Dynamics of tunneling ionization using Bohmian mechanics

Douguet, Nicolas; Bartschat, Klaus

doi:10.1103/physreva.97.013402

Cited by 41 publications

(39 citation statements)

References 46 publications

(73 reference statements)

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“…Furthermore, in deriving Eq. (14) we replaced in the third line the Volkov prop-agatorÛ V (0, t) with the total propagatorÛ (0, t). This is the replacement analogous to the one usually done in the derivation of the Keldysh expression for the ionization amplitude in the framework of the SFA (by replacinĝ U (0, t) on the r.h.s of the Eq.…”

Section: Theorymentioning

confidence: 99%

Simple man model in the Heisenberg picture

Ivanov

Kim

2020

Commun Phys

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We describe an approximate solution to the Heisenberg operator equations of motion for an atom in a laser field. The solution is based on a quantum generalization of the physical picture given by the well-known Simple Man Model (SMM). We provide justification of the plausibility of this generalization and test its validity by applying it for the calculation of the coordinate and velocity autocorrelation functions which, to our knowledge, have not been studied before in the context of the strong field ionization. Both our model and results of the ab initio numerical calculations show distinct types of correlations due to different types of electron's motion providing a useful insight into the strong field ionization dynamics.

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Section: Theorymentioning

confidence: 99%

Simple man model in the Heisenberg picture

Ivanov

Kim

2020

Commun Phys

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“…The potential depth is chosen so that the ground state energy agrees with E ground . As the time-dependent electric field, we choose, as in [17],…”

Section: Time-dependent Circularly Polarized Electric Fieldsmentioning

confidence: 99%

“…The main quantity of conceptual interest is called "tunneling traversal time" in [17], which is the time the electron spends in a classically forbidden region between two turning points. In a constant field, the positions of turning points depend only on the initial energy of the electron and can be easily determined, but the definition is more difficult to implement when the dynamical behavior of the force is crucial [13].…”

Section: Definition Of Tunneling Time For Dynamic Fieldsmentioning

confidence: 99%

“…The examples considered in [13] suggested near-zero tunneling exit times, which has to be interpreted in the context of the pulse (21) with maximum intensity at time zero. In the terminology of [17], the tunneling exit time of [13] is therefore equal to the "tunneling ionization time" defined as the duration between the maximum of the external force and the time when the electron reenters a classically allowed region. The tunneling ionization time can be accessed in observations more directly than the tunneling traversal time.…”

Section: Definition Of Tunneling Time For Dynamic Fieldsmentioning

confidence: 99%

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Canonical tunneling time in ionization experiments

2018

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Canonical semiclassical methods can be used to develop an intuitive definition of tunneling time through potential barriers. An application to atomic ionization is given here, considering both static and time-dependent electric fields. The results allow one to analyze different theoretical constructions proposed recently to evaluate ionization experiments based on attoclocks. They also suggest new proposals of determining tunneling times, for instance through the behavior of fluctuations.

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“…This theory has many applications ranging from nano-scale systems to cosmology [17]. Very recent applications to Maxwell's equations in order to gain the independent manipulation of the optical phase evolution and energy confinement [18] as well as the tunnelling ionization and dynamics of the electron probability [19] have been studied. Its ability as a useful tool for open quantum systems has already been emphasized [20].In this work, the Schrödinger-Langevin-Bohm (SLB) equation is obtained by substituting the polar form of the wave function into the SL nonlinear differential equation [21].…”

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confidence: 99%

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

Mousavi

Miret‐Artés

2019

Eur. Phys. J. Plus

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A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. If a time-dependent Gaussian ansatz for the probability density is assumed, the effect of thermal fluctuations together with thermal wave packets leads to Bohmian stochastic trajectories. From this trajectory based analysis, quantum and classical diffusion coefficients for free particles, thermal arrival times for a linear potential and transmission probabilities and characteristic times such as arrival and dwell times for a parabolic repeller are then presented and discussed. I. INTRODUCTIONIt seems that the first attempt for generalizing Chandrasekhar's phenomenological theory [1] of Brownian motion to the quantum realm was made by introducing a stochastic term in the Caldirola-Kanai framework [2]. It was shown that for the Boltzmann statistics, quantum stochastic dynamics lead to a diffusion constant which is the same as that obtained from the classical Brownian motion. The effect of noise on the Brownian motion of a quantum oscillator via the corresponding Caldirola-Kanai equation with a noise term was also studied [3].On the other hand, Kostin [4,5] derived heuristically the so-called non-linear Schrödinger-Langevin equation (SL) from the quantum Langevin equation through Heisenberg position and momentum operators. This equation fulfills the unitarity condition, satisfies the uncertainty relation but violates the superposition principle due to its non-linear nature [6]. Recently, a different generalized Schrödinger equation has been proposed to describe dissipation in quantum systems [7] where the Kostin equation without the random potential is a special case of this generalized equation. Thanks to its straightforward formulation and its numerical simplicity, the Kostin equation "can be considered as a solid candidate for effective description of open quantum systems hardly accessible to quantum master equations" [8]. Although this equation has been widely used in the literature to study pure dissipative effects [8][9][10][11], only a few works are found where the presence of a stochastic or random force is introduced [8]. A generalized Schrödinger-Langevin equation has been proposed in the literature for nonlinear interaction providing a state-dependent dissipation process exhibiting multiplicative noise [12]. Afterwards, this equation has been extended to a non-Markovian problem [13].Bohmian mechanics [14][15][16] as an alternative interpretation of quantum mechanics has the advantage to give a clear picture of quantum phenomena in terms of trajectories in configuration space. This theory has ...

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Dynamics of tunneling ionization using Bohmian mechanics

Cited by 41 publications

References 46 publications

Simple man model in the Heisenberg picture

Simple man model in the Heisenberg picture

Canonical tunneling time in ionization experiments

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

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