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Physical Review A

Transmission of an isolated attosecond pulse in a strong-field dressed atom

Adrian Nikolaus Pfeiffer, Stephen R. Leone

Published May 29, 2012• 58 citations
Publisher

Abstract

The optical properties of matter can be manipulated by coupling a strong field to an optical transition. The concepts of Autler-Townes splitting and electromagnetically induced transparency, where a control field manipulates the transmission of a probe field, have recently been extended to control the transmission of x rays. The use of a strong femtosecond pulse to control the transmission of an isolated attosecond extreme ultraviolet or soft x-ray pulse opens a new field of investigation, since the duration of the probe pulse is only a fraction of one optical cycle of the control pulse. In this paper a three-state model beyond the rotating wave approximation is formulated that treats the attosecond pulse as an initial value problem in the time domain. Two effects for spectroscopic measurements are elucidated: first the absorption profile of the attosecond pulse is split into multiple lines rather than a doublet in the high-field regime, and second the transmission of the attosecond pulse depends on the relative timing within the optical cycle of the control pulse. An analytical treatment is carried out in the time domain in contrast to the more common approach in the frequency domain. This is appropriate for the field of attosecond physics where the main interest lies in the time evolution of the fields, rather than spectroscopic studies.

DOI
10.1103/physreva.85.053422

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The optical properties of matter can be manipulated by coupling a strong field to an optical transition. The concepts of Autler-Townes splitting and electromagnetically induced transparency, where a control field manipulates the transmission of a probe field, have recently been extended to control the transmission of x rays. The use of a strong femtosecond pulse to control the transmission of an isolated attosecond extreme ultraviolet or soft x-ray pulse opens a new field of investigation, since the duration of the probe pulse is only a fraction of one optical cycle of the control pulse. In this paper a three-state model beyond the rotating wave approximation is formulated that treats the attosecond pulse as an initial value problem in the time domain. Two effects for spectroscopic measurements are elucidated: first the absorption profile of the attosecond pulse is split into multiple lines rather than a doublet in the high-field regime, and second the transmission of the attosecond pulse depends on the relative timing within the optical cycle of the control pulse. An analytical treatment is carried out in the time domain in contrast to the more common approach in the frequency domain. This is appropriate for the field of attosecond physics where the main interest lies in the time evolution of the fields, rather than spectroscopic studies.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
We present a theoretical study of the delay-dependent Autler-Townes (AT) splitting in transient absorption spectroscopy of an isolated attosecond pulse in helium atoms subject to a delayed infrared (IR) pulse. We concentrate on cases in which the IR pulse is resonant with the helium $1s2p\text{\ensuremath{-}}1s2s$ transition and provide a time-domain perspective of the dynamics in the delay-dependent pump-probe system. We identify several interesting delay-dependent features in the transient absorption spectrum such as AT splitting, oscillation between absorption and emission at the resonant absorption frequency, and sub-IR-cycles oscillations. We then explain the origins of these features in the time domain in terms of a strongly driven two-level system, in the language of population transfer and coherent control.
We present a theoretical study of transient absorption spectra of laser-dressed hydrogen atoms, based on numerical solutions of the time-dependent Schr\"odinger equation. The timing of absorption is controlled by the delay between an extreme ultra violet (XUV) pulse and an infrared (IR) laser field. The XUV pulse is isolated and several hundred attoseconds in duration, which acts as a pump to drive the ground-state electron to excited ppp states. The subsequent interaction with the IR field produces dressed states, which manifest as sidebands between the 1s-npnpnp absorption spectra separated by one IR-photon energy. We demonstrate that the population of dressed states is maximized when the timing of the XUV pulse coincides with the zero crossing of the IR field, and that their energies can be manipulated in a subcycle time scale by adding a chirp to the IR field. An alternative perspective to the problem is to think of the XUV pulse as a probe to detect the dynamical ac Stark shifts. Our results indicate that the accidental degeneracy of the hydrogen excited states is removed while they are dressed by the IR field, leading to large ac Stark shifts. Furthermore, we observe the Autler-Townes doublets for the n=2n=2n=2 and 3 levels using the 656 nm dressing field, but their separation does not agree with the prediction by the conventional three-level model that neglects the dynamical ac Stark shifts.
An optical coherent control scheme has been proposed and theoretically investigated where an extreme ultraviolet single attosecond pulse (SAP) propagates through a dense helium gas dressed by a time-delayed femtosecond laser pulse. The laser pulse couples the 2s2p([superscript]1P) and 2s[superscript]2([superscript]1S) autoionizing states when the SAP excites the 2s2p state. After going through the gas, the spectral and temporal profiles of the SAP are strongly distorted. A narrowed but enhanced spike in the spectrum shows up for specific intensities and time delays of the laser, which exemplifies the control of a broadband photon wave packet by an ultrashort dressing field for the first time. We analyze the photon and electron dynamics and determine the dressing condition that maximizes this enhancement. The result demonstrates new possibilities of attosecond optical control.
We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom response by calculating the frequency-dependent absorption cross section for XUV energies between 20 and 24 eV for several dressing wavelengths between 400 and 2000 nm and intensities up to 1012{}^{12}12 W/cm2{}^{2}2. We find that for dressing wavelengths near 1600 nm, there is an Autler-Townes splitting of the $1s\ensuremath{\rightarrow}2p$ transition that can potentially lead to transparency for absorption of XUV light tuned to this transition. We study the effect of this XUV transparency in a macroscopic helium gas by incorporating the time-frequency approach into a solution of the coupled Maxwell-Schr\"odinger equations. We find rich temporal reshaping dynamics when a 61-fs XUV pulse resonant with the $1s\ensuremath{\rightarrow}2p$ transition propagates through a helium gas dressed by an 11-fs, 1600-nm laser pulse.
An optical coherent control scheme has been proposed and theoretically investigated where an extreme ultraviolet single attosecond pulse (SAP) propagates through dense helium gas dressed by a time-delayed femtosecond laser pulse. The laser pulse couples the 2s2p( 1 P) and 2s 2 ( 1 S) autoionizing states when the SAP excites the 2s2p state. After going through the gas, the spectral and temporal profiles of the SAP are strongly distorted. A narrowed but enhanced spike in the spectrum shows up for specific intensities and time delays of the laser, which exemplifies the control of a broadband photon wave packet by an ultrashort dressing field for the first time. We analyse the photon and electron dynamics and determine the dressing condition that maximizes this enhancement. The result demonstrates new possibilities of attosecond optical control.