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Physical Review A

Transition from Rydberg to giant-dipole-moment states of hydrogen atoms in crossed fields: A suggestion for an experiment

Vitali Averbukh, Nimrod Moiseyev, Peter Schmelcher, Lorenz S. Cederbaum

Published May 1, 1999• 14 citations
Publisher

Abstract

The pseudoseparation of the center of mass and relative motion of a hydrogen atom in crossed electric and magnetic fields led to a theoretical prediction of highly extended states localized in the outer potential well. These states correspond to an almost macroscopic separation between a proton and an electron, and give rise to giant dipole moments. In the present work we describe a simple, experimentally feasible, scheme for the preparation of a hydrogen atom in a superposition of such states. The preparation scheme is based on a two-step switching on of an external electric field, in the course of which the relative motion is trapped in the outer well. On the basis of classical simulations we suggest the experimental parameters at which trapping is achieved extremely efficiently.

DOI
10.1103/physreva.59.3695

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Abstract Supersonic beams of hydrogen atoms, prepared selectively in Rydberg–Stark states of principal quantum number n in the range between 25 and 35, have been deflected by 90 ◦ , decelerated and loaded into off-axis electric traps at initial densities of ≈ 10 6 atoms cm −3 and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as n − 4 and corresponding closely to the natural lifetimes of the initially prepared Rydberg–Stark states. The decay rate was found to continually decrease over time and to reach an almost n -independent rate of more than (1 ms) −1 after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared Rydberg–Stark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg–Stark states of higher ∣ m ∣ values. While searching for such a mechanism, we discovered that resonant dipole–dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher ∣ m ∣ values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole–dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative processes that the observed decay of the population of Rydberg atoms in the trap could be satisfactorily reproduced for all n values studied experimentally.

arXiv:1704.03278•Journal of Physics B Atomic Molecular and Optical Physics•Apr 22, 2016•27 citations
The pseudoseparation of the center of mass and relative motion of a hydrogen atom in crossed electric and magnetic fields led to a theoretical prediction of highly extended states localized in the outer potential well. These states correspond to an almost macroscopic separation between a proton and an electron, and give rise to giant dipole moments. In the present work we describe a simple, experimentally feasible, scheme for the preparation of a hydrogen atom in a superposition of such states. The preparation scheme is based on a two-step switching on of an external electric field, in the course of which the relative motion is trapped in the outer well. On the basis of classical simulations we suggest the experimental parameters at which trapping is achieved extremely efficiently.
We have simulated the motion of a Rydberg hydrogen atom in electric and magnetic fields that have a strong position dependence. The orientation and strengths of the fields depend strongly on the spatial position of the atom. The angle between the fields could take on any value. We use the quantum energy levels for a Rydberg state in electric and magnetic fields to derive a spatially dependent potential energy for the centre-of-mass motion of the atom. We compute the radiative decay rate into states with low principal quantum numbers. After the decay, the atom could be trapped using the magnetic moment of the electron. We present results for a specific trap geometry which could be experimentally realized.
This paper reports on the evidence for large permanent electric-dipole moments of Rydberg atoms in crossed electric and magnetic fields. It was found that the dipole moments have a large value if the scaled electric-field strength \ensuremath{\epsilon}=${\mathit{EB}}^{\mathrm{\ensuremath{-}}4/3}$ has the value \ensuremath{\epsilon}\ensuremath{\approxeq}0.75 (with electric- and magnetic-field strengths E and B in atomic units). The experimental technique employed to determine the atomic dipole moment was to add a slight inhomogeneity to the electric field and to measure the deflection of the atoms, this deflection being proportional to the field inhomogeneity and the atomic dipole moment. In order to discuss the experimental results, different theoretical approaches to the E\ifmmode\times\else\texttimes\fi{}B problem are reviewed. The occurrence of Rydberg atoms with large dipole moments can be explained as being caused by a distinct type of classical orbit.
The passage of cold cesium 49S Rydberg atoms through an electric-field-induced multi-level avoided crossing with nearby hydrogen-like Rydberg levels is employed to prepare a cold, dipolar Rydberg atom gas. When the electric field is ramped through the avoided crossing on time scales on the order of 100 ns or slower, the 49S population adiabatically transitions into high- l Rydberg Stark states. The adiabatic state transformation results in a cold gas of Rydberg atoms with large electric dipole moments. After a waiting time of about 1 μ s and at sufficient atom density, the adiabatically transformed highly dipolar atoms become undetectable, enabling us to discern adiabatic from diabatic passage behavior through the avoided crossing. We attribute the state-selectivity to m -mixing collisions between the dipolar atoms. The data interpretation is supported by numerical simulations of the passage dynamics and of binary m -mixing collisions.
High angular momentum Rydberg states of atoms in strong magnetic fields or in strong magnetic and weak crossed electric fields correspond to classical regular drift trajectories around the positive ion core. The motion can be adiabatically separated in a fast cyclotron motion, an oscillation in magnetic field direction, and a slow drift motion. Some of the drift trajectories display huge electric-dipole moments induced by the weak electric field. Corresponding atomic drift states with large electric dipole moments are theoretically predicted. In the experiment drift states are excited by an optical one-photon transition. The excitation of drift-state atoms is very efficient in the vicinity of anti-crossings between Rydberg states with large photoexcitation cross section and drift states. The drift-state atoms are separated from other Rydberg atoms via electric-dipole deflection in an inhomogeneous electric field. The size of the observed dipole moments agrees quite well with theoretical values.
Abstract Supersonic beams of hydrogen atoms, prepared selectively in Rydberg–Stark states of principal quantum number n in the range between 25 and 35, have been deflected by 90 ◦ , decelerated and loaded into off-axis electric traps at initial densities of ≈ 10 6 atoms cm −3 and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as n − 4 and corresponding closely to the natural lifetimes of the initially prepared Rydberg–Stark states. The decay rate was found to continually decrease over time and to reach an almost n -independent rate of more than (1 ms) −1 after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared Rydberg–Stark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg–Stark states of higher ∣ m ∣ values. While searching for such a mechanism, we discovered that resonant dipole–dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher ∣ m ∣ values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole–dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative processes that the observed decay of the population of Rydberg atoms in the trap could be satisfactorily reproduced for all n values studied experimentally.