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Physical Review A

Microwave Hanle effect in Rydberg atoms

I. I. Ryabtsev, Denis B. Tretyakov

Published Aug 13, 2001• 2 citations
Publisher

Abstract

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 ${37S}_{1/2}$ 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 ${37P}_{3/2}$ 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.

DOI
10.1103/physreva.64.033413

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A microwave analog of the interference Hanle effect has been studied in sodium Rydberg atoms. Spontaneous emission of the microwave transition 37P3/2\ensuremath→37S1/2{37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}37P3/2​\ensuremath→37S1/2​ 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.
Microwave Hanle effect has been studied in sodium Rydberg atoms for the first time. Spontaneous emission of the microwave transition 37P3/2 yields 37S1/2 at 70.166 GHz was replaced by an induced transition from a pulsed microwave source. 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 state. The interference occurred in the scheme of transitions similar to the Mach- Zehnder optical interferometer.
A method for quantum interferometry and phase control of degenerate Rydberg states has been proposed and realized experimentally. Phase control was carried out by a pulse of a weak dc electric field which caused a Stark splitting of degenerate Rydberg sublevels for a short time. A strong interference dependence of the probability of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ in sodium Rydberg atoms on a phase difference between the Stark sublevels of the 37P3/2{37P}_{3/2}37P3/2​ state has been detected. Changes in the probability were measured directly by a pulsed resonant microwave radiation applied after the electric-field pulse. Records of the quantum interference signals and Stark spectra of the microwave transition are presented and discussed. An influence of the laboratory magnetic field has been analyzed.
Experimental results of studying the spectrum of the microwave 37 P -37 S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.
New results are presented of an experimental investigation of the spectrum of 36 P → 37 P two-photon microwave transition in Rydberg atoms of sodium in a constant electric field. Depending on the conditions of excitation of the initial 36 P state (the constant electric field is switched on either before or after the exciting laser pulse) and polarization of laser radiation, a strong variation is observed of the amplitudes of individual two-photon transitions between the fine-structure Stark components of the 36 P and 37 P states. This effect is an analog of the Paschen-Back effect in a strong magnetic field and is due to the break of L-S coupling and to the variation of the wave functions of Rydberg electrons in an electric field. It is also found that the break of L-S coupling affects considerably the shape of double Stark resonance arising upon intersection of the virtual intermediate level of two-photon transition with the real intermediate 37 S level.
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.
Electric field measurement techniques based on Rydberg atoms have proven to have unique advantages in high sensitivity and have drawn wide attention in microwave electric field metrology and communication. The Rydberg states employed for microwave sensing are usually excited by two- or three-step laser irradiation. It leads to the Rydberg atoms being populated by some specific magnetic quantum number states determined by the laser polarization configurations, whose further coupling to another Rydberg state is also constrained by the microwave polarization. Based on a three-laser optical excitation, we demonstrate this effect on the microwave spectra of the 85Rb transitions 41F7/2 → 42D5/2 and 41F7/2 → 41G7/2 at various combining polarization configurations. It shows a strong polarization dependence on the microwave spectrum and then affects the sensitivity of Rydberg atom-based microwave field sensing. Advisable polarization schemes for higher sensitivity are suggested by the two types of transitions.