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arXiv:1707.04155 · Physical Review A

Quantum entanglement in strong-field ionization

Szilárd Majorosi, M. G. Benedict, Attila Czirják

Published Oct 13, 2017• 20 citations
arXivHTMLPDF

Abstract

We investigate the time evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion core. Since the standard procedure is numerically prohibitive in this case, we propose a method to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric-field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime.

DOI
10.1103/physreva.96.043412

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We investigate the time evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion core. Since the standard procedure is numerically prohibitive in this case, we propose a method to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric-field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime.
We study the time evolution of entanglement in a model system consisting of an electron and its parent ion during the quantum mechanical process of rescattering due to a strong few-cycle laser pulse. We characterize the entanglement by calculating both the linear entropy and the Neumann entropy for several values of the pulse intensity. We find that the emerging oscillations in the entropy exhibit local maxima at the zero crossings of the electric field of the laser pulse. The time-dependent Wigner function, which is the best tool in connecting the classical and the quantum features of a process, is also calculated and analysed in this model.
Abstract The rapid advancements of ultrafast intense laser technology have opened new avenues for investigating entanglement in laser-induced systems. However, the application of these advances in quantum technology requires a reliable and universally applicable method for enhancing and regulating entanglement. Here we demonstrate how a few-cycle intense laser field can significantly enhance the degree of entanglement compared to its multi-cycle counterpart, using the example of electron–electron entanglement of orbital angular momentum (OAM) states in recollision-excitation non-sequential double ionization of Ar atoms. By confining the ionization dynamics to a specific narrow time window, the few-cycle pulse purifies the electron trajectories, thereby ensuring high coherence between entangled OAM channels and enhancing entanglement. Furthermore, the degree of entanglement can be efficiently modulated by varying the carrier envelope phase of the few-cycle laser pulse, which is achieved by altering the population across OAM channels. Optimizing coherence through electron trajectory purification with a designed specific temporal waveform of laser field provides a general pathway for enhancing entanglement in laser-induced systems.
Attosecond physics enables the study of ultrafast coherent electron dynamics in matter upon photoexcitation and photoionization, revealing spectacular effects such as hole migration and coherent Auger dynamics in molecules. In the photoionization scenario, there has been a strong focus on probing the physical manifestations of internal quantum coherence within the individual parent ion and photoelectron systems. However, quantum correlations between these two subsystems emerging from attosecond photoionization events have thus far remained much more elusive. In this work, we design theoretically and model numerically a direct probe of quantum entanglement in attosecond photoionization in the form of a Bell test. We simulate from first principles a Bell test protocol for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime predicting robust violation of the Bell inequality. This theoretical result paves the way for the direct observation of entanglement in the context of ultrafast photoionization of many-electron systems. Our work provides a novel perspective on attosecond physics directed toward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics, including in the chemical decomposition pathways of molecular ions. Published by the American Physical Society 2024
We study the entanglement between an electron and the photon it scatters, resolved in real space and time. Starting from nonrelativistic QED in Fermi's oscillator representation, we write Fock's coupled equations for components with fixed photon number in the photon configuration space, in the length gauge, where the photon is created around the atom through a nonlocal kernel. Truncated at one photon, the equations are solved numerically without the rotating-wave approximation for a one-dimensional model atom in a waveguide with a single transverse mode and enhanced coupling. The atom is driven by a short, off-resonant laser pulse, with the electron and photon represented on real-space grids. The global electron-photon entanglement is largely transient. It peaks during the pulse and decreases as the polarized electron cloud returns to the core, leaving a state close to a product of the electron state and a superposition of the field vacuum with a single scattered photon. Local entanglement, obtained from walkers sampled across both photon-number components, exhibits opposite spatial patterns for the two particles. The electron entropy is smallest at the nucleus and maps the local strength of the dipole coupling, whereas the photon entropy is largest near the atom, where photons are created and absorbed, and smaller in the outgoing wave packets.
Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.
We report a study of the entanglement between the quantized photon field and an atom arising in the photo-ionization process. Our approach is based on an ab initio solution of the time-dependent Schrödinger equation (TDSE) describing the quantum evolution of a bipartite system consisting of the atom and the quantized electromagnetic field. Using the solution of the TDSE, we calculate the reduced photon density matrix, which we subsequently use to compute entanglement entropy. We explain some properties of the entanglement entropy and propose an approximate formula for the entanglement entropy based on the analysis of the density matrix and its eigenvalues. We present the results of a comparative study of the entanglement in the photo-ionization process for various ionization regimes, including the tunneling and the multiphoton ionization regimes.