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Physical Review A

Quantum interference in the field ionization of Rydberg atoms

Rachel Feynman, Jacob Hollingsworth, Michael Vennettilli, Tamas Budner, Ryan Zmiewski, Donald P. Fahey, Thomas J. Carroll, Michael W. Noel

Published Oct 13, 2015• 19 citations
Publisher

Abstract

We excite ultracold rubidium atoms in a magneto-optical trap to a coherent superposition of the three $|{m}_{j}|$ sublevels of the $37{d}_{5/2}$ Rydberg state. After some delay, during which the relative phases of the superposition components can evolve, we apply an electric field pulse to ionize the Rydberg electron and send it to a detector. The electron traverses many avoided crossings in the Stark levels as it ionizes. The net effect of the transitions at these crossings is to mix the amplitudes of the initial superposition into the same final states at ionization. Similar to a Mach-Zehnder interferometer, the three initial superposition components have multiple paths by which they can arrive at ionization and, since the phases of those paths differ, we observe quantum beats as a function of the delay time between excitation and initiation of the ionization pulse. We present a fully quantum-mechanical calculation of the electron's path to ionization and the resulting interference pattern.

DOI
10.1103/physreva.92.043412

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Physical Review A•Aug 13, 2001•2 citations
We excite ultracold rubidium atoms in a magneto-optical trap to a coherent superposition of the three ∣mj∣|{m}_{j}|∣mj​∣ sublevels of the 37d5/237{d}_{5/2}37d5/2​ Rydberg state. After some delay, during which the relative phases of the superposition components can evolve, we apply an electric field pulse to ionize the Rydberg electron and send it to a detector. The electron traverses many avoided crossings in the Stark levels as it ionizes. The net effect of the transitions at these crossings is to mix the amplitudes of the initial superposition into the same final states at ionization. Similar to a Mach-Zehnder interferometer, the three initial superposition components have multiple paths by which they can arrive at ionization and, since the phases of those paths differ, we observe quantum beats as a function of the delay time between excitation and initiation of the ionization pulse. We present a fully quantum-mechanical calculation of the electron's path to ionization and the resulting interference pattern.
In an experiment performed by our collaborators at Bryn Mawr, we excite rubidium-85 to a coherent superposition of the different |mj| splittings of the 37d5/2 state induced by a small electric field. After waiting for some variable delay time, we apply a time-dependent electric field to ionize the atom and record the ionized current that arrives at the detector. Due to the initial superposition, we observe an interference pattern that depends on the delay time. This thesis describes my continued work with Dr. Carroll to develop a computational model of this experiment. Our initial method of determining the current involved a semi-classical approach that did not accurately describe the phase, so the more recent developments have focused on including the continuum states in our calculation.
Rydberg atoms are traditionally alkali metal atoms with their valence electron excited to a state of very large principle quantum number. They possess exaggerated properties, and are consequently an attractive area of study for physicists. An example of their exaggerated properties is seen in their response to the presence of an applied electric field. In this work, we study the energy distribution of Rydberg atoms when subjected to a dynamic electric field intended to ionize them. We excite 85Rb atoms to a superposition of the 46D5/2 |mj| = 1/2 and |mj| = 3/2 states in the presence of a small initial electric field. After a delay time, the electric field is pulsed in order to ionize the atoms. The current produced by the ejected electrons is measured. Calculations and experimental data are presented which display interference effects between the amplitude from the components of the initial superposition.
The lll-mixing effect and state-transfer induced by an external electric field pulse in ultracold Rydberg gases are observed with cesium atoms excited to nS\mathit{nS}nS states, and measured with a state selective field ionization technique. High-lll states are populated from the initially excited nS\mathit{nS}nS states due to non-adiabatic transitions through avoided crossings that are formed between the nS\mathit{nS}nS state and the ($n\ensuremath{-}4$) manifold. The population of the product state is investigated as a function of the electric field pulse parameters. The coherent property of the transfer is demonstrated using a 2-pulse sequence and the results are consistent with the theoretical calculations. This lll-mixing phenomenon in the electric field may be used to help forming a molecular potential and create Rydberg molecules.
Pulsed dye lasers are used to excite sodium atoms into a coherent superposition of high Rydberg nd(2D32,2D52)\mathrm{nd} (^{2}\mathrm{D}_{\frac{3}{2}},^{2}D_{\frac{5}{2}})nd(2D23​​,2D25​​) states. Analysis of the field ionization behavior of these atoms reveals the time evolution of the superposition state. Rapid application of a weak electric field projects different components of the superposition state onto states having identifiably different field ionization behavior. Analysis of the signal from subsequent field ionization as a function of the time of weak-field application reveals fine-structure quantum beats. These beats result from the time development of the original superposition state. Measurements of the fine-structure quantum beat frequency are presented for the principal quantum numbers n=32,34,35,36,38,and40n=32, 34, 35, 36, 38, \mathrm{and} 40n=32,34,35,36,38,and40.
Rydberg atoms, which have a highly excited outer electron, are easily manipulated by electric fields. Using a magneto-optical trap, we cool Rubidium atoms to a few hundred millionths of a Kelvin above absolute zero and then excite to Rydberg states. Our first project looks at the dipole-dipole interactions of two atoms starting in the 33p state and ending in the 34s and 33s states. The standard technique is to apply an increasing electric field that ionizes the Rydberg electron and sends it to a detector, but unfortunately the signals overlap. A genetic algorithm is used to separate the signals by controlling the ionization pathway. In order to understand how a Rydberg atom ionizes we need to build a model. The current model, which uses a semi-empirical formula, neglects important quantum phase information. In our second project we are building a computational model that includes continuum states along with discrete states. We present progress on a new model which takes into account the differences in normalization for continuum and discrete states.
A microwave analog of the interference Hanle effect has been studied in sodium Rydberg atoms. Spontaneous emission of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ at 70.166 GHz was replaced by an induced transition from a pulsed microwave source. A dependence of population of the 37S1/2{37S}_{1/2}37S1/2​ state on the magnetic field was recorded in various conditions. Good agreement with the theoretical calculations has been found. The widths and shapes of observed resonances were defined by the spectral widths of the pulsed microwave radiation and parameters of laser excitation of the initial 37P3/2{37P}_{3/2}37P3/2​ state. The quantum beats of magnetic sublevels appeared in the signals when the polarization of exciting laser emission was orthogonal to the magnetic field, and the interference occurred in the scheme of transitions similar to the Mach-Zehnder optical interferometer.