arXiv subjects

Varun Makhija

Publications and source records attributed to Varun Makhija.

12 recordsLinked to original sources

arXiv2025

Molecular Axis Distribution Moments in Ultrafast Transient Absorption Spectroscopy: A Path Towards Ultrafast Quantum State Tomography

In ultrafast experiments with gas phase molecules, the alignment of the molecular axis relative to the polarization of the interacting laser pulses plays a crucial role in determining the dynamics following this light-matter interaction. The molecular axis distribution is influenced by the interacting pulses and is intrinsically linked to the electronic coherences of the excited molecules. However, in typical theoretical calculations of such interactions, the signal is either calculated for a single molecule in the molecular frame or averaged over all possible molecular orientations to compare with the experiment. This averaging leads to the loss of information about anisotropy in the molecular-axis distribution, which could significantly affect the measured experimental signal. Here, we calculate the laboratory frame transient electronic first-order polarization ($P^{(1)}$) spectra in terms of separated molecular frame and laboratory frame quantities. The laboratory frame polarizations are compared with orientation-averaged Quantum Master Equation (QME) calculations, demonstrating that orientation-averaging captures only the isotropic contributions. We show that our formalism allows us to also evaluate the anisotropic contributions to the spectrum. Finally, we discuss the application of this approach to achieve ultrafast quantum state tomography using transient absorption spectroscopy and field observables in nonlinear spectroscopy.

physics.chem-ph↗

arXiv2024

Time resolved quantum tomography in molecular spectroscopy by the Maximal Entropy Approach

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography: the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules; and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem: a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science.

physics.chem-ph↗

arXiv2023

Ultrafast Field-Resolved Nonlinear Optical Spectroscopy in the Molecular Frame

We resolve the real-time electric field of a femtosecond third-order nonlinear optical signal in the molecular frame. The electric field emitted by the induced third-order polarization from impulsively pre-aligned gas-phase molecules at room temperature, in a degenerate four-wave mixing (DFWM) scheme, is measured using a spectral interferometry technique. We show that by measuring both the amplitude and phase of the emitted femtosecond pulse, information related to electronic symmetries can be accessed. The nonlinear signal is measured around a rotational revival to extract its molecular-frame angle dependence from pump-probe time delay scans. By comparing these measurements for two linear molecules, carbon dioxide (CO2) and Nitrogen (N2), we show that the measured second-order phase parameter (temporal chirp) of the signal is sensitive to the valence electronic symmetry of the molecules, whereas the amplitude of the signal does not show such sensitivity. We compare these measurements to theoretical calculations of the chirp observable in the molecular frame. This work is an important step towards using field-resolved nonlinear optical measurements to study ultrafast dynamics in electronically excited molecules.

physics.optics↗

arXiv2023

Ultrafast Molecular Frame Quantum Tomography

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically non-adiabatic wavepacket in ammonia (NH$_3$). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH$_3$, we observe that electronic coherences are induced by nuclear dynamics which non-adiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is non-adiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer time scales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

physics.chem-ph↗

arXiv2023

Applying Bayesian Inference and deterministic anisotropy to retrieve the molecular structure $|Ψ(\boldsymbol{R})|^2$ distribution from gas-phase diffraction experiments

Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. In this work, we develop a broadly applicable method that addresses this inverse problem by approximating the molecular frame structure $|Ψ(\boldsymbol{R}, t)|^2$ distribution independent of these complex simulations. We retrieve the vibronic ground state $|Ψ(\boldsymbol{R})|^2$ for both simulated stretched NO$_2$ and measured N$_2$O. From measured N$_2$O, we observe 40 mAngstroms coordinate-space resolution from 3.75 inverse Angstroms reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO$_2$, typical to high signal-to-noise levels predict 100--1000X resolution improvements, down to 0.1 mAngstroms. By directly measuring the width of $|Ψ(\boldsymbol{R})|^2$, we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.

physics.atom-ph↗

arXiv2023

Topical Review: Extracting Molecular Frame Photoionization Dynamics from Experimental Data

Methods for experimental reconstruction of molecular frame (MF) photoionization dynamics, and related properties - specifically MF photoelectron angular distributions (PADs) and continuum density matrices - are outlined and discussed. General concepts are introduced for the non-expert reader, and experimental and theoretical techniques are further outlined in some depth. Particular focus is placed on a detailed example of numerical reconstruction techniques for matrix-element retrieval from time-domain experimental measurements making use of rotational-wavepackets (i.e. aligned frame measurements) - the ``bootstrapping to the MF" methodology - and a matrix-inversion technique for direct MF-PAD recovery. Ongoing resources for interested researchers are also introduced, including sample data, reconstruction codes (the \textit{Photoelectron Metrology Toolkit}, written in python, and associated \textit{Quantum Metrology with Photoelectrons} platform/ecosystem), and literature via online repositories; it is hoped these resources will be of ongoing use to the community.

physics.chem-ph↗

arXiv2022

A Laboratory Frame Density Matrix for Ultrafast Quantum Molecular Dynamics

In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experimentally accessible are rejected by the orientation-averaged reduced vibronic density matrix. Instead, Molecular Angular Distribution Moments (MADMs) are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography, and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.

physics.chem-ph↗

arXiv2021

Molecular Frame Photoelectron Angular Distributions in Polyatomic Molecules from Lab Frame Coherent Rotational Wavepacket Evolution

The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and consequently takes a relatively simple numerical form (matrix transform making use of the Moore-Penrose inverse). Significantly, the simplicity allows application of the method to the successful reconstruction of MFPADs for polyatomic molecules. The scheme is demonstrated numerically for two realistic cases, $N_2$ and $C_2H_4$. The new technique is expected to be generally applicable for a range of MF reconstruction problems involving photoionization of polyatomic molecules.

physics.chem-ph↗

arXiv2018

Quantum Beat Photoelectron Imaging Spectroscopy of Xe in the VUV

Time-resolved pump-probe measurements of Xe, pumped at 133~nm and probed at 266~nm, are presented. The pump pulse prepared a long-lived hyperfine wavepacket, in the Xe $5p^5(^2P^{\circ}_{1/2})6s~^2[1/2]^{\circ}_1$ manifold ($E=$77185 cm$^{-1}=$9.57 eV). The wavepacket was monitored via single-photon ionization, and photoelectron images measured. The images provide angle- and time-resolved data which, when obtained over a large time-window (900~ps), constitute a precision quantum beat spectroscopy measurement of the hyperfine state splittings. Additionally, analysis of the full photoelectron image stack provides a quantum beat imaging modality, in which the Fourier components of the photoelectron images correlated with specific beat components can be obtained. This may also permit the extraction of isotope-resolved photoelectron images in the frequency domain, in cases where nuclear spins (hence beat components) can be uniquely assigned to specific isotopes (as herein), and also provides phase information. The information content of both raw, and inverted, image stacks is investigated, suggesting the utility of the Fourier analysis methodology in cases where images cannot be inverted.

physics.atom-ph↗

arXiv2017

Time-resolved multi-mass ion imaging: femtosecond UV-VUV pump-probe spectroscopy with the PImMS camera

The Pixel-Imaging Mass Spectrometry (PImMS) camera allows for 3D charged particle imaging measurements, in which the particle time-of-flight is recorded along with $(x,y)$ position. Coupling the PImMS camera to an ultrafast pump-probe velocity-map imaging spectroscopy apparatus therefore provides a route to time-resolved multi-mass ion imaging, with both high count rates and large dynamic range, thus allowing for rapid measurements of complex photofragmentation dynamics. Furthermore, the use of vacuum ultraviolet wavelengths for the probe pulse allows for an enhanced observation window for the study of excited state molecular dynamics in small polyatomic molecules having relatively high ionization potentials. Herein, preliminary time-resolved multi-mass imaging results from C$_2$F$_3$I photolysis are presented. The experiments utilized femtosecond UV and VUV (160.8~nm and 267~nm) pump and probe laser pulses in order to demonstrate and explore this new time-resolved experimental ion imaging configuration. The data indicates the depth and power of this measurement modality, with a range of photofragments readily observed, and many indications of complex underlying wavepacket dynamics on the excited state(s) prepared.

physics.chem-ph↗

arXiv2017

Bootstrapping to the Molecular Frame with Time-domain Photoionization Interferometry

Photoionization of molecular species is, essentially, a multi-path interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets ($N_2$) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wavepacket controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle this methodology provides a time-domain route to complete photoionization experiments, and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.

physics.chem-ph↗

arXiv2016

Orientation Resolution through Rotational Coherence Spectroscopy

The rich information content of measurements in the molecular frame rather than the laboratory frame has motivated the development of several methods for aligning gas phase molecules in space. Even so, for asymmetric tops the problem of making molecular frame measurements remains challenging due to its inherently multi-dimensional nature. In this Letter we present a method, based on the analysis of observables measured from rotational wavepackets, that does not require either 3D alignment or coincident momentum measurements to access the molecular frame. As an application we describe the first fully-orientation-resolved measurements of strong-field ionization and dissociation of an asymmetric top (ethylene).

physics.atom-ph↗