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

Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses

B. Chatel, J. Degert, B. Girard

Published Nov 30, 2004• 47 citations
Publisher

Abstract

Two-photon excitation of a quantum ladder system by an ultrashort chirped pulse leads to interferences in the excited-state population, between direct and sequential paths. Experimental results have been obtained in atomic sodium vapor. The presence of several intermediate and final states leads to new phenomena. The interplay between the two sequential paths leads to strongly contrasted oscillations and a large enhancement of the transition probability for precise values of the chirp. A cubic spectral phase modifies significantly the behavior of the quantum interferences and can be used to enhance the two-photon absorption rate.

DOI
10.1103/physreva.70.053414

Related papers

Competition between sequential and direct paths in a two-photon transition

B. Chatel, J. Degert, Sabine Stock +1 more

Two-photon excitation of a quantum ladder system by a chirped pulse leads to interferences in the excited-state population, due to the phase differences between direct and sequential paths. First, based on an analytical approach, we separate and discuss the features of the contributions arising from these two paths. Then interferences with two intermediate levels are observed experimentally in atomic sodium vapor. Interplay between the two sequential paths leads to strongly contrasted oscillations and a great enhancement of the transition probability for some values of the chirp.

Physical Review A•Oct 22, 2003•77 citations

Interference in climbing a quantum ladder system with frequency-chirped laser pulses

Péter Balling, D. J. Maas, Lambertus D. Noordam

Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ oscillator amplified at 10 Hz.

Physical Review A•Nov 1, 1994•99 citations

Chirping a two-photon transition in a multistate ladder

Wolfgang Merkel, Holger Mack, Wolfgang P. Schleich +3 more

We consider a two-photon transition in a specific ladder system driven by a chirped laser pulse. In the weak field limit, we find that the excited state probability amplitude arises due to interference of multiple quantum paths which are weighted by quadratic phase factors. The excited state population has the form of a Gauss sum which plays a prominent role in number theory.

arXiv:quant-ph/0702122•Physical Review A•Aug 20, 2007•12 citations

Strong-Field Quantum Control of Energy Ladder Climbing

Sangkyung Lee, Jongseok Lim, Jaewook Ahn

We demonstrate coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level model system of atomic sodium, we controlled the quantum interference of sequential 2+1 photons and direct three-photon transitions.

Conference on Lasers and Electro-Optics•Jan 1, 2011•0 citations

Strong-field quantum control of 2 + 1 photon absorption of atomic sodium

Sangkyung Lee, Jongseok Lim, Chang Yong Park +1 more

We demonstrate ultrafast coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level system that models optical interactions with sodium atoms, we control the quantum interference of sequential 2 + 1 photons and direct three-photon transitions. Dynamic change in energy levels predicts an enormous enhancement of |7p>-state excitation in the strong-field regime by a negatively chirped pulse. In addition, the |4s>-state excitation is enhanced symmetrically by nonzero linear chirp rates given as a function of laser peak intensity and laser detuning. Experiments performed by ultrafast shaped-pulse excitation of ground-state atomic sodium verifies the various strong-field contributions to |3s>-|7p> and |3s>-|4s> transitions. The result suggests that for systems of molecular level understanding adiabatic control approach with analytically shaped pulses becomes a more direct control than feedback-loop black-box approaches.

Optics Express•Jan 24, 2011•17 citations

Coherent control of resonant two-photon transitions by counterpropagating ultrashort pulse pairs

Woojun Lee, Hyosub Kim, Kyungtae Kim +1 more

We describe optimized coherent control methods for two-photon transitions in atoms of a ladder-type three-state energy configuration. Our approach is based on the spatial coherent control scheme, which uses counterpropagating ultrashort laser pulses to produce complex excitation patterns in an extended space. Because coherent control requires constructive interference of constituent transition pathways, applying it to an atomic transition with a specific energy configuration requires specially designed laser pulses. We show in an experimental demonstration that two-photon transition with an intermediate resonant energy state can be coherently controlled and retrieved from the resonance-induced background, when phase flipping of the laser spectrum near the resonant intermediate transition is used. A simple reason for this behavior is the fact that the transition amplitude function (added to give an overall two-photon transition) changes its sign at the intermediate resonant frequency and, thus, by proper spectral-phase programing, the excitation patterns (or the position-dependent interference of the transition given as a consequence of the spatial coherent control) can be well isolated in space along the focal region of the counterpropagating pulses.

arXiv:1503.02378•Physical Review A•Sep 14, 2015•6 citations
Two-photon excitation of a quantum ladder system by an ultrashort chirped pulse leads to interferences in the excited-state population, between direct and sequential paths. Experimental results have been obtained in atomic sodium vapor. The presence of several intermediate and final states leads to new phenomena. The interplay between the two sequential paths leads to strongly contrasted oscillations and a large enhancement of the transition probability for precise values of the chirp. A cubic spectral phase modifies significantly the behavior of the quantum interferences and can be used to enhance the two-photon absorption rate.
Two-photon excitation of a quantum ladder system by a chirped pulse leads to interferences in the excited-state population, due to the phase differences between direct and sequential paths. First, based on an analytical approach, we separate and discuss the features of the contributions arising from these two paths. Then interferences with two intermediate levels are observed experimentally in atomic sodium vapor. Interplay between the two sequential paths leads to strongly contrasted oscillations and a great enhancement of the transition probability for some values of the chirp.
Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​ oscillator amplified at 10 Hz.
We demonstrate ultrafast coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level system that models optical interactions with sodium atoms, we control the quantum interference of sequential 2 + 1 photons and direct three-photon transitions. Dynamic change in energy levels predicts an enormous enhancement of |7p>-state excitation in the strong-field regime by a negatively chirped pulse. In addition, the |4s>-state excitation is enhanced symmetrically by nonzero linear chirp rates given as a function of laser peak intensity and laser detuning. Experiments performed by ultrafast shaped-pulse excitation of ground-state atomic sodium verifies the various strong-field contributions to |3s>-|7p> and |3s>-|4s> transitions. The result suggests that for systems of molecular level understanding adiabatic control approach with analytically shaped pulses becomes a more direct control than feedback-loop black-box approaches.
We describe optimized coherent control methods for two-photon transitions in atoms of a ladder-type three-state energy configuration. Our approach is based on the spatial coherent control scheme, which uses counterpropagating ultrashort laser pulses to produce complex excitation patterns in an extended space. Because coherent control requires constructive interference of constituent transition pathways, applying it to an atomic transition with a specific energy configuration requires specially designed laser pulses. We show in an experimental demonstration that two-photon transition with an intermediate resonant energy state can be coherently controlled and retrieved from the resonance-induced background, when phase flipping of the laser spectrum near the resonant intermediate transition is used. A simple reason for this behavior is the fact that the transition amplitude function (added to give an overall two-photon transition) changes its sign at the intermediate resonant frequency and, thus, by proper spectral-phase programing, the excitation patterns (or the position-dependent interference of the transition given as a consequence of the spatial coherent control) can be well isolated in space along the focal region of the counterpropagating pulses.