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Scientific Reports

Entanglement in photo-ionization process

Igor A. Ivanov, Kyung Taec Kim

Published May 18, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-024-62198-6

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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.
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.
The recently available high-intensity quantum light pulses provide novel tools for controlling light-matter interactions. However, the rigor of the theoretical frameworks currently used to describe the interaction of strong quantum light with atoms and molecules remains unverified. Here, we establish a rigorous benchmark by solving the fully quantized time-dependent Schrödinger equation for an atom exposed to bright squeezed vacuum light. Our \textit{ab initio} simulations reveal a critical limitation of the widely used QQQ-representation: although it accurately reproduces the total photoelectron spectrum after tracing over photon states, it completely fails to capture the electron-photon joint energy spectrum. To overcome this limitation, we develop a general theoretical framework based on the Feynman path integral that properly incorporates the electron-photon quantum entanglement. Our results provide both quantitative benchmarks and fundamental theoretical insights for the emerging field of strong-field quantum optics.
Using the analytically obtained solution of the Schrödinger equation for an electron in a quantized electromagnetic field, the ionization of an atom has been considered in the framework of a simple one-dimensional model. Expressions for the ionization rate and photoelectron spectrum have been derived and analyzed. We discuss a difference between the results obtained in the model in which the electromagnetic field is described classically and the results obtained in the model of quantized electromagnetic field. In particular, in the latter model the photoelectron spectrum can have a minimum at a certain number of absorbed photons. The minimum is a consequence of destructive interference between the contributions of two parts of the interaction operator.
In this paper, effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Under strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated by using the quantum reduced entropy and the quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and mutiphoton (k>2) are revealed respectively. The preparation of entangled states is discussed. The Einstein-Podolsky-Rosen states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.
Objectives: To study of entanglement between two electronic qubits,without observing spin orbit interaction (SOI), produced by double photo ionization from Xeon atom following the absorption of a photon. Methods: In absence of SOI, Russel-Salunders coupling (L-S coupling) is applicable. As the estimations of entanglement we have considered PeresHorodecki condition and negativity. In case of L-Scoupling, all the properties of electronic qubits are predicted merely with the knowledge of the spins of the target atom, the residual photoion, emitted electrons and the state of polarization of the absorbed photon. Findings: We have found that the electronic qubits may be totally entangled, partially entangled or separable depending on spin states of target Xe, residualdication Xe2+,emitted electrons and the state of polarization of incident photon as well as of the direction sspin quantization and ejection of the photoelectrons. Applications/ Improvements: Studies of quantumen tanglement and its paradoxical properties hold the key to various Quantum information (QI) tasks such as quantum teleportation, quantum cryptography and quantum computer technology. Keywords: Density Operator PACS No. 32.30, L-S Coupling, Negativity, Peres-Horodecki Condition
We describe a procedure that allows us to solve the three-dimensional time-dependent Schrödinger equation for an atom interacting with a quantized one-mode electromagnetic field. Atom-field interaction is treated in an ab initio way prescribed by quantum electrodynamics. We use the procedure to calculate probability distributions of absorbed photons in the regime of tunneling ionization. We analyze evolution of the reduced photon density matrix describing the state of the field. We show that non-diagonal density matrix elements decay quickly, as a result of the decoherence process. A stochastic model, viewing ionization as a Markovian birth-death process, reproduces the main features of the calculated photon distributions.