arXiv subjects

A. Martín-Ruiz

Publications and source records attributed to A. Martín-Ruiz.

At least 55 records · Page 3Linked to original sources

arXiv2020

Quantized electrochemical transport in Weyl semimetals

We show that under the effect of an external electric field and a gradient of chemical potential, a topological electric current can be induced in Weyl semimetals without inversion and mirror symmetries. We derive analytic expressions for the nonlinear conductivity tensor and show that it is nearly quantized for small tilting when the Fermi levels are close to the Weyl nodes. When the van Hove point is much larger than the largest Fermi level, the band structure is described by two linearly dispersing Weyl fermions with opposite chirality. In this case, the electrochemical response is fully quantized in terms of fundamental constants and the scattering time, and it can be used to measure directly the topological charge of Weyl points. We show that the electrochemical chiral current may be derived from an electromagnetic action similar to axion electrodynamics, where the position-dependent chiral Fermi level plays the role of the axion field. This posits our results as a direct consequence of the chiral anomaly.

cond-mat.mes-hall↗

arXiv2020

Fano resonances induced by the topological magnetoelectric effect

We investigate the interaction between a topological insulator nanoparticle and a quantum dot in an impulse magnetic field. Since topological insulators are nonmagnetic, after the impulse has ended only the localised topological surface modes, which are quantised in terms of dipolar bosonic modes, thus coupling dipolarly to the quantum dot. Hence, the hybrid system can be treated as a single bosonic mode interacting with a two-level system, where the coupling strength is quantised in terms of the magnetoelectric polarizability. We implement the interaction of the hybrid with the environment through the coupling with a continuum reservoir of radiative output modes and a reservoir of phonon modes. Using the method of Zubarev's Green functions, we derive an expression for the optical absorption spectrum of the system. We find the emergence of Fano resonances which are direct manifestations of the $\mathbb{Z}_{2}$ invariant of topological insulators. We present numerical results for a topological insulator nanosphere made of TlBiSe$_2$ interacting with a CdSe quantum dot.

quant-ph↗

arXiv2020

On the four-body problem in the Born-Oppenheimer approximation

The quantum problem of four particles in $\mathbb{R}^d$ ($d\geq 3$), with arbitrary masses $m_1,m_2,m_3$ and $m_4$, interacting through an harmonic oscillator potential is considered. This model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. The study is restricted to the ground state level. We pay special attention to the case of two equally heavy masses $m_1=m_2=M$ and two light particles $m_3=m_4=m$. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $σ=\frac{m}{M}$, of the exact phase $Φ$ of the wave function $ψ_0=e^{-Φ}$ and the corresponding ground state energy $E_0$, coincide exactly with the values obtained in the Born-Oppenheimer approximation. A physically relevant rough model of the $H_2$ molecule and of the chemical compound $H_2O_2$ (Hydrogen peroxide) is described in detail. The generalization to an arbitrary number of particles $n$, with $d$ degrees of freedom ($d\geq n-1$), interacting through an harmonic oscillator potential is briefly discussed as well.

quant-ph↗

arXiv2020

Lorentz violating scalar Casimir effect for a $D$-dimensional sphere

We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by the term $λ(u \cdot \partial ϕ) ^{2}$, where the parameter $λ$ and the background vector $u^μ$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D$, the Casimir stress by using Green's function techniques for two specific choices of the vector $u ^μ$. In the timelike case, $u ^μ = (1,0,...,0)$, the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor $(1 + λ) ^{-1/2}$. For the radial spacelike case, $u ^μ = (0,1,0,...,0)$, we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value $λ_{c} = λ_{c} (D)$ at which the Casimir stress transits from a repulsive behavior to an attractive one for any $D> 2$. The physically relevant case $D = 3$ is analyzed in detail where the critical value $λ_{c}|_{\small D=3} = 0.0025$ was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of $D$.

hep-th↗

arXiv2020

Optical response of a topological-insulator--quantum-dot hybrid interacting with a probe electric field

We study the interaction between a topological insulator nanoparticle and a quantum dot subject to an applied electric field. The electromagnetic response of the topological insulator is derived from axion electrodynamics in the quasistatic approximation. Localized modes are quantized in terms of dipolar bosonic modes, which couples dipolarly to the quantum dot. Hence, we treat the hybrid as a two-level system interacting with a single bosonic mode, where the coupling strength encodes the information concerning the nontrivial topology of the nanoparticle. The interaction of the hybrid with the environment is implemented through the coupling with a continuum reservoir of radiative output modes and a reservoir of phonon modes. In particular, we use the method of Zubarev's Green functions to derive an expression for the optical absorption spectrum of the system. We apply our results to a realistic system which consists of a topological insulator nanoparticle made of TlBiSe$_{2}$ interacting with a cadmium selenide quantum dot, both immersed in a polymer layer such as poly(methyl methacrylate). The optical absorption spectrum exhibits Fano resonances with a line shape that strongly depends on the polarization of the electric field as well as on the topological magnetoelectric polarizability $θ$. Our results and methods can also be applied to nontopological magnetoelectric materials such as Cr$_{2}$O$_{3}$.

quant-ph↗

arXiv2020

Quantum phase transition of two-level atoms interacting with a finite radiation field

We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a maximum number of excitations. The approach adopted here leads to a nonlinear extension of the Dicke model that takes into account both an intensity dependent coupling between the atoms and the radiation field, and an additional nonlinear Kerr-like or Pösch-Teller-like oscillator term, depending on the degree of nonlinearity. We use the energy surface minimization method to demonstrate that the extended Dicke model exhibits a quantum phase transition, and we analyze its dependence upon the maximum number of excitations of the model. Our analysis is carried out via three methods: through mean-field analysis (i.e. by using the tensor product of coherent states), by using parity-preserving symmetry-adapted states (using the critical values obtained in the mean-field analysis and numerically minimizing the energy surface) and by means of the exact quantum solution (i.e. by numerically diagonalizing the Hamiltonian). Possible connections with the $qp$-deformed algebras are also discussed.

quant-ph↗

arXiv2020

A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance $L$, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor $h^{\,μν}$ that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that $\mathcal{F}_c(L)=\mathcal{F}_0(\tilde{L})/\sqrt{-{\rm det}\, h^{\,μν}}$, where $\mathcal{F}_0$ is the Lorentz-invariant expression, and $\tilde{L}$ is the plate separation rescaled by the component of $h^{\,μν}$ normal to the plates, $\tilde{L}=L/\sqrt{-h^{nn}}$. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.

hep-th↗

arXiv2020

Casimir effect in Lorentz-violating scalar field theory: a local approach

We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $λ\left( u \cdot \partial ϕ\right )^{2}$, where the parameter $λ$ and the background four-vector $u ^μ$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density $\mathcal{E}_{C}$ (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density $\mathcal{E}_{0}$ as follows \begin{align} \mathcal{E}_{C} (L) = \sqrt{\frac{1-λu_{n} ^{2}}{1 + λu ^{2}}} \mathcal{E}_{0} (\tilde{L}) , \notag \end{align} where $\tilde{L} = L / \sqrt{1-λu_{n} ^{2}}$ is a rescaled plate-to-plate separation and $u_{n}$ is the component of $\vec{u}$ along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.

hep-th↗

arXiv2020

Quantum-Optical set-up for the Monty Hall problem

A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined by considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. We also discuss the influence of noise on the game outcome when the parties play through a noisy quantum channel. The experimental set-up can be used to quickly verify the counter-intuitive result of the Monty Hall problem, adding pedagogic value to the proposal.

quant-ph↗

arXiv2020

Casimir effect in polymer scalar field theory

In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance $L$, due to the presence of a minimal length $λ$ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming $λ\ll L$, we expressed it as an expansion in powers of $1/N$, being $N=L/ λ$ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

hep-ph↗

arXiv2020

Aislantes Topológicos

We present a brief introduction to the topological phases of matter. This is a brief review article written for the Boletin de la Sociedad Mexicana de Fisica

physics.gen-ph↗

arXiv2019

Magnetoelectric effect of a conducting sphere near a planar topological insulator

When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular bispherical coordinate system. We find that the electromagnetic fields can be interpreted in terms of point electric and image magnetic charges as if the medium were the vacuum. As a manifestation of the magnetoelectric effect, we highlight the resulting magnetic field, which we analyze in detail along the symmetry axis, since such estimates could be useful in evaluating the experimental possibility of its measurement via sensible magnetometers. Our numerical estimates show that the proposed setup provides a magnetic field strength in the range of 10-100 mG, which is attainable with present day sensitivities in NV center-diamond magnetometers, for example.

cond-mat.mes-hall↗

arXiv2019

Gravitational Searches for Lorentz Violation with Ultracold Neutrons

We investigate the consequences of Lorentz violation (as expressed within the gravity sector of the Standard-Model Extension) for gravitational quantum states of ultracold neutrons (UCNs). Since our main aim is to compare our theoretical results with the recent high-sensitivity GRANIT experiment, we frame this work according to the laboratory conditions under which it was carried out. This offers the possibility of testing Lorentz invariance by experiments using UCNs. Thus we consider the nonrelativistic Hamiltonian describing the quantum mechanics of an unpolarized neutron's beam in presence of a weak-gravity field, and the latter is described by a post-Newtonian expansion of the metric up to order $O (2)$ and linear in the Lorentz-violating coefficients $\bar{s} ^{μν}$. Using a semi-classical wave packet, which is appropriate to describe an intense beam of UCNs, we derive the effective Hamiltonian describing the neutron's motion along the axis of free fall and then we compute the Lorentz-violating shifts on the energy levels. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for a particular combination of the Lorentz-violating coefficients.

hep-ph↗

arXiv2019

Electromagnetic fields induced by an electric charge near a Weyl semimetal

Weyl semimetals (WSM) are a new class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking, as well as a chiral magnetic effect due to inversion symmetry breaking. These unusual electromagnetic responses can be characterized by an axion term $θ\textbf{E} \cdot \textbf{B}$ with space and time dependent axion angle $θ(\textbf{r} ,t)$. In this paper we compute the electromagnetic fields produced by an electric charge near to a topological Weyl semimetal with two Weyl nodes in the bulk Brillouin zone. We find that, as in ordinary metals and dielectrics, outside the WSM the electric field is mainly determined by the optical properties of the material. The magnetic field is, on the contrary, of topological origin in nature due to the magnetoelectric effect of topological phases. We show that the magnetic field exhibits a particularly interesting behavior above the WSM: the field lines begin at the surface and then end at the surface (but not at the same point). This behavior is quite different from that produced by an electric charge near the surface of a topological insulator, where the magnetic field above the surface is generated by an image magnetic monopole beneath the surface, in which case, the magnetic field lines are straight rays. The unconventional behavior of the magnetic field is an experimentally observable signature of the anomalous Hall effect in the bulk of the WSM. We discuss a simple candidate material for testing our predictions, as well as two experimental setups which must be sensitive to the effects of the induced magnetic field.

hep-th↗

arXiv2019

Exact solution of the Schrödinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface

When an hydrogen atom is brought near to the interface between $θ$-media, the quantum-mechanical motion of the electron will be affected by the electromagnetic interaction between the atomic charges and the $θ$-interface, which is described by an axionic extension of Maxwell electrodynamics in the presence of a boundary. In this paper we investigate the atom-surface interaction effects upon the energy levels and wave functions of an hydrogen atom placed at the interface between a $θ$-medium and the vacuum. In the approximation considered, the Schrödinger equation can be exactly solved by separation of variables in terms of hypergeometic functions for the angular part and hydrogenic functions for the radial part. In order to make such effects apparent we deal with unrealistic high values of the $θ$-parameter. We also compute the energy shifts using perturbation theory for a particular small value of $θ$ and we demonstrate that they are in a very good agreement with the ones obtained from the exact solution.

cond-mat.mes-hall↗

arXiv2018

Magnetoelectric effect in cylindrical topological insulators

Topological insulators (TIs) exhibit a quantized magnetoelectric response when time-reversal symmetry is broken on its surface. This unusual electromagnetic (EM) response is a unique macroscopic manifestation of the quantum Hall effect on the TI surface and it is described by a quantized Chern-Simons theory. In this paper, we construct the Green's function (GF) describing the EM response of two topological media separated by a cylindrical interface. This GF, in the appropriate limits, describes the magnetoelectric effect of both i) a cylindrical TI surrounded by a dielectric fluid, and ii) a TI with a cylindrical dielectric-filled cavity. We calculate the EM fields produced by a line charge and a line current near the TI surface and we show that, in addition to the standard image electromagnetic sources, charge and current densities of magnetic monopoles will also appear. We discuss some experimental setups which could be used to test these magnetic monopole fields.

cond-mat.mes-hall↗

arXiv2018

The magnetoelectric coupling in Electrodynamics

We explore a model akin to axion electrodynamics in which the axion field $θ(t,\mathbf{x})$ rather than being dynamical is a piecewise constant effective parameter $θ$ encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a $θ$-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green's function formulation of what amounts to typical boundary-value problems of $θ$-media, when external sources or boundary conditions are given. As an illustration of our methods, which we have also extended to ponderable media, we interpret the constant $θ$ as a novel topological property of vacuum, a so called $θ$-vacuum, and restrict our discussion to the cases where the permittivity and the permeability of the media is one. In this way we concentrate upon the effects of the additional $θ$ coupling which induce remarkable magnetoelectric effects. The issue of boundary conditions for electromagnetic radiation is crucial for the occurrence of the Casimir effect, therefore we apply the methods described above as an alternative way to approach the modifications to the Casimir effect by the inclusion of topological insulators.

hep-th↗

arXiv2018

Testing Lorentz- and CPT-invariance with ultracold neutrons

In this paper we investigate, within the standard model extension framework, the influence of Lorentz- and CPT-violating terms on gravitational quantum states of ultracold neutrons. Using a semiclassical wave packet, we derive the effective nonrelativistic Hamiltonian which describes the neutrons vertical motion by averaging the contributions from the perpendicular coordinates to the free falling axis. We compute the physical implications of the Lorentz- and CPT-violating terms on the spectra. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the symmetries-violation $c_{μν} ^{n}$ coefficients. We find that ultracold neutrons are sensitive to the $a _{i} ^{n}$ and $e _{i} ^{n}$ coefficients, which thus far are unbounded by experiments in the neutron sector. We propose two additional problems involving ultracold neutrons which could be relevant for improving our current bounds; namely, gravity-resonance-spectroscopy and neutron whispering gallery wave.

hep-th↗