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Bulletin of the American Physical Society

Microwave-driven He Rydberg atoms: Floquet-state degeneracy lifted by a second frequency, Stueckelberg oscillations, and their destruction by added noise

Suzanne Yoakum, Leszek Sirko, A. F. E. M. Haffmans, Patrick M. Koch

Published May 1, 1993• 0 citations
OpenAlex

Abstract

We investigate excitation of He 28{sup 3}S atoms and find that a 2nd microwave field lifts the degeneracy of certain Floquet states describing the [atom + single microwave field] system. As a result a microwave pulse produces two patterns of Stueckelberg oscillations. They depend sensitively on the frequencies and amplitudes of both microwave fields and are influenced differently by added by added noise. We present two-frequency (2-f) Floquet maps showing the origin of the intererferences. We are able theoretically to reproduce reasonably well our observed 2-f Stueckelberg oscillations for (stronger) 30 GHz and (much weaker) 36 GHz 2-field. The case of both fields strong is much more complicated. It still remains theoretically to explain why the noise influences the two patterns of Stueckelberg oscillations differently.

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Microwave-driven He Rydberg atoms: Floquet-state degeneracy lifted by a second frequency, Stueckelberg oscillations, and their destruction by added noise

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We present experimental and theoretical results on highly excited Rydberg atoms passing through a waveguide. The waveguide is excited in a coherent mode with a superimposed component of technically generated noise. In the theoretical part of the paper we derive and solve a master equation for a Rydberg atom driven by a monochromatic coherent microwave field in the presence of noise. We show that a Rydberg atom subjected to a mixture of coherent modes and noise fields exhibits four dynamical regimes: (i) diffusive broadening, (ii) localization, (iii) destruction of coherence and localization, and (iv) relaxation to equilibrium. The four regimes are passed one after the other as a function of irradiation time. They occur on different time scales and are thus temporally well separated from each other. The theory is checked by an experiment on the time dependence of the population distribution of highly excited rubidium Rydberg atoms initially prepared in a unique and well-defined Rydberg state and irradiated by a strong microwave field. The localization regime, characterized by a ``freezing'' of the width of the wave packet with respect to the Rydberg levels, has been observed. The addition of a small noise component was shown to lead to delocalization after times inversely proportional to the noise power, as predicted by our theory.

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In this chapter experiments on rubidium Rydberg atoms in external fields are reviewed [1 – 8]. In the first part results on the interaction of microwave radiation with rubidium Rydberg atoms are described. The Rydberg atoms interact with a microwave pulse of a well-defined duration. When applying coherent microwave radiation with a frequency exceeding a certain value, the experimentally observed microwave field strength at which 10% of the atoms are ionized has to be much larger than the value found by classical trajectory calculations. The atoms are stabilized by the dynamical localization. An extremely weak microwave broadband noise which is added to the coherent wave at least partially destroys the localization. This phenomenon depends on the bandwidth of the added noise. In further experiments the dependence of the 10% ionization microwave field strength on the duration τ of the microwave pulse has been investigated. For increasing noise level the 10% ionization field strength ∈ 0.1 develops from a behavior ∈ 0.1 ∼ τ −1/4 to a ∈ 0.1 ∼ τ −1/2 dependence, which is characteristic for a classical diffusion process. The second part of the chapter deals with experiments in strong static crossed electric and magnetic fields. Below as well as above the ionization energy the observed quasi-Landau(QL)-resonances are explained using classical trajectories. The ionization behavior of the QL-resonances is clearly influenced by the spatial structure of the associated classical orbits. In further experiments the dependence of the observed ionization energy on the magnetic field was investigated in the presence of a fixed static electric field.

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Microwave ionization of Rb Rydberg atoms: Frequency dependence

Leszek Sirko, Markus Arndt, P. M. Koch +1 more

We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np${)}^{2}$${\mathit{P}}_{3/2}$(\ensuremath{\Vert}${\mathit{M}}_{\mathit{J}}$\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.

Physical Review A•May 1, 1994•7 citations
We investigate excitation of He 28{sup 3}S atoms and find that a 2nd microwave field lifts the degeneracy of certain Floquet states describing the [atom + single microwave field] system. As a result a microwave pulse produces two patterns of Stueckelberg oscillations. They depend sensitively on the frequencies and amplitudes of both microwave fields and are influenced differently by added by added noise. We present two-frequency (2-f) Floquet maps showing the origin of the intererferences. We are able theoretically to reproduce reasonably well our observed 2-f Stueckelberg oscillations for (stronger) 30 GHz and (much weaker) 36 GHz 2-field. The case of both fields strong is much more complicated. It still remains theoretically to explain why the noise influences the two patterns of Stueckelberg oscillations differently.
We investigate microwave excitation of helium 28 3^{3}3S Rydberg atoms and find that a second microwave field lifts the degeneracy of certain Floquet states describing the 28 3^{3}3S He atom plus single microwave field system. As a result a microwave pulse produces two patterns of Stueckelberg oscillations. They depend sensitively on the frequencies and amplitudes of both microwave fields and are influenced differently by added noise. We present two-frequency Floquet maps showing the origin of the interferences.
We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28) 3S^{3}\mathrm{S}3S Rydberg atoms. They are produced by the coherent evolution along two isolated Floquet potential curves as the microwave electric field amplitude varies along a half-sine-wave pulse shape. The measured visibility and separation of the oscillations depends sensitively on the Floquet structure, on the atomic beam velocity, and particularly on additive noise, which smears and broadens the pattern.
The authors prepare n{sup 3}S He Rydberg atoms with selected values n {ge} 25 in a fast beam using CO{sub 2} lasers and double-resonance excitation. They then fly through a TE{sub 121} mode cavity, exposing them to a half-sine pulse (about 350 field osc.) of 9.904 GHz electric field whose polarization can be varied; linear (LP), elliptical (EP), and circular (CP). Making EP close to LP can lead to substantial changes in microwave-power-dependent transitions to nearby bound states. In at least one case, a sharp dip in the LP signal is transformed by EP into a pattern reminiscent of Stueckelberg oscillations, previously observed with LP at higher frequencies. Calculations suggest that pulse-shape-induced dynamics at Floquet avoided-crossing(s) explain the LP behavior. Changing the field to EP clearly must modify this behavior. The authors will discuss this kind of data as well as the polarization dependence of microwave ionization of n{sup 3}S He Rydberg atoms.
We present experimental and theoretical results on highly excited Rydberg atoms passing through a waveguide. The waveguide is excited in a coherent mode with a superimposed component of technically generated noise. In the theoretical part of the paper we derive and solve a master equation for a Rydberg atom driven by a monochromatic coherent microwave field in the presence of noise. We show that a Rydberg atom subjected to a mixture of coherent modes and noise fields exhibits four dynamical regimes: (i) diffusive broadening, (ii) localization, (iii) destruction of coherence and localization, and (iv) relaxation to equilibrium. The four regimes are passed one after the other as a function of irradiation time. They occur on different time scales and are thus temporally well separated from each other. The theory is checked by an experiment on the time dependence of the population distribution of highly excited rubidium Rydberg atoms initially prepared in a unique and well-defined Rydberg state and irradiated by a strong microwave field. The localization regime, characterized by a ``freezing'' of the width of the wave packet with respect to the Rydberg levels, has been observed. The addition of a small noise component was shown to lead to delocalization after times inversely proportional to the noise power, as predicted by our theory.
In this chapter experiments on rubidium Rydberg atoms in external fields are reviewed [1 – 8]. In the first part results on the interaction of microwave radiation with rubidium Rydberg atoms are described. The Rydberg atoms interact with a microwave pulse of a well-defined duration. When applying coherent microwave radiation with a frequency exceeding a certain value, the experimentally observed microwave field strength at which 10% of the atoms are ionized has to be much larger than the value found by classical trajectory calculations. The atoms are stabilized by the dynamical localization. An extremely weak microwave broadband noise which is added to the coherent wave at least partially destroys the localization. This phenomenon depends on the bandwidth of the added noise. In further experiments the dependence of the 10% ionization microwave field strength on the duration τ of the microwave pulse has been investigated. For increasing noise level the 10% ionization field strength ∈ 0.1 develops from a behavior ∈ 0.1 ∼ τ −1/4 to a ∈ 0.1 ∼ τ −1/2 dependence, which is characteristic for a classical diffusion process. The second part of the chapter deals with experiments in strong static crossed electric and magnetic fields. Below as well as above the ionization energy the observed quasi-Landau(QL)-resonances are explained using classical trajectories. The ionization behavior of the QL-resonances is clearly influenced by the spatial structure of the associated classical orbits. In further experiments the dependence of the observed ionization energy on the magnetic field was investigated in the presence of a fixed static electric field.
We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np)2{)}^{2})2P3/2{\mathit{P}}_{3/2}P3/2​(\ensuremath{\Vert}MJ{\mathit{M}}_{\mathit{J}}MJ​\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.