Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantum interference in microwave multiphoton transitions

M. Gatzke, R. B. Watkins, Thomas F. Gallagher

Published Jun 1, 1995• 16 citations
Publisher

Abstract

We observe interference in the resonant microwave multiphoton transition probability between the 21s state and the 19,3 Stark state of K in a static field as a function of the duration and intensity of a microwave pulse at 9 GHz. The 19,3 state adiabatically connects to the 19f state in zero field. The ac Stark effect shifts the 21s state through a multiphoton resonance with the 19,3 Stark state during both the rising and falling edges of the microwave pulse. The transitions that occur during each traversal of the resonance lead to an interference in the net transition probability as a function of the relative phase accumulated by each state during the pulse. We measure both the frequency of the interference oscillations for different detunings from resonance and the amplitude of the fringes for different degrees of pulse asymmetry. The latter results are in complete agreement with the predictions of a Landau-Zener model for the resonance transitions.

DOI
10.1103/physreva.51.4835

Related papers

Quantum interference in half-cycle microwave multiphoton transitions

C. W. S. Conover, Julia H. Rentz

We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l\ensuremath{\geqslant}2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schr\"odinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.

Physical Review A•May 1, 1997•7 citations

Ramsey interference fringes in single pulse microwave multiphoton transitions

M. C. Baruch, Thomas F. Gallagher

In microwave multiphoton transitions between Rydberg atoms driven by short microwave pulses we have observed that the rise and fall of the pulse are as important as the peak and together can produce readily visible interference in the transition probability. Furthermore, the transition probability vanishes for some tunings and can be suppressed if the ac Stark shift brings the two states into resonance at the peak of the microwave pulse with a large Rabi frequency.

Physical Review Letters•Jun 15, 1992•50 citations

Microwave multiphoton transitions between Rydberg states of potassium

R. C. Stoneman, D. S. Thomson, Thomas F. Gallagher

Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.

Physical Review A•Mar 1, 1988•56 citations

Probing strong-field two-photon transitions through dynamic interference

Attila Tóth, András Csehi

Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 14, 2021•32 citations

Effect of quantum interference on the suppression of the ac Stark shifting of a multiphoton resonance

L. Deng, W. R. Garrett, J. Y. Zhang +1 more

We report detailed experimental results in xenon that confirm theoretical predictions [Payne et al., Phys. Rev. A 48, 2334 (1993)] on the interference-based suppression of ac Stark shifting of even-photon resonances under circumstances where the shift is produced through strong coupling to a state that is also coupled back to the ground state. In the copropagating-beam configuration and in the pressure range of 0.5--250 Torr, the multiphoton ionization spectral line shape is unchanged regardless of the presence of the second laser field, i.e., the ac Stark shift introduced by the second laser is totally suppressed due to a complete destructive interference between two excitation pathways. In the counterpropagating-beam configuration, however, the ac Stark shift persists in the range of the pressure studied. By choosing a different set of energy levels where no four-wave-mixing field is permitted, we show that the very same ac Stark shift introduced by the second laser field persists even with copropagating-beam configuration, as predicted by theory.

Physical Review A•Jul 1, 1995•11 citations

Effect of pressure-dependent quantum interference on the ac Stark shifting of two-photon resonances

M. G. Payne, J.Y. Zhang, W. R. Garrett

We describe ac Stark shift production and measurement in a two-laser mode where a first laser is tuned through a two-photon resonance between the ground state and an excited state in order to record a line shape for the corresponding resonantly enhanced multiphoton ionization. A second laser is tuned to a fixed wavelength which is close to a resonance between the upper state in the two-photon transition and a third state which has dipole-allowed transitions back to the ground state. At low concentrations the second laser leads to very large ac Stark shifts in the two-photon excitation and in the related resonantly enhanced multiphoton ionization. However, at high concentrations a destructive interference occurs involving the three-photon coupling between the third state and the ground state and the one-photon coupling due to the four-wave-mixing field at frequency 2${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$. This interference leads to a pressure-dependent suppression of the amplitude for the third state. When this destructive interference occurs, the ac Stark shift due to the second laser undergoes a corresponding pressure-dependent suppression. The criteria for the pressure to be high enough to completely suppress the ac Stark shift is that the real part of phase mismatch \ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert} at the angular frequency 2${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$ and (or) the absorption coefficient \ensuremath{\beta} at the same frequency should be very large, so that with unfocused focused beams \ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert}L>5[(${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$\ensuremath{\tau}${]}^{1/2}$, where L is the thickness of gas penetrated before the shift is measured, ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$ is the maximum ac Stark shift at very low pressure, and \ensuremath{\tau} is the pulse length of the lasers.At positions and concentrations such that 1\ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert}L\ensuremath{\le}2[(${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$\ensuremath{\tau})${]}^{1/2}$ the ac Stark shift is present but the two-photon excitation is suppressed due to a destructive interference between excitation by two photons from the first laser and by two-photon excitation between a four-wave-mixing photon and a photon from the second laser.

Physical Review A•Sep 1, 1993•17 citations
We observe interference in the resonant microwave multiphoton transition probability between the 21s state and the 19,3 Stark state of K in a static field as a function of the duration and intensity of a microwave pulse at 9 GHz. The 19,3 state adiabatically connects to the 19f state in zero field. The ac Stark effect shifts the 21s state through a multiphoton resonance with the 19,3 Stark state during both the rising and falling edges of the microwave pulse. The transitions that occur during each traversal of the resonance lead to an interference in the net transition probability as a function of the relative phase accumulated by each state during the pulse. We measure both the frequency of the interference oscillations for different detunings from resonance and the amplitude of the fringes for different degrees of pulse asymmetry. The latter results are in complete agreement with the predictions of a Landau-Zener model for the resonance transitions.
We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l\ensuremath{\geqslant}2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schr\"odinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.
Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.
Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.
We report detailed experimental results in xenon that confirm theoretical predictions [Payne et al., Phys. Rev. A 48, 2334 (1993)] on the interference-based suppression of ac Stark shifting of even-photon resonances under circumstances where the shift is produced through strong coupling to a state that is also coupled back to the ground state. In the copropagating-beam configuration and in the pressure range of 0.5--250 Torr, the multiphoton ionization spectral line shape is unchanged regardless of the presence of the second laser field, i.e., the ac Stark shift introduced by the second laser is totally suppressed due to a complete destructive interference between two excitation pathways. In the counterpropagating-beam configuration, however, the ac Stark shift persists in the range of the pressure studied. By choosing a different set of energy levels where no four-wave-mixing field is permitted, we show that the very same ac Stark shift introduced by the second laser field persists even with copropagating-beam configuration, as predicted by theory.
We describe ac Stark shift production and measurement in a two-laser mode where a first laser is tuned through a two-photon resonance between the ground state and an excited state in order to record a line shape for the corresponding resonantly enhanced multiphoton ionization. A second laser is tuned to a fixed wavelength which is close to a resonance between the upper state in the two-photon transition and a third state which has dipole-allowed transitions back to the ground state. At low concentrations the second laser leads to very large ac Stark shifts in the two-photon excitation and in the related resonantly enhanced multiphoton ionization. However, at high concentrations a destructive interference occurs involving the three-photon coupling between the third state and the ground state and the one-photon coupling due to the four-wave-mixing field at frequency 2${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$. This interference leads to a pressure-dependent suppression of the amplitude for the third state. When this destructive interference occurs, the ac Stark shift due to the second laser undergoes a corresponding pressure-dependent suppression. The criteria for the pressure to be high enough to completely suppress the ac Stark shift is that the real part of phase mismatch \ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert} at the angular frequency 2${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$ and (or) the absorption coefficient \ensuremath{\beta} at the same frequency should be very large, so that with unfocused focused beams \ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert}L>5[(${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$\ensuremath{\tau}]1/2{]}^{1/2}]1/2, where L is the thickness of gas penetrated before the shift is measured, ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$ is the maximum ac Stark shift at very low pressure, and \ensuremath{\tau} is the pulse length of the lasers.At positions and concentrations such that 1\ensuremath{\Vert}\ensuremath{\Delta}k\ensuremath{\Vert}L\ensuremath{\le}2[(${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{(\mathrm{max})}$\ensuremath{\tau})]1/2{]}^{1/2}]1/2 the ac Stark shift is present but the two-photon excitation is suppressed due to a destructive interference between excitation by two photons from the first laser and by two-photon excitation between a four-wave-mixing photon and a photon from the second laser.