publications | Philip Caesar M. Flores

Publications

2026

PRA
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

Physical Review A, 2026

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We examine the spin-resolved photoionization of randomly oriented chiral molecules via circularly polarized light, and revisit earlier predictions of Cherepkov [J. Phys. B: At. 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 were earlier predicted by Cherepkov to fully describe the 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.

When a chiral molecule absorbs light and releases an electron, the emitted electron can carry information about the molecule’s handedness through both its direction of motion and its spin. In this work, we show that these effects can be understood through a simple geometric picture: a small set of intrinsic molecular directions governs how the molecule’s handedness is transferred to the outgoing electron. This provides an intuitive way to understand the connection between molecular chirality and electron spin in photoionization.
@article{flores2026geometric, category = {publication}, 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 = {Physical Review A}, year = {2026}, url = {https://journals.aps.org/pra/abstract/10.1103/cqqs-77rg}, }

2024

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.

Quantum tunneling allows a particle to cross a barrier that it could not overcome according to classical physics, raising the question of how long the particle spends tunneling through it. In this work, we study this question using quantum time-of-arrival operators and show that the tunneling time is zero across a broad class of possible definitions of these operators. This demonstrates that the prediction of instantaneous tunneling is not simply an artifact of one particular mathematical construction.
@article{flores2024instantaneous, category = {publication}, 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}, volume = {110}, number = {6}, pages = {062223}, year = {2024}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062223}, }
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.

Quantum tunneling allows a particle to pass through a barrier even when it does not have enough energy to cross it classically. A long-standing question is whether this process takes a finite amount of time or is effectively instantaneous, and the literature has not reached a clear consensus. In this work, we try to reconcile these different results by distinguishing between full tunneling from partial tunneling. We find that full tunneling is instantaneous within our framework, while partial tunneling takes a finite amount of time.
@article{flores2024partial, category = {publication}, 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

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.

In quantum mechanics, even the question of when a particle arrives somewhere is surprisingly subtle, especially when relativity is involved. In this work, we construct a relativistic quantum description of arrival time for spin-0 particles and use it to study tunneling through an energy barrier. We find that, under the conditions considered, a relativistic particle can tunnel across the barrier with zero traversal time, suggesting that instantaneous tunneling can arise as a genuine quantum effect rather than from a particular approximation.
@article{flores2023quantized, category = {publication}, 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}, }
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.

Earlier work using a nonrelativistic theory suggested that quantum tunneling can occur instantaneously, raising the question of whether this result survives once relativity is taken into account. In this work, we develop a relativistic description of quantum arrival time for spin-0 particles and use it to study tunneling through a barrier. We find that the components of the particle that truly tunnel through the barrier contribute zero traversal time, while only the components energetic enough to pass over the barrier take a finite time. This shows that instantaneous tunneling is not simply a consequence of using a nonrelativistic theory.
@article{caesar2022instantaneous, category = {publication}, 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

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.

In quantum mechanics, predicting when a particle will arrive at a particular place is more subtle than it is in classical physics, especially when relativistic effects become important. In this work, we develop a relativistic quantum description of arrival time for massive spin-0 particles moving freely. We show how this framework can be used to construct arrival-time distributions and find that quantum particles may arrive earlier or later than classical physics would predict, while still remaining fully consistent with special relativity.
@article{flores2022relativistic, category = {publication}, 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

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.

Galileo showed that a heavy object and a light one fall at the same rate, this is called the Weak Equivalence Principle. Here, we investigated whether this principle still holds for objects so small that quantum mechanics takes over. By working out when a quantum particle fired upward should arrive at a given point, we found that the arrival time has a small dependence on the particle’s mass.
@article{flores2019quantum, category = {publication}, 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}, }

2016

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.

A quantum particle does not always arrive at a destination at exactly the time predicted by classical physics. In this work, we show that these quantum differences in arrival time can be reduced by carefully shaping the phase of the particle’s wave function. This makes it possible, in principle, to synchronize a quantum clock with a classical clock, showing how quantum effects in time measurements can be controlled rather than simply accepted as unavoidable.
@article{flores2016synchronizing, category = {publication}, 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}, }

Preprints

2026

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.

A chapter in a community roadmap on attosecond science, the use of extremely short flashes of light (billionths of a billionth of a second) to watch and steer electrons in real time. Our contribution looks at the role of electron spin in these ultrafast processes in atoms and molecules.

2025

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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Chirality-induced spin selectivity (CISS) refers to phenomena where molecular chirality governs spin polarization. While symmetry simply requires chiral molecules to support spin-vector correlations, we show that CISS is fundamentally a conditioned measurement of these correlations. We illustrate this principle for spin-resolved one-photon ionization of a randomly oriented ensemble of chiral molecules. We introduce and quantify the phenomenon of enantio-sensitive locking of the photoelectron current to its spin, thereby providing a complete description of spin-conditioned photoelectron currents in one-photon ionization.

When a chiral molecule absorbs light and releases an electron, the electron’s spin can become linked to the direction in which it moves. In this work, we study these spin–current correlations and show how they are shaped by the molecule’s handedness. The results reveal how chirality can connect electron motion and spin during photoionization, providing another route for understanding spin-dependent effects in chiral molecules.
@article{flores2025spin, category = {preprint}, 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}, }
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 underlies diverse functionalities across molecular, mesoscopic and bulk matter. A particularly intriguing example is chirality-induced spin selectivity (CISS), where chiral structures generate enantio-sensitive spin polarization. Despite extensive research, its microscopic origin and unexpectedly large magnitude remain unresolved. Here, we isolate the intrinsic coupling between chirality and spin by considering spin-resolved photoionization of randomly oriented chiral molecules under isotropic illumination. We show that electric-dipole photoionization in the presence of spin-orbit coupling generates intrinsic correlations between molecular orientation and photoelectron spin that survive complete isotropic averaging. We identify these spin-orientation correlations as the microscopic origin of CISS in photoionization and reveal their complementary manifestation: selecting the photoelectron spin orients the residual molecular ensemble, realizing spin-orientation locking, whereas selecting molecular orientation produces CISS. Both effects are governed by the same correlation strength, set by the magnitude of a molecular-frame photoionization Bloch vector that defines an enantio-sensitive molecular compass. An analogous compass emerges in photoexcitation. Our results establish spin - orientation correlations as a fundamental ingredient of chiral spin photodynamics and provide a microscopic framework for understanding and exploiting spin selectivity in chiral matter.

When a chiral molecule absorbs light and releases an electron, the electron’s spin can become linked to the molecule’s orientation in a way that depends on its handedness. In this work, we identify an intrinsic molecular compass that governs this connection between molecular geometry and electron spin. The same underlying correlation explains both how molecular orientation can influence the emitted electron’s spin and, conversely, how selecting the electron spin can reveal information about the molecule’s orientation.
@article{flores2025enantiosensitive, category = {preprint}, 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}, }

Proceedings

2019

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, category = {proceedings}, 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

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, category = {proceedings}, 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

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, category = {proceedings}, 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

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{flores2016synchronizingspp, category = {proceedings}, 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

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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@inproceedings{flores2015resolvent,
  category = {proceedings},
  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},
}