research

Chiral molecules are molecules that can exist in two mirror-image forms, much like our left and right hands. These two forms, called enantiomers, have the same chemical composition but differ in their handedness. Chirality is especially important in biology and chemistry, where the two enantiomers of a molecule can interact differently with other chiral systems and can therefore have very different biological effects.

Being able to distinguish between enantiomers is therefore important, motivating the search for new ways to detect and characterize molecular handedness. One approach is to ionize a molecule with light and examine the emitted electron. The direction in which the electron is emitted can already carry information about the molecule's chirality.

In this project, we explore an additional property of the emitted electron: its spin. We ask whether the spin polarization of photoelectrons can provide new observables that are sensitive to molecular handedness, and what determines these spin-dependent signatures. By studying randomly oriented molecules in the gas phase, we identify which spin-polarization effects survive molecular orientation averaging and can therefore serve as signatures of chirality in an isotropic sample.

When randomly oriented chiral molecules are ionized by circularly polarized light, the angular distribution of the emitted photoelectrons displays a pronounced forward-backward asymmetry along the light-propagation axis, known as photoelectron circular dichroism (PECD)  [1,2,3]. This asymmetry, which switches sign upon reversal of either the light helicity or the molecular handedness, arises entirely within the electric-dipole approximation, and exceeds conventional absorption circular dichroism by up to two orders of magnitude  [4]. PECD was first predicted theoretically in the 1970s-80s  [1,2] and detected experimentally by Böwering et al. in 2001  [5]. Since then, it has been extended to multiphoton and strong-field ionization regimes  [6,7,8,9,10], and to liquid and aqueous-phase targets  [11,12], and has been proposed as a key mechanism in an astrophysical scenario for the origin of life's homochirality  [13]. This maturity, recently surveyed in Ref.  [14], makes PECD the natural reference point for the present project: can molecular handedness also be converted into large spin- and enantio-sensitive observables in gas-phase conditions when the photoelectron spin is resolved?

This question is closely related to chirality-induced spin selectivity (CISS), which describes a broad range of phenomena wherein molecular handedness governs spin polarization  [15,16,17,18]. First observed in spin-dependent electron transmission through organized films of chiral molecules by Ray et al. in 1999  [19,20], CISS has attracted considerable attention because of its potential applications in molecular spintronics, enantioselective chemistry, catalysis, and energy conversion  [15,17,18,21]. Despite preceding the first gas-phase detection of PECD by Böwering et al. in 2001  [5], the theoretical development of CISS has followed a markedly different trajectory. PECD is now understood within an electric-dipole photoionization framework, arising from interference between the partial waves of the outgoing photoelectron whose relative phases are shaped by the chiral molecular potential  [1,2,3,4,5,14]. By contrast, a microscopic theory of CISS remains incomplete since the experimentally reported spin polarizations are often much larger than expected from the weak intrinsic spin-orbit coupling of light-element organic molecules  [15,16]. This discrepancy has motivated a broad range of proposed mechanisms, including helical scattering potentials  [22,23,24], geometry-induced effective spin-orbit coupling  [25], vibronic and polaronic effects  [26,27,28], and electron correlations  [29,30] among many others  [31], yet there is still no consensus on which mechanisms are essential in different experimental settings  [15,16,17,18].

The interpretation of CISS signals in experiments is also nontrivial. Direct measurements typically rely on spin polarimetry, e.g., Mott polarimetry, which requires ordered molecular films, surfaces, or junction-like geometries  [20]. Indirect measurements, e.g., magnetoresistance measurements, can access CISS-related effects in device-relevant settings, but the measured signal is then influenced not only by molecular chirality but also by ferromagnetic contacts, substrate spin-orbit coupling, molecule-surface hybridization, interfacial electric fields, molecular packing, and device geometry  [15,16,17,18,21,31,32]. Disentangling intrinsic molecular spin selectivity from environmental and interfacial amplification therefore remains one of the central challenges of the field.

These challenges motivate the current project to consider chiral molecules in gas phase where substrate, interface, contact, and molecular-packing effects are absent. This direction has important historical precedent in the gas-phase electron-scattering experiments of Farago, Kessler, and co-workers, which predate the modern CISS literature  [33,34,35,36,37,38]. These experiments established that spin-polarized electrons interact differently with opposite enantiomers, but also showed that the corresponding asymmetries in isotropic gas-phase samples are very small, typically of order (10^-4), and are enhanced in molecules containing heavy atoms, where spin-orbit coupling is stronger  [33,34,35]. Further theoretical work showed that oriented molecular targets can amplify spin-dependent chiral asymmetries  [36], pointing to a central question in CISS: is large spin selectivity an intrinsic single-molecule response, or does it require amplification by molecular orientation, interfaces, and transport geometry?

Spin-resolved photoionization of gas-phase chiral molecules thereby presents a complementary route to address this question. As in PECD where the momentum of the outgoing photoelectron can be correlated to the light propagation axis, including the photoelectron spin opens a larger class of symmetry-allowed spin- and enantio-sensitive observables. Spin-resolved photoionization is thus uniquely positioned between PECD and CISS: it retains the clean, substrate-free conditions that makes PECD a benchmark probe of molecular chirality while also addressing the spin degree of freedom that lies at the heart of CISS. The theoretical foundations for this direction has been previously considered by Cherepkov for one-photon ionization  [39]. Recent work on spin-polarized PECD has demonstrated the promise of this direction in strong-field multiphoton ionization, i.e., for randomly oriented 1-iodo-2-methylbutane enantiomers, a 10% spin polarization was reported, albeit not enantio-sensitive while the same framework predicts a 15% spin-dependent, enantio-sensitive PECD for uniaxially oriented molecules  [40].

Building on these foundations, our work revisits spin-resolved one-photon ionization of randomly oriented chiral molecules and identifies the universal geometric mechanisms that generate large spin- and enantio-sensitive observables within the electric-dipole regime (see the publications below). These observables are governed by pseudovectors stemming from the geometric properties of the photoionization dipoles in real space and in spin space, providing a compact physical picture that connects the established PECD framework to the spin selectivity at the heart of CISS.

Equivalently, chiral molecules possess an intrinsic “compass axis” that aligns the electron spin without any magnetic field. For a single chiral molecule fixed in space, this compass orients the spin of the emitted (or excited) electron differently for opposite enantiomers — the same kind of enantio-sensitive spin polarization observed in the CISS effect.

• P. C. M. Flores, S. Carlström, S. Patchkovskii, M. Ivanov, A. F. Ordonez, O. Smirnova, Geometric mechanisms enabling spin- and enantio-sensitive observables in one-photon ionization of chiral molecules, Phys. Rev. A 114, 013110 (2026).
  • Spin- and enantio-sensitive observables in one-photon ionization of randomly oriented chiral molecules arise purely from the electric-dipole interaction.
  • They are governed by the geometric properties of the photoionization dipoles in real space and in spin space.
  • All allowed spin- and momentum-resolved observables reduce to moments of three pseudovectors, making spin-resolved photoionization a fundamentally richer problem than PECD.
• P. C. M. Flores, S. Carlström, S. Patchkovskii, M. Ivanov, A. F. Ordonez, O. Smirnova, Spin-current correlations in photoionization of chiral molecules, arXiv:2505.23460
  • The photoelectron current is enantio-sensitively “locked” to the photoelectron spin, mediated by two complementary geometric mechanisms.
  • The strength of the spin-current correlations is a molecular pseudoscalar: the flux of the momentum-resolved Bloch vector through the energy shell.
  • Photon spin adds triple correlations between the photoelectron momentum, its spin and the photon spin.
• P. C. M. Flores, S. Carlström, S. Patchkovskii, M. Ivanov, V. Mujica, A. F. Ordonez, O. Smirnova, Enantiosensitive molecular compass, arXiv:2505.22433
  • Spin-orbit coupling in electric-dipole photoionization creates correlations between molecular orientation and photoelectron spin that survive complete isotropic averaging, identified as the microscopic origin of CISS in photoionization.
  • Selecting the photoelectron spin orients the cation ensemble (spin-orientation locking), whereas selecting molecular orientation produces CISS; both share one correlation strength set by the molecular-frame photoionization Bloch vector, the enantio-sensitive molecular compass.

Work done at the Max Born Institute, Berlin, in the Strong Field Theory group with Prof. Dr. Olga Smirnova, supported by her ERC Advanced Grant ULISSES (Grant Agreement No. 101054696).

Classical mechanics treats time as a parameter that marks the evolution of a system, a label with respect to which change is described. It is the variable 't' that we use in Newton's equation of motion to describe the change in a particle's position, and in Maxwell's equations to describe the evolution of electromagnetic fields. While the concept of time as a parameter in classical mechanics is largely uncontroversial, it carries with it several fundamental questions, such as the apparent asymmetry in the direction of time and the logical inconsistencies associated with traveling backwards in time. The former is particularly intriguing because the fundamental equations of classical mechanics are generally invariant under time reversal, whereas our everyday experience distinguishes a definite direction of time. The discovery of quantum mechanics has introduced yet another fundamental difficulty concerning the role of time, commonly referred to as the quantum time problem (QTP).

A simple example that illustrates the QTP is to ask: when does a particle arrive at a particular location? In classical mechanics, this question can be answered by inverting the particle's equation of motion. For instance, a freely moving particle with constant velocity arrives at a given location after a time equal to the distance traveled divided by its velocity. At first glance, the problem appears straightforward. However, quantum mechanics offers no universally accepted prescription for answering the same question. Unlike a classical particle, a quantum particle is described by a wavefunction that can be spatially delocalized, making it impossible, in general, to assign a definite trajectory and consequently a unique arrival time. Instead, one expects the possible arrival times to be described probabilistically.

The difficulty becomes more apparent when we consider the fundamentally different roles played by time in classical and quantum mechanics. In the standard formulation of quantum mechanics, time remains an external parameter that describes the evolution of a quantum state, rather than an observable represented by an operator. This is in contrast to physical quantities such as position, momentum, and energy, which are represented by operators whose measurement outcomes are governed by the postulates of quantum mechanics. Yet classical intuition tells us that time can certainly be measured using a clock. If the time at which a quantum particle arrives at a particular location is a measurable physical quantity, how should we describe its possible measurement outcomes and their corresponding probabilities? More importantly, can we construct a quantum mechanical operator that represents the time of arrival?

This project (my Bachelor to PhD work at the University of the Philippines Diliman, with Eric Galapon) builds time-of-arrival (TOA) operators: we take the classical formula for when a particle reaches a point and turn it into a quantum operator, then ask what it predicts. Two questions drove most of the work: (i) Do quantum objects fall like classical ones? and (ii) How long does quantum tunneling take?

• P. C. M. Flores, D. A. Pablico, E. A. Galapon, Instantaneous tunneling time within the theory of time-of-arrival operators, Phys. Rev. A 110, 062223 (2024).
• P. C. M. Flores, D. A. Pablico, E. A. Galapon, Partial and full tunneling processes across potential barriers, EPL 145, 65002 (2024).
• P. C. M. Flores, E. A. Galapon, Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem, Eur. Phys. J. Plus 138, 1 (2023).
• P. C. M. Flores, E. A. Galapon, Instantaneous tunneling of relativistic massive spin-0 particles, EPL 141, 10001 (2023).
• P. C. M. Flores, E. A. Galapon, Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy, Phys. Rev. A 105, 062208 (2022).
• P. C. M. Flores, E. A. Galapon, Quantum free-fall motion and quantum violation of the weak equivalence principle, Phys. Rev. A 99, 042113 (2019).
• P. C. M. Flores, R. C. F. Caballar, E. A. Galapon, Synchronizing quantum and classical clocks made of quantum particles, Phys. Rev. A 94, 032123 (2016).