Time correlation inside a laser pulse (original) (raw)
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Time-Resolved Quantum Dynamics of Double Ionization in Strong Laser Fields
Physical Review Letters, 2007
Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1-d coordinates for the electrons. The time resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration, and reveal the relative importance of sequential and non-sequential double ionization, even when ionization takes place during the same field cycle.
Physical Review A, 2006
Electron-momentum distributions for above-threshold ionization of argon in a few-cycle, linearly polarized laser pulse are investigated. Spectral features characteristic of multiphoton as well as tunneling ionization coexist over a range of the Keldysh parameter ␥ in the transition regime ␥ ϳ 1. Surprisingly, the simple strong-field approximation ͑SFA͒ is capable of reproducing the key features of the two-dimensional momentum distributions found in the full solution of the time-dependent Schrödinger equation, despite the fact that SFA is known to severely underestimate the total ionization probability.
Sub-laser-cycle electron pulses for probing molecular dynamics
Experience shows that the ability to make measurements in any new time regime opens new areas of science. Currently, experimental probes for the attosecond time regime (10 218 –10 215 s) are being established. The leading approach is the generation of attosecond optical pulses by ionizing atoms with intense laser pulses. This nonlinear process leads to the production of high harmonics during collisions between electrons and the ionized atoms. The underlying mechanism implies control of energetic electrons with attosecond precision. We propose that the electrons themselves can be exploited for ultrafast measurements. We use a 'molecular clock', based on a vibrational wave packet in H 2 1 to show that distinct bunches of electrons appear during electron–ion collisions with high current densities, and durations of about 1 femtosecond (10 215 s). Furthermore, we use the molecular clock to study the dynamics of non-sequential double ionization. A substantial effort is under way to develop single attosecond optical pulses 1–3 , or trains of attosecond pulses 4–6 , using the physical processes occuring in high-harmonic generation 7. High harmonics are produced during the electron–ion collisions induced by strong-field laser ionization, usually referred to as 'recollision'. Within one optical period an electron is removed from the atom, is driven back when the laser field reverses its direction, and collides with the parent ion. The duration of the electron–ion recollision largely determines the duration of the attosecond photon pulse. Here we study the recollision electron wave packet, measuring both the probability of recollision and its time structure. Although only one electron is involved in the electron–ion recollision, we adopt the language of electron beams to indicate the potential applications of recollision electrons. These applications are the topic of the final section of this Article. We characterize the unusually large current density and its time structure as seen by the ion following ionization. To do this, we use H 2 molecules in a low-density gas as a molecular clock. As ionization simultaneously forms two wave packets—one a vibrational wave packet moving on the H 2 þ (X 2 S g þ) surface; the other, the electron wave packet that we wish to study—ionization starts the vibrational clock in H þ 2 : We choose H þ 2 as the molecular clock because of the speed of its vibrational wave packet, and because all excited states of H þ 2 directly dissociate. By choosing the molecular axis perpendicular to the laser electric field, we decouple the X 2 S þ g and A 2 S þ u surfaces in H þ 2 ; ensuring that the clock remains accurate in the presence of the field. To read the clock, we observe the kinetic energy of the protons produced by inelastic scattering when the electron recollides with the parent ion. The kinetic energy distribution measures the position of the vibrational wave packet at the time of recollision, and therefore the recollision time. In our experiment the time resolution is ,1 fs. Next, we apply the molecular clock to follow the subcycle correlated electron dynamics. Non-sequential double ionization (two-electron ionization that cannot be described by two sequential single-electron ionization processes) is a common occurrence during strong-field ionization of atoms or molecules containing two or more electrons 7–13. We distinguish the double ionization due to recollision from instantaneous double ionization by using the molecular clock, and find that electron recollision dominates others by at least two orders of magnitude. We confirm that the most important route to non-sequential ionization is through the production of excited states by recollision that can later ionize in the strong laser field. Finally, we compare the double-ionization yield due to recollision in H 2 and helium 8,11,13. We find that double ionization (excitation) is about ten times more probable in hydrogen molecules than in helium 11,13. Selecting the fragmentation channel We now proceed to fully characterize the current density using H 2 double-ionization (excitation) for all aspects of the measurement. (For convenience, we will use 'double-ionization' when referring to either the non-sequential emission of two electrons, or the emission of one and the correlated excitation of the other.) First, we identify collision-induced excitation or double ioniz-ation through the previously observed 14,15 high kinetic energy of the fragment protons that are produced. We show that recollision is responsible for these energetic protons by comparing the kinetic-energy spectrum measured with linear and elliptically polarized light 16. Second, the ellipticity dependence of the proton yield measures the initial velocity spread of the electron wave packet. With this input, we calculate the current density seen by the newly ionized ion. Third, we confirm the predicted temporal structure by comparing the calculated and measured kinetic-energy spectrum. Finally, we confirm the magnitude of the current density by
Time double-slit interferences in strong-field tunneling ionization
Physical Review A, 2006
We show that interference phenomena plays a big role for the electron yield in ionization of atoms by an ultra-short laser pulse. Our theoretical study of single ionization of atoms driven by fewcycles pulses extends the photoelectron spectrum observed in the double-slit experiment by Lindner et al, Phys. Rev. Lett. 95, 040401 (2005) to a complete three-dimensional momentum picture. We show that different wave packets corresponding to the same single electron released at different times interfere, forming interference fringes in the two-dimensional momentum distributions. These structures reproduced by means of ab initio calculations are understood within a semiclassical model.
Probing electron-electron correlation with attosecond pulses
The European Physical Journal D - Atomic, Molecular and Optical Physics, 2003
We study two-photon double ionization of helium in its ground state at sufficiently low laser intensities so that three and more photon absorptions are negligible. In the regime where sequential ionization dominates, the two-photon double ionization one-electron energy spectrum exhibits a well defined double peak structure directly related to the electron-electron correlation in the ground state. We demonstrate that when helium is exposed to subfemtosecond or attosecond pulses, both peaks move and their displacement is a signature of the time needed by the He + orbital to relax after the ejection of the first electron. This result rests on the numerical solution of the corresponding non-relativistic time-dependent Schrödinger equation.
Tunneling in attosecond optical ionization and a dynamical time operator
Physical Review A, 2017
The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ionization experiments. The parameter status of time in the time dependent Schrödinger equation (TDSE) is supported by the well-known Pauli's objection as well as by its interpretation as an emerging property of entanglement with a classical environment. On the other hand, the introduction of a self-adjoint dynamical time operator in Dirac's formulation of electron's relativistic quantum mechanics (RQM), yields an additional system observable that represents an internal time. In the present paper the relation of this internal time with the parametric (laboratory) time and its relevance to the tunneling measurements in these experiments is examined within the standard framework of RQM.
Time-independent theory of multiphoton ionization of an atom by an intense field
Physical Review A, 1988
We formulate a computationally feasible method for calculating multiphoton ionization rates for atoms exposed to intense fields in the intensity regime where perturbation theory ceases to apply. The method is based on the time-independent picture of ionization, which starts with the Floquet ansatz. The question of the gauge of the radiation field is discussed in some detail. Various expressions for the ionization amplitude are derived from a variational principle, with the radiation field expressed in the velocity gauge. We consider in particular an approximation in which the wave vector developing from the initial state is replaced by a trial vector that is the Floquet expansion truncated just below the threshold for ionization, and in which the wave vector developing into the final state is replaced by a trial vector that is just the wave vector appearing in the Kroll-Watson lowfrequency approximation in scattering theory. We have applied this approximation to hydrogen and we present some results for both nonresonant and resonant multiphoton ionization. We argue that the experimentally observed resonance structure in the above-threshold peaks of the ionization signal occurs through the electron jumping from one dressed-state energy-eigenvalue curve to another.
Spatial and temporal correlation in dynamic, multi-electron quantum systems
Journal of Physics B: Atomic, Molecular and Optical Physics, 2001
Cross sections for ionization with excitation and for double excitation in helium are evaluated in a full second Born calculation. These full second Born calculations are compared to calculations in the independent electron approximation, where spatial correlation between the electrons is removed. Comparison is also made to calculations in the independent time approximation, where time correlation between the electrons is removed. The two-electron transitions considered here are caused by interactions with incident protons and electrons with velocities ranging between 2 and 10 au. Good agreement is found between our full calculations and experiment, except for the lowest velocities, where higher Born terms are expected to be significant. Spatial electron correlation, arising from internal electron-electron interactions, and time correlation, arising from time ordering of the external interactions, can both give rise to observable effects. Our method may be used for photon impact.
Double ionization probed on the attosecond timescale
Nature Physics, 2014
Double ionization following the absorption of a single photon is one of the most fundamental processes requiring interaction between electrons 1-3. Information about this interaction is usually obtained by detecting emitted particles without access to real-time dynamics. Here, attosecond light pulses 4,5 , electron wave packet interferometry 6 and coincidence techniques 7 are combined to measure electron emission times in double ionization of xenon using single ionization as a clock, providing unique insight into the two-electron ejection mechanism. Access to many-particle dynamics in real time is of fundamental importance for understanding processes induced by electron correlation in atomic, molecular and more complex systems. The emergence of attosecond science (1 as = 10 −18 s) in the new millennium opened an exciting area of physics bringing the dynamics of electron wave functions into focus. The important goal of real-time visualization of the interplay between electrons and their role in molecular bonding now seems to be in reach. After a decade where attosecond light sources 4,5 were characterized and their potential demonstrated, the next phase will include the exploration of correlated electron dynamics in complex systems. A series of groundbreaking studies on single ionization (SI) in atoms using attosecond light pulses sheds light on the escaping electron and its interaction with the residual ion 6,8 , and the resulting coherent superposition of neutral bound states 9,10. Double ionization (DI) by absorption of a single photon is an inherently more challenging phenomenon, both experimentally and theoretically 1-3. The two-electron ejection can be understood only through interactions between electrons, and is usually discussed in terms of different mechanisms 11. In the knockout mechanism, the electron excited by interaction with the light field (the photoelectron) collides with another electron on its way out, resulting in two emitted electrons. In the shake-off mechanism, orbital relaxation following the creation of a hole ionizes a second electron. Electron correlations may also lead to indirect DI processes via highly excited states of the singly-charged ion 12. One-photon experimental investigations with the pair of electrons detected in coincidence can provide a fairly complete DI description without, however, following the dynamics of the electron correlation in real time. Multiphoton experimental investigations have been performed both on the femtosecond and attosecond timescales 13,14 , but DI in strong laser fields does not require electron correlation. In this work, we study DI of xenon in the near-threshold region using attosecond extreme ultraviolet (XUV) pulses for excitation