and a short laser pulse of arbitrary intensity). In the limit of a weak laser pulse, final state electron wave packet motion is examined and related to the closed classical electron orbits in crossed static fields predicted by Peters and Delos [Phys. Rev. A \textbf{47}, 3020 (1…
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension one. Several bifurcation scenarios are described in detail. They are shown to have as their constituents the generic codimension-one bifurcations, which combine into a rich variety of complicated scenarios. We propose heuristic criteria for a classification of closed orb…
Circular Rydberg states with $n=70$ have been prepared in helium using a modified version of the crossed-fields method. This approach to the preparation of high-$n$ circular Rydberg states overcomes limitations of the standard crossed-fields method which arise at this, and higher, values of $n$. The experiments were performed with atoms traveling in pulsed supersonic beams that were initially laser photoexcited from the metastable 1s2s$\,^3$S$_1$ level to the 1s73s$\,^3$S$_1$ level by resonance-enhanced two-color two-photon excitation in a magnetic field of 16.154 G. These excited atoms were t…
Recurrence relations of perturbation theory for hydrogen ground state are obtained. With their aid polarizabilities in constant perpendicular electric and magnetic fields are computed up to 80th order. The high orders asymptotic is compared with its quasiclassical estimate. For the case of arbitrary mutual orientation of external fields a general sixth order formula is given.
Absolute dielectronic recombination (DR) rates for lithium-like Ni$^{25+}$($1s^2 2s$) ions were measured at high-energy resolution at the Heidelberg heavy-ion storage ring TSR. We studied the center-of-mass energy range 0--130 eV which covers all $Δn$=0 core excitations. The influence of external crossed electric (0--300 V/cm) and magnetic (41.8--80.1 mT) fields was investigated. For the measurement at near-zero electric field resonance energies and strengths are given for Rydberg levels up to n$=$32; also Maxwellian plasma rate coefficients for the $Δn$=0 DR at electron temperatures between 0…
Effects of weak electric fields on resonant energy transfer between NH$_3$ in the X $^1$A$_1$ ground electronic state, and Rydberg He atoms in triplet states with principal quantum numbers $n = 36$-$41$ have been studied in a crossed beam apparatus. For these values of $n$, electric-dipole transitions between the Rydberg states that evolve adiabatically to the $|ns\rangle$ and $|np\rangle$ states in zero electric field can be tuned into resonance with the ground-state inversion transitions in NH$_3$ using electric fields, with energy transfer occurring via Förster resonance. In the experiments…
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 acquires vibrational character and we encounter two- and three-dimensional…
We report the first observation of mechanical momentum transferred to atoms and molecules upon application of crossed electric and magnetic fields. We identify this momentum as the microscopic analogue of the classical Abraham force. Several predictions of additional magneto-electrically induced mechanical momentum are addressed. One of them, proposed to result from the interaction with the quantum vacuum, is experimentally refuted, others are found to be currently below experimental detection.
We report the experimental observation of alignment to orientation conversion in the 7D_3/2 and 9D_3/2 states of Cs in the presence of an external dc electric field, and without the influence of magnetic fields or atomic collisions. Initial alignment of angular momentum states was created by two-step excitation with linearly polarized laser radiation. The appearance of transverse orientation of angular momentum was confirmed by the observation of circularly polarized light. We present experimentally measured signals and compare them with the results of a detailed theoretical model based on the…
In this work we present the eigenspectra of a novel species of Wannier excitons when exposed to crossed electric and magnetic fields. In particular, we compute the eigenenergies of giant-dipole excitons in $\textrm{Cu}_2\textrm{O}$ in crossed fields. In our theoretical approach, we calculate the excitonic spectra within both an approximate as well as a numerically exact approach for arbitrary field configurations. We verify that stable bound excitonic giant-dipole states are only possible in the strong magnetic field limit, as this is the only regime providing sufficiently deep potential wells…
By utilizing strong optical resonant interactions in arrays of atoms with electric dipole transitions, we show how to synthesize collective optical responses that correspond to those formed by arrays of magnetic dipoles and other multipoles. Optically active magnetism with the strength comparable with that of electric dipole transitions is achieved in collective excitation eigenmodes of the array. By controlling the atomic level shifts, an array of spectrally overlapping, crossed electric and magnetic dipoles can be excited, providing a physical realization of a nearly-reflectionless quantum H…
