Physical Review A

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

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

Published Feb 1, 1993• 40 citations

Abstract

We investigate microwave excitation of helium 28 $^{3}$S Rydberg atoms and find that a second microwave field lifts the degeneracy of certain Floquet states describing the 28 $^{3}$S 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.

DOI: 10.1103/physreva.47.r782

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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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Bulletin of the American Physical SocietyMay 1, 19930 citations

Stueckelberg oscillations in the multiphoton excitation of helium Rydberg atoms: Observation with a pulse of coherent field and suppression by additive noise

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Sensitive Polarization Dependence for Helium Rydberg Atoms Driven by Strong Microwave Fields

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Microwave multiphoton excitation of helium Rydberg atoms: The analogy with atomic collisions

Willem van de Water, K. A. H. van Leeuwen, Suzanne Yoakum +5 more

Physical Review LettersAug 14, 198914 citations

Microwave ionization of Rb Rydberg atoms: Frequency dependence

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

Physical Review AMay 1, 19947 citations

Coherent states of the driven Rydberg atom: Quantum-classical correspondence of periodically driven systems

Luz V. Vela-Arevalo, Ronald F. Fox

Physical Review AJun 9, 200520 citations

Physical Review A

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

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

Published Feb 1, 1993• 40 citations

Publisher

Abstract

We investigate microwave excitation of helium 28

^{3}

S Rydberg atoms and find that a second microwave field lifts the degeneracy of certain Floquet states describing the 28

^{3}

S 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.

DOI: 10.1103/physreva.47.r782

Related papers

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 +1 more

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 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.

Bulletin of the American Physical SocietyMay 1, 19930 citations

Stueckelberg oscillations in the multiphoton excitation of helium Rydberg atoms: Observation with a pulse of coherent field and suppression by additive noise

Suzanne Yoakum, Leszek Sirko, P. M. Koch

We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28) $^{3}\mathrm{S}$ 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.We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28) $^{3}\mathrm{S}$ 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.

Physical Review LettersSep 28, 199256 citations

Sensitive Polarization Dependence for Helium Rydberg Atoms Driven by Strong Microwave Fields

S. A. Zelazny, M. R. W. Bellermann, L. L. Smith +1 more

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.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.

Bulletin of the American Physical SocietyMay 1, 19960 citations

Microwave multiphoton excitation of helium Rydberg atoms: The analogy with atomic collisions

Willem van de Water, K. A. H. van Leeuwen, Suzanne Yoakum +5 more

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the ${n}^{3}$ S to ${n}^{3}$ (L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the ${n}^{3}$S to ${n}^{3}$(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

Physical Review LettersAug 14, 198914 citations

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.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 AMay 1, 19947 citations

Coherent states of the driven Rydberg atom: Quantum-classical correspondence of periodically driven systems

Luz V. Vela-Arevalo, Ronald F. Fox

A methodology to calculate generalized coherent states for a periodically driven system is presented. We study wave packets constructed as a linear combination of suitable Floquet states of the three-dimensional Rydberg atom in a microwave field. The driven coherent states show classical space localization, spreading, and revivals and remain localized along the classical trajectory. The microwave strength and frequency have a great effect in the localization of Floquet states, since quasienergy avoided crossings produce delocalization of the Floquet states, showing that tuning of the parameters is very important. Using wavelet-based time-frequency analysis, the classical phase-space structure is determined, which allows us to show that the driven coherent state is located in a large regular region in which the $z$ coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory.A methodology to calculate generalized coherent states for a periodically driven system is presented. We study wave packets constructed as a linear combination of suitable Floquet states of the three-dimensional Rydberg atom in a microwave field. The driven coherent states show classical space localization, spreading, and revivals and remain localized along the classical trajectory. The microwave strength and frequency have a great effect in the localization of Floquet states, since quasienergy avoided crossings produce delocalization of the Floquet states, showing that tuning of the parameters is very important. Using wavelet-based time-frequency analysis, the classical phase-space structure is determined, which allows us to show that the driven coherent state is located in a large regular region in which the $z$ coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory.

Physical Review AJun 9, 200520 citations

We investigate microwave excitation of helium 28

^{3}

S Rydberg atoms and find that a second microwave field lifts the degeneracy of certain Floquet states describing the 28

^{3}

We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28)

^{3}\mathrm{S}

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.

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the

{n}^{3}

S to

{n}^{3}

(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

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.

z

coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory.