publications

2026

1. arXiv

   20. Attosecond spin dynamics in atoms and molecules

   Stefanos Carlström, Philip Flores, Serguei Patchkovskii, Felipe Morales, Olga Smirnova, and Misha Ivanov

   Roadmap on Attosecond Science, 2026

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   Twenty-five years have passed since the first experimental demonstration of attosecond pulses, marking the advent of our ability to resolve and control electron motion in real time. What began as a technological breakthrough - generating the shortest flashes ever produced - has evolved into a powerful approach for probing and steering electronic dynamics in atoms, molecules, and solids. This roadmap, authored by leading experts in the field, surveys the recent rapid progress in the generation and characterization of attosecond pulses, emerging attosecond measurement and control techniques, and their expanding range of applications. It reviews current and future developments in attosecond light sources, including novel laser technologies, waveform synthesizers, new schemes for high-order harmonic generation, attosecond pulse generation at free-electron lasers, and structured light. Advances in attosecond measurement methodologies are also discussed, encompassing all-attosecond pump-probe spectroscopy, attosecond four-wave mixing, attosecond microscopy, spectroscopy with light transients, and attosecond interferometry. Furthermore, the roadmap addresses applications of attosecond spectroscopy to reveal electron dynamics in molecules and condensed matter systems from both theoretical and experimental perspectives, and highlights emerging directions at the interface with quantum optics and quantum entanglement. Overall, this work aims to serve as a comprehensive resource for navigating the evolving landscape of attosecond science.

2. arXiv

   Geometric mechanisms enabling spin- and enantio-sensitive observables in one photon ionization of chiral molecules

   Philip Caesar M Flores, Stefanos Carlström, Serguei Patchkovskii, Andres F Ordonez, and Olga Smirnova

   arXiv:2603.02735, 2026

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   We examine spin-resolved photoionization of randomly oriented chiral molecules via circularly polarized light, and revisit earlier predictions of Cherepkov (J. Phys. B: Atom. Mol. Phys. 16, 1543, 1983). We will show that the dynamical origin of spin- and enantio-sensitive observables arise from two intrinsic mechanisms that are quantified by two pseudovectors stemming from the geometric properties of the photoionization dipoles in spin space and in real space, and an extrinsic mechanism which is a directional bias introduced by the well-defined direction of light polarization. These mechanisms arise solely from electric dipole interactions. Consequently, this means that the ten independent parameters that was earlier predicted by Cherepkov to fully describe spin-resolved photoionization of chiral molecules can be reduced as moments of these three pseudovectors. We also find that the molecular pseudoscalars describing the spin- and enantio-sensitive components of the yield can be described by the flux of these pseudovectors through the energy shell, which changes sign upon switching enantiomers. Our results provide compact expressions for these observables which provide an intuitive picture on what determines the strength of these spin- and enantio-sensitive observables. The approach can be readily generalized to photoexcitation, multiphoton processes, and arbitrary field polarizations. Regardless of the specific driving conditions, the resulting spin- and enantio-sensitive observables are still controlled by the same three pseudovectors, underscoring their universal role as the primary generators of chirality-induced spin asymmetries, emphasizing their fundamental geometric origin and the universality of the mechanism identified here.

   @article{flores2026geometric,
     title = {Geometric mechanisms enabling spin- and enantio-sensitive observables in one photon ionization of chiral molecules},
     author = {Flores, Philip Caesar M and Carlstr{\"o}m, Stefanos and Patchkovskii, Serguei and Ordonez, Andres F and Smirnova, Olga},
     journal = {arXiv:2603.02735},
     year = {2026},
     url = {https://arxiv.org/abs/2603.02735},
   }

2025

1. arXiv

   Spin-current correlations in photoionization of chiral molecules

   Philip Caesar M Flores, Stefanos Carlström, Serguei Patchkovskii, Andres F Ordonez, and Olga Smirnova

   arXiv:2505.23460, 2025

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   Chiral molecular structures enable time-odd pseudotensor that controls correlations between photoelectron spin and molecular orientation in photoionization (arXiv:2505.22433). We show that chiral structures also support time-even correlations between the photoelectron spin and its momentum. Fundamentally, these correlations can only be revealed in conditioned measurements. We argue that conditioned measurements are the sole origin of a broad class of phenomena termed chirality-induced spin selectivity (CISS), because all these phenomena require a correlated detection of the spin and another variable, e.g., electron current. We consider one-photon ionization of an isotropic ensemble of randomly oriented chiral molecules and show that the direction of the resulting photoelectron current is enantio-sensitively ‘locked’ to the photoelectron spin even under isotropic illumination. We also identify molecular frame spin texture created by photoionization in which its flux through the energy shell is the molecular pseudoscalar that quantifies the underlying spin-current correlations. Next, we consider the effect of the photon spin on these correlations and find that chiral structure also leads to triple correlations between the photoelectron momentum, its spin and the photon spin. Our results identify two molecular pseudovectors underlying the full complexity of the multitude of spin-conditioned measurements of the photoelectron current.

   @article{flores2025spin,
     title = {Spin-current correlations in photoionization of chiral molecules},
     author = {Flores, Philip Caesar M and Carlstr{\"o}m, Stefanos and Patchkovskii, Serguei and Ordonez, Andres F and Smirnova, Olga},
     journal = {arXiv:2505.23460},
     year = {2025},
     url = {https://arxiv.org/abs/2505.23460},
   }

2. arXiv

   Enantiosensitive molecular compass

   Philip Caesar M Flores, Stefanos Carlström, Serguei Patchkovskii, Misha Ivanov, Vladimiro Mujica, Andres F Ordonez, and Olga Smirnova

   arXiv:2505.22433, 2025

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   Chirality describes the asymmetry between an object and its mirror image and manifests itself in diverse functionalities across all scales of matter - from molecules and aggregates to thin films and bulk chiral materials. A particularly intriguing example is chirality-induced spin selectivity (CISS), where chiral structures orient electron spins enantio-sensitively. Despite extensive research, the fundamental origin of spin-chirality coupling, the unexpectedly large magnitude of the CISS effect, and the possible role of electromagnetic fields in it remain unclear. Here, we address these issues by examining the simplest scenario: spin-resolved photoionization of randomly oriented chiral molecules. We uncover a universal mechanism of spin-selective chiral photodynamics, arising solely from electric-dipole interactions and previously unrecognized. This mechanism embodies a chiral molecular compass - a photoinduced magnetization vector that orients the photoelectron spin. It arises in photoexcited chiral molecules even under isotropic illumination, operates even in isotropic chiral media, and enables a phenomenon central to CISS: locking of the photoelectron spin orientation to molecular geometry. It shows that chiral molecules can sustain time-odd correlations whereas achiral molecules cannot. Our findings have broad implications, from unambiguously identifying the origin of CISS effect in photoionization to harvesting correlations underlying this effect in other forms of CISS in various chiral materials.

   @article{flores2025enantiosensitive,
     title = {Enantiosensitive molecular compass},
     author = {Flores, Philip Caesar M and Carlstr{\"o}m, Stefanos and Patchkovskii, Serguei and Ivanov, Misha and Mujica, Vladimiro and Ordonez, Andres F and Smirnova, Olga},
     journal = {arXiv:2505.22433},
     year = {2025},
     url = {https://arxiv.org/abs/2505.22433},
   }

2024

1. PRA

   Instantaneous tunneling time within the theory of time-of-arrival operators

   Philip Caesar M Flores, Dean Alvin L Pablico, and Eric A Galapon

   Physical Review A, 2024

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   It has been shown in Phys. Rev. Lett., 108 170402 (2012), that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This raises the question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.

   @article{flores2024instantaneous,
     title = {Instantaneous tunneling time within the theory of time-of-arrival operators},
     author = {Flores, Philip Caesar M and Pablico, Dean Alvin L and Galapon, Eric A},
     journal = {Physical Review A},
     pages = {062223},
     year = {2024},
     url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062223},
   }

2. EPL

   Partial and full tunneling processes across potential barriers

   Philip Caesar M Flores, Dean Alvin L Pablico, and Eric A Galapon

   Europhysics Letters, 2024

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   We introduce the concept of partial-tunneling and full-tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above- and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full tunneling, and partial tunneling. The distinction among the three depends on the support of the incident wave packet’s energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial- and full-tunneling processes, respectively.

   @article{flores2024partial,
     title = {Partial and full tunneling processes across potential barriers},
     author = {Flores, Philip Caesar M and Pablico, Dean Alvin L and Galapon, Eric A},
     journal = {Europhysics Letters},
     pages = {65002},
     year = {2024},
     url = {https://iopscience.iop.org/article/10.1209/0295-5075/ad2e7a},
   }

2023

1. EPJP

   Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

   Philip Caesar M Flores, and E. A. Galapon

   The European Physical Journal Plus, 2023

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   We provide a full account of our recent report (Flores and Galapon in EPL 141:10001, 2023) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a square barrier. It was shown that the tunneling time of a relativistic spin-0 particle is instantaneous under the condition that the barrier height $V_o$is less than the rest mass energy. This implies that instantaneous tunneling is an inherent quantum effect in the context of arrival times.

   @article{flores2023quantized,
     title = {Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem},
     author = {Flores, Philip Caesar M and Galapon, E. A.},
     journal = {The European Physical Journal Plus},
     pages = {375},
     year = {2023},
     url = {https://doi.org/10.1140/epjp/s13360-023-03952-z},
   }

2. EPL

   Instantaneous tunneling of relativistic massive spin-0 particles

   Philip Caesar M Flores, and Eric A Galapon

   Europhysics Letters, 2023

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   The tunneling time problem earlier studied in Phys. Rev. Lett. 108, 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous implying that the wavepacket becomes superluminal below the barrier. The non-relativistic treatment raises the question whether the superluminal behavior is a mere non-relativistic phenomenon or an an inherent quantum effect in all energy scales. Here we extend the analysis by constructing a relativistic TOA-operator for spin-0 particles across a square potential barrier by quantizing the corresponding classical quantity, and imposing that the barrier height Vo is less than the rest mass energy. We show that only the above barrier energy components of the incident wavepacket’s momentum distribution contribute to the barrier traversal time while the below barrier components are transmitted instantaneously.

   @article{caesar2022instantaneous,
     title = {Instantaneous tunneling of relativistic massive spin-0 particles},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     journal = {Europhysics Letters},
     pages = {10001},
     year = {2023},
     url = {https://iopscience.iop.org/article/10.1209/0295-5075/acad9a},
   }

2022

1. PRA

   Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy

   Philip Caesar M Flores, and Eric A Galapon

   Physical Review A, 2022

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   A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi’s original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.

   @article{flores2022relativistic,
     title = {Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     journal = {Physical Review A},
     volume = {105},
     number = {6},
     pages = {062208},
     year = {2022},
     publisher = {APS},
     url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.062208},
   }

2019

1. PRA

   Quantum free-fall motion and quantum violation of the weak equivalence principle

   Philip Caesar M Flores, and Eric A Galapon

   Physical Review A, 2019

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   The weak equivalence principle (WEP) in the quantum regime has been the subject of many studies with a broad range of approaches to the problem. Here, we tackle the problem anew through the time of arrival (TOA) operator approach. This is done by constructing the TOA operator for a nonrelativistic and structureless particle that is projected upward in a uniform gravitational field with an intended arrival point below the classical turning point. The TOA operator is constructed under the constraint that the inertial and gravitational masses are equivalent and that Galilean invariance is preserved. These constraints are implemented by Weyl quantization of the corresponding classical TOA function for the projectile. The expectation value of the TOA operator is explicitly shown to be equal to the classical time of arrival plus mass-dependent quantum correction terms, implying incompatibility of the WEP with quantum mechanics. The full extent of the violation of the WEP is shown through the mass dependence of TOA distribution for the projectile.

   @article{flores2019quantum,
     title = {Quantum free-fall motion and quantum violation of the weak equivalence principle},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     journal = {Physical Review A},
     volume = {99},
     number = {4},
     pages = {042113},
     year = {2019},
     publisher = {APS},
     url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.042113},
   }

2. SPP

   Violation of the weak equivalence principle via the Born-Jordan quantized TOA operator

   Philip Caesar M Flores, and Eric A Galapon

   In Proceedings of the Samahang Pisika ng Pilipinas, 2019

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   In classical physics, the weak equivalence principle (WEP) states that bodies fall with the same acceleration regardless of their composition and mass. On the contrary, studies on the quantum image of a particle undergoing free-fall has shown a violation of the WEP. Here, we show that these violation is manifested through quantum corrections to the classical time of arrival (TOA). We start by constructing a TOA operator by quantizing the classical TOA function using Born-Jordan ordering rule. The expectation value of the TOA operator is then calculated and expressed as an asymptotic expansion of ℏ. The leading term of the expansion is shown to be equal to the classical TOA while the rest are quantum correction terms. However, these quantum corrections vanish in the large momentum limit thereby recovering the WEP. We trace this quantum violation of the WEP to fact that there is no velocity operator in quantum mechanics.

   @inproceedings{flores2019violation,
     title = {Violation of the weak equivalence principle via the Born-Jordan quantized TOA operator},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     booktitle = {Proceedings of the Samahang Pisika ng Pilipinas},
     year = {2019},
     url = {https://proceedings.spp-online.org/article/view/SPP-2019-2G-05},
   }

2018

1. SPP

   Violation of the weak equivalence principle via the time of arrival operator

   Philip Caesar M Flores, and Eric A Galapon

   In Proceedings of the Samahang Pisika ng Pilipinas, 2018

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   The weak equivalence principle for quantum systems states that particles with the same velocity wavefunction behave identically in free fall implying that the TOA distribution of different particles should be identical regardless of mass as long as they have the same initial momentum. This leads us to study the distribution of the first time of arrival for spinless particles fired upward using the theory of quantum time of arrival operators. We start by constructing an appropriate time of arrival operator that is conjugate with the system Hamiltonian using Weyl quantization. The time of arrival distribution was then constructed and shown to be mass-dependent, implying violation of the weak equivalence principle.

   @inproceedings{flores2018violation,
     title = {Violation of the weak equivalence principle via the time of arrival operator},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     booktitle = {Proceedings of the Samahang Pisika ng Pilipinas},
     year = {2018},
     url = {https://paperview.spp-online.org/proceedings/article/view/SPP-2018-1D-04},
   }

2017

1. SPP

   Covariance property of the confined time of arrival operators

   Philip Caesar M Flores, and Eric A Galapon

   In Proceedings of the Samahang Pisika ng Pilipinas, 2017

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   An expression for the transition amplitude of the energy translation generated by the confined time of arrival (CTOA) operators on the Hamiltonian eigenfunctions was obtained using resolvent functional calculus. It is then showed numerically that the CTOA operators are not generators of energy translation.

   @inproceedings{flores2017covariance,
     title = {Covariance property of the confined time of arrival operators},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     booktitle = {Proceedings of the Samahang Pisika ng Pilipinas},
     year = {2017},
     url = {https://proceedings.spp-online.org/article/view/235},
   }

2016

1. PRA

   Synchronizing quantum and classical clocks made of quantum particles

   Philip Caesar M Flores, Roland Caballar, and Eric A Galapon

   Physical Review A, 2016

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   We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), can be eliminated up to a given order of ℏ by choosing an appropriate position-dependent phase for the object’s wave function. This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock, which tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock by making use of a quantum object with a position-dependent phase imprinted on the object’s initial wave function with the use of an impulsive potential.

   @article{flores2016synchronizing,
     title = {Synchronizing quantum and classical clocks made of quantum particles},
     author = {Flores, Philip Caesar M and Caballar, Roland and Galapon, Eric A},
     journal = {Physical Review A},
     volume = {94},
     number = {3},
     pages = {032123},
     year = {2016},
     publisher = {APS},
     url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.032123},
   }

2. SPP

   Synchronizing quantum and classical clocks made of quantum particles up to ħ2

   Philip Caesar M Flores, Roland Cristopher F Caballar, and Eric A Galapon

   In Proceedings of the Samahang Pisika ng Pilipinas, 2016

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   Quantum corrections to the classical time of arrival arises if time is treated quantum mechanically, i.e. time is a dynamical observable. Here, we demonstrate how to eliminate these quantum corrections for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), can be eliminated up to ħ2 using an appropriate position dependent phase. By doing so, we are able to synchronize classical and quantum clocks that tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock.

   @inproceedings{flores2016synchronizinh,
     title = {Synchronizing quantum and classical clocks made of quantum particles up to ħ2},
     author = {Flores, Philip Caesar M and Caballar, Roland Cristopher F and Galapon, Eric A},
     booktitle = {Proceedings of the Samahang Pisika ng Pilipinas},
     year = {2016},
     url = {https://proceedings.spp-online.org/article/view/309},
   }

2015

1. SPP

   The resolvent operators of the confined time of arrival operators

   Philip Caesar M Flores, and Eric A Galapon

   In Proceedings of the Samahang Pisika ng Pilipinas, 2015

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   The resolvent operator for the confined time of arrival operator is obtained explicitly, and the transcendental characteristic equations for the eigenvalues reported earlier are reproduced.

   @inproceedings{flores2015resolvent,
     title = {The resolvent operators of the confined time of arrival operators},
     author = {Flores, Philip Caesar M and Galapon, Eric A},
     booktitle = {Proceedings of the Samahang Pisika ng Pilipinas},
     year = {2015},
     url = {https://proceedings.spp-online.org/article/view/1157},
   }