Angel S. Sanz

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Verified

Angel verified their affiliation via an institutional email.

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• PhD in Physics
• Professor (Associate) at Complutense University of Madrid

The quantum Cramér-Rao bound (QCRB) stands as a cornerstone of quantum metrology. Yet, akin to its classical counterpart, it provides only local information and overlooks higher-order details. We leverage the theory of higher-order asymptotics to circumvent these issues, providing corrections to the performance of estimators beyond the QCRB. While...

Even the most classical states are still governed by quantum theory. A number of physical systems can be described by their Majorana constellations of points on the surface of a sphere, where concentrated constellations and highly symmetric distributions correspond to the least and most quantum states, respectively. If these points are chosen rando...

Surface plasmon polaritons have received much attention over the last decades in fields such as photonics or nanotechnology due to their inherent high sensitivity to metal surface variations (e.g., presence of adsorbates or changes in the roughness). Because of this important property, it is expected that they will find promising major applications...

Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very similar, on the other hand, to effects observable in analogous optical systems. This work focuses on how Bohmian m...

The propagation of Airy beams in free space is characterized by being non dispersive, which warrants the shape invariance of their intensity distribution, and self-accelerating along the transverse direction. These distinctive traits are still present in partially coherent Airy beams as long as the reach of their back tail (and hence their energy c...

Quantum mechanics is able to produce challenging behaviors even in the simplest situations. This is possible because of the important dynamical role that phase plays in the evolution of quantum systems, very similar, nonetheless, to effects observable in analogous optical systems. The present work focuses on how Bohmian mechanics proves to be a rat...

In the last decades, the experimental research on Bose–Einstein interferometry has received much attention due to promising technological implications. This has thus motivated the development of numerical simulations aimed at solving the time-dependent Gross–Pitaevskii equation and its reduced one-dimensional version to better understand the develo...

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the t...

Airy wave packets constitute a very peculiar type of structured light: during their propagation, their transverse profile undergoes a self-accelerating displacement while it remains shape invariant. They are thus the only non-dispersive beam-type solution to the Helmholtz paraxial equation in free space. Such properties are possible by virtue of th...

We consider the concept of velocity fields, taken from Bohmian mechanics, to investigate the dynamical effects of entanglement in bipartite realizations of Young’s two-slit experiment. In particular, by comparing the behavior exhibited by factorizable two-slit states (cat-type state analogs in the position representation) with the dynamics exhibite...

A precise knowledge of the polarization state of light is crucial in technologies that involve the generation and application of structured light fields. The implementation of efficient methods to determine and characterize polarization states is mandatory; more importantly, these structured light fields must be at any spatial location at a low exp...

The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time evolution. We resort to the notion of quantum trajectories to reinterpret this singular behavior. We show that the blow...

Recently, we have proposed an alternative method to characterize the polarization state of three-dimensional fields. Here, we show the interest of this new methodology in the analysis of radially polarized beams with a topological charge.

Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they also manifest in the case of partially coherent Airy-type beams. Here, these properties are further investigate...

Airy beams are solutions to the paraxial Helmholtz equation known for exhibiting shape invariance along their self-accelerated propagation in free space. These two properties are associated with the fact that they are not square integrable, that is, they carry infinite energy. To circumvent this drawback, families of so-called finite-energy Airy-ty...

Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they also manifest in the case of partially coherent Airy-type. Here, these properties are further investigated by i...

In the last decades, the experimental research on Bose-Einstein interferometry has received much attention due to promising technological implications. This has thus motivated the development of numerical simulations aimed at solving the time-dependent Gross-Pitaevskii equation and its reduced one-dimensional version to better understand the develo...

Airy beams are solutions to the paraxial Helmholtz equation known for exhibiting shape invariance along their self-accelerated propagation in free space. These two properties are associated with the fact that they are not square integrable, that is, they carry infinite energy. To circumvent this drawback, families of so-called finite-energy Airy-ty...

In Optics it is common to split up the formal analysis of diffraction according to two convenient approximations, in the near and far fields (also known as the Fresnel and Fraunhofer regimes, respectively). Within this scenario, geometrical optics, the optics describing the light phenomena observable in our everyday life, is introduced as the short...

The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space—a common meeting point to both classical and quantum density statistical descriptors. Here, this issue is tackled by investigating the be...

Even the most classical states are still governed by quantum theory. A fantastic array of physical systems can be described by their Majorana constellations of points on the surface of a sphere, where concentrated constellations and highly symmetric distributions correspond to the least and most quantum states, respectively. If these points are cho...

The correspondence principle plays a fundamental role in quantum mechanics. It provides us with a bridge to relate and somehow explain the dynamical behavior shown by quantum systems in terms of the dynamics exhibited by their classical counterparts. This naturally leads to inquire whether it is possible to define close classical analogs of quantum...

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, for...

When teaching Optics, it is common to split up the formal analysis of diffraction according to two convenient approximations, in the near and far fields. Moreover, apart from a slight mention to the relationship between the wavelength and the typical size of the aperture that light is incident on, such analysis does not often involve any explicit m...

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, for...

The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference proc...

The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type patterns formed in quantum cavities constitute ideal systems to study the robustness of the underlying interference process against the harmful effects of decoherence. This fact i...

After having proven that an uncertainty relation holds for the on-axis power content of highlyfocused fields, in this Communication we explore and discuss the consequences of such a relation concerning the polarization state characterizing the fields that satisfy it.

A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. Interestingly, the energy resource of the control Hamiltonian and the control time define a pair of conjugate variables that minimize the energy-time uncertainty relation. The resulting control protocol is applied to a single qubit as...

In the analysis of the on-axis intensity for a highly focused optical field, it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of the region where the axial power content mainly concentrates is proposed on the basis of an unc...

In the analysis of the on-axis intensity for a highly focused optical field it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of region where axial power content is mainly concentrated is proposed on the basis of an uncertain...

Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and...

Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discusse...

A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. The solution is found to be adiabatic irrespective of the energy resource, and includes as a particular case the result in [Phys. Rev. Lett. 114, 100502 (2015)] for a Hilbert-Schmidt norm equal to one. Interestingly, the energy resour...

Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preservin...

A novel measure is proposed to estimate the size of the region where axial power content of highly focused fields mainly concentrates. This measure is established on the basis of a newly defined uncertainty principle.

Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. [J. Opt. Soc. Am. A 3, 536 (1986)] found a paraxial solution to Maxwell's equation in vacuum, which includes polarization in a natural way, though still preserving t...

Optical cloaking consists in hiding from sight an object by properly deviating the light that comes from it. An optical cloaking device (OCD) is an artifact that hides the object and, at the same time, its presence is not (or should not be) noticeable for the observer, who will have the impression of being looking through it. At the level of paraxi...

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass $m$ confined in a one-dim...

In a diffraction pattern of a laser beam on a sharp edge of a half-plane two characteristic regions are noticeable. In the central region, one can notice the diffraction of laser light in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. There are also, on both sides of the edge, very long light t...

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimen...

By only considering the principles of geometrical optics in paraxial approximation, it is possible to build a a simple optical cloaking device (OCD) with four lenses, as shown by Choi and Howell [Opt. Exp. 22, 29465 (2014)]. Inspired by the simplicity and elegance of this experiment, we decided to take it to the classroom in order to make of it a t...

Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative analysis at different levels of approximation in the problem of the diffraction of helium atoms from a substrat...

Bohmian mechanics is widely known within the field of the quantum foundations, although it has been a quite useful resource for computational and interpretive tasks in a wide number of problems. In the present work, it is used to established a comparative analysis at different levels of approximation in the problem of the diffraction of helium atom...

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimen...

The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the time-dependent Schr\"odinger equation. Unlike other methods in the related literature, in this approach the att...

The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the time-dependent Schr\"odinger equation. Unlike other methods in the related literature, in this approach the att...

Perhaps because of the popularity that trajectory-based methodologies have always had in Chemistry and the important role they have played, Bohmian mechanics has been increasingly accepted within this community, particularly in those areas of the theoretical chemistry based on quantum mechanics, e.g., quantum chemistry, chemical physics, or physica...

The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic picture of quantum mechanics, in order to elucidate its physical consequences beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion is focused around the connection...

The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion turns around the co...

In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where it can be noticed the diffraction of laser light in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both si...

Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm's proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational asp...

The numerical analysis of the diffraction features rendered by transmission electron microscopy (TEM) typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advan- tageous (relatively simple implementations and low computation...

The numerical analysis of the diffraction features rendered by transmission electron microscopy (TEM) typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advan- tageous (relatively simple implementations and low computation...

Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework t...

Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely, Glauber and SU(2) coherent states. Although these states are often regarded as classical, the analysis here shows that the corresponding ele...

To date, quantum mechanics has proven to be our most successful theoretical model. However, it is still surrounded by a "mysterious halo" that can be summarized in a simple but challenging question: Why quantum phenomena are not understood under the same logic as classical ones? Although this is an open question (probably without an answer), from a...

Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here, this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework...

Weak-measurement-based experiments [Kocsis et al., Science 332 (2011) 1170] have shown that, at least for pure states, the average evolution of independent photons in Young’s two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated ass...

Atomic three-grating Mach–Zehnder interferometry constitutes an important tool to probe fundamental aspects of the quantum theory. There is, however, a remarkable gap in the literature between the oversimplified models and robust numerical simulations considered to describe the corresponding experiments. Consequently, the former usually lead to par...

Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful resource to analyze the role of the phase as the mechanism responsible for the dynamical evolution of quantum systems. Here this role is discussed in the context of quantum interference. Specifically, it is shown that when dealing with two wave-packet coherent...

Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all...

Young's two-slit experiment constitutes the paradigm of quantum complementarity. According to the complementarity principle, complementary aspects of quantum systems cannot be measured at the same time by the same experiment. This has been a long debate in quantum mechanics since its inception. But, is this a true constraint? In 2011, an astounding...

We address a trajectory picture of quantum polarization by applying the tools of the Bohmian representation of quantum mechanics to some relevant examples of two-mode field states, such as Glauber and SU(2) coherent states. We show that the corresponding electric-field trajectories are incompatible with classical electrodynamics, despite the fact t...

Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the principles and formal body of this theory shows that, beyond longstanding prejudices, there is still room enough fo...

The relationship between position and momentum in quantum mechanics formally translates into a Fourier transform between the position (configuration) and momentum representations of the wave function. These two representations are usually introduced without a proper physical contextualization. Here this issue is tackled by means of a simple and ped...

The existence of wavy properties associated with material particles is one of the fundamental achievements of quantum mechanics. Thus, the experimental use of single, double, or multiple slits has become a standard test of the universality of matter diffraction phenomena, independently of both the type of diffracted particle (charged or neutral, el...

The presence of impurities, defects or adsorbates on a surface greatly affects its physics and chemistry. They are responsible for the formation of intensity peaks in between Bragg angles, thus giving rise to diffusive scattering. This phenomenon is characterized by an incoherence among particles scattered from different defects and is well illustr...

In this chapter, elastic scattering or diffraction by light particles described in terms of quantum trajectories is carried out. In particular, how the so-called quantum turning points are related to the effective surface corrugation and/or electron density of the surface and how resonance processes can be interpreted in terms of a causal theory. F...

Up to now we have considered quantum systems which are not subject to any external force except for open systems. Such systems are usually associated with translational properties. On the contrary, bound systems generally describe properties related to some internal degrees of freedom (e.g., vibrations, rotations, absorption and emission processes,...

Apart from technological applications, interference experiments with massive particles in ample range of masses (electrons, neutrons, atoms, small clusters, organic molecules, or even Bose-Einstein condensates) have attracted a lot of attention in the last years due to their fundamental aspect as exploring tools of the limits of quantum mechanics....

The problem of many-body interactions—or, equivalently, many degrees of freedom—can be tackled from different points of view, since it appears in many different physical and chemical contexts. Here, in particular, we are going to face it from a chemical physics point of view. The application of the Schrödinger equation to discern electronic structu...

In this chapter, the role of the initial conditions of a wave packet colliding with a ramp potential is first studied in terms of quantum trajectories. This study is carried out since this problem illustrates how the spreading and translation motions can affect the tunneling dynamics. In particular, it is also analyzed the effect of a smooth appear...

In spite of its apparent simplicity, the dynamics of single wave packets contains valuable physical information to understand more complex quantum-mechanical time-dependent problems and phenomena. In this chapter, an analysis of wave packet dynamics stressing different aspects of physical interest is presented, such as the role of translational mot...

Effective descriptions accounting for the evolution of quantum systems that are acted on by a bath are desirable. As the number of bath degrees of freedom increases and full quantum simulations turn out computationally prohibitive, simpler models become essential to understand and gain an insight into the main physical mechanisms involved in the sy...

Here Bohmian mechanics is used to explore the dynamics of mixed states, often regarded as the result of classical-like ignorance, or incoherence inhibiting interference. Because of the nonlinear nature of the Bohmian guidance equation, it is shown that the corresponding trajectories do not exhibit the behavior expected from a typical context of cla...

Magnetic trapping is a cornerstone for modern ultracold physics and its applications (e.g., quantum information processing, quantum metrology, quantum optics, or high-resolution spectroscopies). Here a comprehensive analysis and discussion of the basic physics behind the most commonly used magnetic traps in Bose-Einstein condensation is presented....

Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics and much less to analyze their effects on the dynamics of quantum systems. Here we provide a Bohmian analysis of the friction dynamics led by hypothetical quantum viscid media, which will be simulated by means of the so-cal...

The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and extended to quantum optical polarization. As is shown, this approach properly combines definite time-evolving traject...

We present a trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both t...

The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and extended to quantum optical polarization. As is shown, this approach properly combines definite time evolving traject...

We present a trajectory based interpretation for Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both...

The role of incoherent tunneling in the diffusion of light atoms on surfaces is investigated. With this purpose, a Chudley-Elliot master equation constrained to nearest neighbors is considered within the Grabert-Weiss approach to quantum diffusion in periodic lattices. This model is applied to recent measurements of atomic H and D on Pt(111), rende...

We present a novel approach to study transmission through waveguides in terms of optical streamlines. This theoretical framework combines the computational performance of beam propagation methods with the possibility to monitor the passage of light through the guiding medium by means of these sampler paths. In this way, not only can the optical flo...

A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br(2) complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three-dimensional wave packet si...

Essentially the only notion of trajectory we have in optics is that of a light ray, regardless of whether it refers to the rays of geometric optics (i.e., satisfying Fermat’s principle) or they are just virtual rays used to explain interference and diffraction. However, based on the idea of Bohmian trajectory, it is also possible to reformulate ele...

Strictly speaking, real physical systems do not exist in complete isolation in nature. The interaction with the environment generally causes the system to become a statistical mixture, leading to correlation or entanglement between them and decoherence. The theory of open quantum systems was formulated precisely to deal with this kind of problems a...

Bohmian mechanics constitutes a different way to understand quantum mechanics, where the role of an external observer is not present, and quantum phenomena and processes are explained in a causal way, connecting system configurations at different times by means of trajectories. However, in order to better understand the ideas and concepts behind th...

The time-evolution of interacting “small” systems is usually described by means of quantum mechanics. However, very often, it happens that a first approach to these dynamics by means of classical mechanics provides a better understanding of the processes and phenomena involved. Here, an overview on classical mechanics is presented, ranging from reg...

The theoretical framework for dissipative and stochastic dynamics of open classical systems is presented and discussed. Only linear friction is explicitly considered. In spite of the different approaches one may find in the literature, there are essentially three main ways to introduce stochasticity. First, phenomenologically, describing Brownian-l...

Although the concept of wave appears in the description of many different physical processes, it acquires a special relevance in the case of matter and radiation. The use of trajectories (or rays) and waves to describe both matter and radiation has led to a strongly intertwined historical development of both quantum mechanics and electromagnetism....

Bohmian mechanics allows to understand the quantum world in a classical-like fashion, by means of trajectories evolving throughout configuration space. This appealing feature has stimulated its application nowadays to many different problems from atomic and molecular physics, condensed matter physics, chemical physics or quantum chemistry, for exam...