Session E04: Focus Session: Coherence and Entanglement in Attosecond Spectroscopy

Control of ion+photoelectron entanglement in attosecond experiments

Quantum mechanical entanglement is a vibrant research topic, which received a lot of attention in recent years and was rewarded with last years Nobel prize. Entanglement is not only a key element in quantum computing or teleportation. It also plays a crucial role in pump-probe experiments, which involve ionization.

In attosecond science, it is common to use radiation in the extreme ultra-violet (XUV) regime. Due to their high photon energy, attosecond pulses are highly ionizing radiation for any sample placed in their way, creating multicomponent quantum systems. Entanglement between different sub-systems can have measurable consequences, especially when the experiment only includes measurements in one of the sub-systems, which means for example in the case of molecular photoionization only measuring the ion or photoelectron.

To emphasize the role of entanglement in photoionization, we designed an experimental protocol, which utilizes a pair of phase-locked XUV pulses and a near-infrared (NIR) pulse to ionize hydrogen molecules. We investigated the limiting role entanglement between the ion and photoelectron has in regards to vibrational coherence and electronic coherence. In the former case the two XUV pulses generate a coherent superposition of vibrational states in the 1sσ_g state of the H₂⁺ ion, which is subsequently probed by the NIR pulse. In the latter case the XUV pulses create an entangled ion+photoelectron system, which is converted by the NIR pulse into a coherent superposition of the gerade and ungerade electronic states of the H₂⁺ ion.

In both cases the degree of ion+photoelectron entanglement is controlled by changing the time delay between the two XUV pulses and as a consequence the degree of vibrational or electronic coherence is altered. Our studies show the crucial role of entanglement in attosecond science and are a first approach to link ultrafast science with quantum information.   

Ultrafast Molecular Frame Quantum Tomography

Quantum Tomography is the experimental determination of the quantum state of a system, specifically its density matrix. Using a combination of high-resolution spectroscopic measurements and ultrafast pump-probe measurements on the same pair of resonantly excited electronic states of the ammonia molecule, we determine the time and orientation-angle dependent Lab Frame Density Matrix after resonant excitation. With this density matrix in hand, we construct the time evolving molecular frame electronic probability density for molecules at various orientations. We observe that the electronic probability density rotates around the molecular symmetry axis in different directions for molecules at different orientations, and does not rotate at all in some orientations. We are able to correlate this motion with the behavior of the electronic coherence, the off-diagonal element of the density matrix, at the different orientations. Such a quantum tomography is a perquisite for exploring quantum information processing in isolated molecules; allows studies of entanglement between molecular degrees of freedom; can be used to implement quantum control protocols and can facilitate direct imaging of charge migrating across the molecular frame.   

Pure charge migration and non-adiabatic dynamics in biologically relevant molecules

Correlation driven charge migration dynamics has been widely studied computationally and experimentally for a number of biological systems over the past decade[1]. Studying the pure charge migration dynamics within the sub-femtosecond timescale reveals the basic chemical behavior of the molecule. Understanding this behavior can later help in monitoring the subsequent dynamics and/or manipulate it with suitable laser field. In this study we present the correlation driven attosecond to sub-femtosecond pure charge migration dynamics in uracil[2,3] and thymine tautomers. To study this we have used the large cc-pvdz basis set, correlation effects as implemented by the non-Dyson ADC approach[4]. Furthermore, we present the electron-nuclei coupled non-adiabatic dynamics in uracil decoding the interstate population transfer in time domain between the states excited by the broadband of the incident laser field[5].

References

[1] F. Calegari et al. Science 346.6207 (2014) 336-339.

[2] K. Chordiya et al. Phys. Rev. A 105 (2022) 062808

[3] K. Chordiya et al. Phys. Chem. Chem. Phys., 10.1039/D2CP02681C (2022)

[4] J. Schirmer, A. B. Trofimov, and G. Stelter. J. Chem. Phys. 109.12 (1998), 4734–4744.

[5] G. A. Worth, et al. 15 (2004), 583-617.   

Author not Attending

Quantum states of the light, e.g., single photons, entanglement and squeezing, opens up a new avenue for spectroscopy by utilizing the parameters of quantum optical fields as novel control knobs and through the variation of photon statistics. With the advance of cavity quantum electrodynamics and light source technology, imaging and controlling the electron and vibrational motions of molecules can be achieved, towards unprecedented resolution and precision, not accessible by the classical light pulses [1]. In this talk, I will present our recent works on multidimensional spectroscopy using quantum states of light, including 2D photon-coincidence counting and Raman spectroscopy [2,3]. Microscopic models for molecular relaxation will be incorporated for a unified understanding of the signals.   

Ultrafast Phase Control: Quantum Coherence in Helium Atoms, and Entangled States in Hydrogen Molecules, Modified by Attosecond Delays

Coherence arises when a quantum system is excited into a superposition of states.  Entanglement additionally requires a spatial separation of the quantum system into (at least) two parts, each of which can be separately measured, and the measurement of one will have consequences on the other part.

Atoms&molecules naturally exhibit quantum correlated ground and excited states.  If these correlated states are coherently excited and then the system splits into (at least) two spatially separated entities, they can quickly turn into building blocks (e.g. quantum bits) of quantum-technological applications operating at the ultimate speed limit of the electromagnetic interaction: the time-scale of electronic motion.

Here, I will discuss some of our recent experiments that address these questions, focusing on two systems: Helium atoms and hydrogen molecules.

In transient-absorption measurements on Helium, we introduced a mechanism to manipulate phase shifts of coherently excited quantum states on few-fsec to asec time scales.  Even complex (multi-level) systems can be controlled and their dynamics reconstructed.  At the highest intensities, the lifetime of coherence is reduced due to mechanisms such as ionization and dephasing caused by complex coupling to other states.

For H₂ in a reaction microscope, we measure both spatially separating photoproducts (a free electron and a proton) in coincidence after interaction with a two-color field, composed of an XUV asec-pulse train and an NIR laser pulse.  Depending on the asec timing between the two fields, we observe substantial changes in the emission direction of the proton with respect to the electron.

The experimental observation can be explained by the quantum interference of externally controllable dissociation pathways.  The wavefunction of the two electrons can be described as a Bell-type state |1,2> + exp(-i*phi) |2,1>, where the phase phi can be modified by the sub-femtosecond time-delay between the attosecond pulse train and the laser field.

Our results show that it is possible to manipulate relative quantum phases of coherent and entangled states in fundamental atomic and molecular systems on femtosecond-to-attosecond time scales, which may, after much further development, form the basis of future optically programmable molecular-scale quantum processors.   

Long Lived Electronic Coherences in Molecules Studied with Pulse Shape Spectroscopy

Electronic coherences tend to decay much more rapidly in molecules than in atoms as a consequence of averaging over the different rates of phase advance for different internuclear separations associated with non-local nuclear wave functions. However, pairs of states whose potential energy surfaces are parallel can exhibit long lived electronic coherences. We use few cycle pulses from an ultrafast pulse shaper to study such long lived coherences.  Our experiments measure the photoelectron spectrum as a function of pulse shape, which show clear modulations in the yield as a result of interfering contributions from excited states.  We interpret our measurements using strong-field ionization dynamics calculations, which include multiphoton resonance, dynamic Stark shifts, as well as vibrational dynamics during the ionization process. The calculations illuminate how pairs of nearly parallel excited states maintain electronic coherence for hundreds of femtoseconds.   

Simulating ultrafast electron dynamics in molecules using high-order time-dependent density-functional theory schemes

Time-dependent density-functional theory (TDDFT) has emerged as a tool of choice in the simulation and analysis of ultrafast electron dynamics in molecules [1,2]. But the TDDFT equations are nonlinear and obtaining accurate solutions using high-order numerical schemes is challenging. In this presentation I will discuss how high-order symplectic split-operator schemes can be used to simulate ultrafast electron dynamics accurately and efficiently on grids using TDDFT [3]. These symplectic schemes are exactly unitary and time reversible while keeping memory requirements low. I will illustrate the performance of these schemes with far-from equilibrium electronic dynamics in one-dimensional carbon chains.