Physical Review Letters

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

Published Sep 28, 1992• 56 citations

Abstract

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.

DOI: 10.1103/physrevlett.69.1919

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Physical Review Letters

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

Published Sep 28, 1992• 56 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevlett.69.1919

Related papers

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 +1 more

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.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.

Physical Review AFeb 1, 199340 citations

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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

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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

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 ionization and excitation of helium Rydberg atoms

Willem van de Water, Suzanne Yoakum, Ton van Leeuwen +5 more

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_{0}$ $^{3}$ S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_{0}$ =25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_{0}$ $^{3}$ S\ensuremath{\rightarrow} ${\mathit{n}}_{0}$ $^{3}$ L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_{0}$ $^{3}$S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_{0}$=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_{0}$ $^{3}$S\ensuremath{\rightarrow}${\mathit{n}}_{0}$ $^{3}$L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

Physical Review AJul 1, 199040 citations

Half-Cycle Microwave Excitation of Rubidium Rydberg Atoms

G. M. Lankhuijzen, Lambertus D. Noordam

Excitation from $\mathrm{ns}$ , $\mathrm{np}$ , and $\mathrm{nd}$ Rydberg states of rubidium to the adjacent manifolds by electrical pulses of 140 and 9 ns duration up to 200 V/cm is studied. These pulses correspond to half cycles of microwave fields of 2.6 GHz and 40 MHz. The observed population transfer (up to 40%) is not monotonically increasing with the field strength. For the 140 ps pulse local minima are found due to the absence of avoided crossings of appropriate size at the peak of the pulse. For the long pulses Stueckelberg oscillations are observed in the transfer yield.Excitation from $\mathrm{ns}$, $\mathrm{np}$, and $\mathrm{nd}$ Rydberg states of rubidium to the adjacent manifolds by electrical pulses of 140 and 9 ns duration up to 200 V/cm is studied. These pulses correspond to half cycles of microwave fields of 2.6 GHz and 40 MHz. The observed population transfer (up to 40%) is not monotonically increasing with the field strength. For the 140 ps pulse local minima are found due to the absence of avoided crossings of appropriate size at the peak of the pulse. For the long pulses Stueckelberg oscillations are observed in the transfer yield.

Physical Review LettersJan 16, 199521 citations

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

^{3}\mathrm{S}

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.

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 experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited

{\mathit{n}}_{0}

^{3}

S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range

{\mathit{n}}_{0}

=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of

{\mathit{n}}_{0}

^{3}

S\ensuremath{\rightarrow}

{\mathit{n}}_{0}

^{3}

L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

Excitation from

\mathrm{ns}

\mathrm{np}

, and

\mathrm{nd}

Rydberg states of rubidium to the adjacent manifolds by electrical pulses of 140 and 9 ns duration up to 200 V/cm is studied. These pulses correspond to half cycles of microwave fields of 2.6 GHz and 40 MHz. The observed population transfer (up to 40%) is not monotonically increasing with the field strength. For the 140 ps pulse local minima are found due to the absence of avoided crossings of appropriate size at the peak of the pulse. For the long pulses Stueckelberg oscillations are observed in the transfer yield.