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Optics Letters

Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses

Chuan‐Cun Shu, Yu Guo, Kai‐Jun Yuan, Daoyi Dong, André D. Bandrauk

Published Jan 13, 2020• 29 citations
Publisher

Abstract

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.

DOI
10.1364/ol.386879

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Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, H2+{\rm H}_2^ +H2+​H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.
Multiphoton light-matter interactions invoke a so-called "black box" in which the experimental observations contain the quantum interference between multiple pathways. Here, we employ polarization-controlled attosecond photoelectron metrology with a partial wave manipulator to deduce the pathway interference within this quantum 'black box" for the two-photon ionization of neon atoms. The angle-dependent and attosecond time-resolved photoelectron spectra are measured across a broad energy range. Two-photon phase shifts for each partial wave are reconstructed through the comprehensive analysis of these photoelectron spectra. We resolve the quantum interference between the degenerate p→d→p and p→s→p two-photon ionization pathways, in agreement with our theoretical simulations. Our approach thus provides an attosecond time-resolved microscope to look inside the "black box" of pathway interference in ultrafast dynamics of atoms, molecules, and condensed matter.
We make a theoretical investigation of photoionization of an H2{\mathrm{H}}_{2}H2​ molecule, induced by the irradiation of an ultrashort extreme ultraviolet (XUV) laser pulse. We consider a system composed of a photoelectron ejected from H2{\mathrm{H}}_{2}H2​ and the resultant H2+{{\mathrm{H}}_{2}}^{+}H2​+ as a bipartite system. In order to clarify how the interparticle correlations among two electrons and two protons in H2{\mathrm{H}}_{2}H2​ are reflected to the bipartite system, we examine the entanglement between the photoelectron and the vibrational states of H2+{{\mathrm{H}}_{2}}^{+}H2​+ as well as the coherence in the vibrational states of H2+{{\mathrm{H}}_{2}}^{+}H2​+ by simulating the photoionization process of one-dimensional H2{\mathrm{H}}_{2}H2​. In the simulation, we solve a time-dependent Schr\"odinger equation using a symmetry-adapted grid method. On the basis of the simulations with ten different sets of three parameters characterizing an ultrashort XUV laser pulse, i.e., the pulse duration, the wavelength, and the peak intensity, we show that the extent of the entanglement depends sensitively on the coherence in the vibrational states of H2+{{\mathrm{H}}_{2}}^{+}H2​+.
By solving the three-dimensional, time-dependent Schr\"odinger equation, we have demonstrated that the ultrafast charge-transfer process in ion-atom collisions can be mapped out with attosecond extreme uv (xuv) pulses. During the dynamic-charge transfer from the target atom to the projectile ion, the electron coherently populates the two sites of both nuclei, which can be viewed as a ``short-lived'' molecular state. A probing attosecond xuv pulse can instantly unleash the delocalized electron from such a ``transient molecule,'' so that the resulting photoelectron may exhibit a ``double-slit'' interference. On the contrary, either reduced or no photoelectron interference will occur if the attosecond xuv pulse strikes well before or after the collision. Therefore, by monitoring the photoelectron interference visibility, one can precisely time the ultrafast charge-transfer process in atomic collisions with time-delayed attosecond xuv pulses.
The generation and control of extreme ultraviolet (XUV) radiation by high harmonic generation (HHG) have advanced ultrafast science, providing direct insights into electron dynamics on their natural time scale. Attosecond science has established the capability to resolve ultrafast quantum phenomena in matter by characterizing and controlling the classical properties of the high harmonics. Recent theoretical proposals have introduced novel schemes for generating and manipulating XUV HHG with distinct quantum features, paving the way to attosecond quantum optics. In this work, we transfer fundamental concepts in quantum optics into attosecond science. By driving the HHG process with a combination of an infrared bright squeezed vacuum (BSV, a non-classical state of light), and a strong coherent field, we imprint the quantum correlations of the input BSV onto both the ultrafast electron wavefunction and the harmonics' field. Performing in-situ HHG interferometry provides an insight into the underlying sub-cycle dynamics, revealing squeezing in the statistical properties of one of the most fundamental strong-field phenomena -- field induced tunneling. Our measurement allows the reconstruction of the quantum state of the harmonics through homodyne-like tomography, resolving correlated fluctuations in the harmonic field that mirror those of the input BSV. By controlling the delay between the two driving fields, we manipulate the photon statistics of the emitted attosecond pulses with sub-cycle accuracy. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.
Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.
Molecular or atomic coherence generated with the irradiation of ultrashort optical pulses should make a significant role for realizing the control of quantum states in a matter. By virtue of the advancement of the ultrashort light sources towards the short wavelength region, the energy range of the quantum states that could be coherently generated reached much more than 15 eV at the present [1] . In particular, Ramsey-type interference fringes observed by scanning the delay between a pair of phase-locked XUV femtosecond pulses unveiled spectral information of the atomic states [2] - [4] . The time ranges of the delay scans in such preceding studies were long enough to finely resolve the spectral features, while the XUV pulse pairs could not temporally overlap because the light sources were split into two before generating the XUV pulses. The near 0 delay control of the XUV pulse pair is important for investigating the dynamics of a cationic system entangled with an ionized continuum electron [5] . In this paper, we performed the delay scan of the XUV pulse pair starting from the complete temporal overlap to show that the optical interference seamlessly continued to the Ramsey-type atomic interference as a prototype of such study.