arXiv subjects

C. Farina

Publications and source records attributed to C. Farina.

At least 37 records · Page 2Linked to original sources

arXiv2020

Efficient algebraic solution for a time-dependent quantum harmonic oscillator

Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial state. We find an iterative analytical solution given by simple recurrence relations that are very well suited for numerical calculations. We use our solution to reproduce and analyse some results from literature in order to prove the usefulness of the method and, based on these references, we discuss efficiency in squeezing, when comparing the parametric resonance modulation and the Janszky-Adam scheme.

quant-ph↗

arXiv2020

New BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras

In this work we demonstrate new BCH-like relations involving the generators of the su(1, 1), su(2) and so(2, 1) Lie algebras. We use our results to obtain in a straightforward way the composition of an arbitrary number of elements of the corresponding Lie groups. In order to make a self-consistent check of our results, as a first application we recover the non-trivial composition law of two arbitrary squeezing operators. As a second application, we show how our results can be used to compute the time evolution operator of physical systems described by time-dependent hamiltonians given by linear combinations of the generators of the aforementioned Lie algebras.

math-ph↗

arXiv2020

A time-dependent harmonic oscillator with two frequency jumps: an exact algebraic solution

We consider a harmonic oscillator (HO) with a time dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω_{0}, then, at t = 0, its frequency suddenly increases to ω_{1} and, after a finite time interval τ, it comes back to its original value ω_{0}. Contrary to what one could naively think, this problem is a quite non-trivial one. Using algebraic methods we obtain its exact analytical solution and show that at any time t > 0 the HO is in a squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω_{0} to ω_{1}), remaining constant after the second jump (from ω_{1} back to ω_{0}). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.

quant-ph↗

arXiv2019

Resonance energy transfer at percolation transition

We compute the resonance energy transfer (RET) in a system composed of two quantum emitters near a host dielectric matrix in which metallic inclusions are inserted until the medium undergoes a dielectric-metal transition at percolation. We show that there is no peak in the RET rate at percolation, in contrast to what happens with the spontaneous emission rate of an emitter near the same critical medium. This result suggests that RET does not strongly correlate with the local density of states.

cond-mat.mes-hall↗

arXiv2019

Quantum two-photon emission in a photonic cavity

We derive a new expression for the two-photon spontaneous emission (TPSE) rate of an excited quantum emitter in the presence of arbitrary bodies in its vicinities. After investigating the influence of a perfectly conducting plate on the TPSE spectral distribution (Purcell effect), we demonstrate the equivalence of our expression with the more usual formula written in terms of the corresponding dyadic Green's function. We establish a general and convenient relation between the TPSE spectral distribution and the corresponding Purcell factors of the system. Next, we consider an emitter close to a dielectric medium and show that, in the near field regime, the TPSE spectral distribution is substantially enhanced and changes abruptly at the resonance frequencies. Finally, motivated by the suppression that may occur in the one-photon spontaneous emission of an excited atom between two parallel conducting plates, we discuss the TPSE for this same situation and show that complete suppression can never occur for $s \rightarrow s$ transitions.

physics.optics↗

arXiv2019

An Integrodifferential Equation for Electromagnetic Fields in Linear Dispersive Media

We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in Fourier space. However, it can be rewarding to consider these properties as causal functions of time. Due to temporal non locality, this procedure gives rise to an integrodifferential equation for the electromagnetic fields, which we also call a wave equation. We have not found this equation in the literature and we show in this paper why it can be useful.

physics.class-ph↗

arXiv2018

The 1989 and 2015 outbursts of V404 Cygni: a global study of wind-related optical features

The black hole transient V404 Cygni exhibited a bright outburst in June 2015 that was intensively followed over a wide range of wavelengths. Our team obtained high time resolution optical spectroscopy (~90 s), which included a detailed coverage of the most active phase of the event. We present a database consisting of 651 optical spectra obtained during this event, that we combine with 58 spectra gathered during the fainter December 2015 sequel outburst, as well as with 57 spectra from the 1989 event. We previously reported the discovery of wind-related features (P-Cygni and broad-wing line profiles) during both 2015 outbursts. Here, we build diagnostic diagrams that enable us to study the evolution of typical emission line parameters, such as line fluxes and equivalent widths, and develop a technique to systematically detect outflow signatures. We find that these are present throughout the outburst, even at very low optical fluxes, and that both types of outflow features are observed simultaneously in some spectra, confirming the idea of a common origin. We also show that the nebular phases depict loop patterns in many diagnostic diagrams, while P-Cygni profiles are highly variable on time-scales of minutes. The comparison between the three outbursts reveals that the spectra obtained during June and December 2015 share many similarities, while those from 1989 exhibit narrower emission lines and lower wind terminal velocities. The diagnostic diagrams presented in this work have been produced using standard measurement techniques and thus may be applied to other active low-mass X-ray binaries.

astro-ph.HE↗

arXiv2018

Repulsive van der Waals interaction between a quantum particle and a conducting toroid

We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient method developed by Eberlein and Zietal that essentially relates the quantum problem of calculating dispersion forces between a quantum particle and a perfectly conducting surface of arbitrary shape to a corresponding classical problem of electrostatics. Considering the quantum particle in the symmetry axis of the toroid, we use this method to find an exact analytical result for the van der Waals interaction between the quantum particle and the conducting toroid. Surprisingly, we show that for appropriate values of the two radii of the toroid the dispersive force on the quantum particle is repulsive. This is a remarkable result since repulsion in dispersive interactions involving only electric objects (and particles) in vacuum is rarely reported in the literature. Final comments are made about particular limiting cases as, for instance, the quantum particle-nanoring system.

quant-ph↗

arXiv2017

Characterizing critical exponents via Purcell effect

We investigate the role of phase transitions into the spontaneous emission rate of quantum emitters embedded in a critical medium. Using a Landau-Ginzburg approach, we find that, in the broken symmetry phase, the emission rate is reduced or even suppressed due to the photon mass generated by the Higgs mechanism. Moreover, we show that the spontaneous emission presents a remarkable dependence upon the critical exponents associated to a given phase transition, allowing for an optical determination of the universality class. Our findings not only demonstrate that the Purcell effect constitutes an efficient optical probe of distinct critical phenomena, but they also unveil that a more general connection between phase transitions and spontaneous emission exist, as previous experimental and numerical evidences suggest.

quant-ph↗

arXiv2016

Is the tautochrone curve unique?

The answer to this question is no. In fact, in addition to the solution first obtained by Christiaan Huygens in 1658, given by the cycloid, we show that there is an infinite number of tautochrone curves. With this goal, we start by briefly reviewing an the problem of finding out the possible potential energies that lead to periodic motions of a particle whose period is a given function of its mechanical energy. There are infinitely many solutions, called sheared potentials. As an interesting example, we show that a Pöschl-Teller and the one-dimensional Morse potentials are sheared relative to one another for negative energies, clarifying why they share the same periods of oscillations for their bounded solutions. We then consider periodic motions of a particle sliding without friction over a track around its minimum under the influence of an uniform gravitational field. After a brief historical survey of the tautochrone problem we show that, given the period of oscillations, there is an infinity of tracks which lead to the same periods. As a bonus, we show that there are infinitely many tautochrones.

physics.class-ph↗

arXiv2016

Purcell effect at metal-insulator transitions

We investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near-field, the Purcell factor can be enhanced by two-orders of magnitude relative to the case of an homogeneous metallic medium, and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways on the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findings are robust against change in material properties, shape of inclusions, and apply for different effective medium theories as well as for a wide range of transition frequencies.

cond-mat.mes-hall↗

arXiv2016

Supernova 2014J at M82: II. Direct Analysis of Spectra Obtained with Isaac Newton and William Herschel Telescopes

We analyze a time series of optical spectra of SN~2014J from almost two weeks prior to maximum to nearly four months after maximum. We perform our analysis using the SYNOW code, which is well suited to track the distribution of the ions with velocity in the ejecta. We show that almost all of the spectral features during the entire epoch can be identified with permitted transitions of the common ions found in normal SNe Ia in agreement with previous studies. We show that 2014J is a relatively normal SN Ia. At early times the spectral features are dominated by Si II, S II, Mg II, and Ca II. These ions persist to maximum light with the appearance of Na I and Mg I. At later times iron-group elements also appear, as expected in the stratified abundance model of the formation of normal type Ia SNe. We do not find significant spectroscopic evidence for oxygen, until 100 days after maximum light. The +100 day identification of oxygen is tentative, and would imply significant mixing of unburned or only slight processed elements down to a velocity of 6,000 km/s. Our results are in relatively good agreement with other analyses in the IR. We briefly compare SN 2011fe to SN 2014J and conclude that the differences could be due to different central densities at ignition or differences in the C/O ratio of the progenitors.

astro-ph.SR↗

arXiv2015

Active magneto-optical control of spontaneous emission in graphene

We investigate the spontaneous emission rate of a two-level quantum emitter near a graphene-coated substrate under the influence of an external magnetic field or strain induced pseudo-magnetic field. We demonstrate that the application of the magnetic field can substantially increase or decrease the decay rate. We show that a suppression as large as 99$\%$ in the Purcell factor is achieved even for moderate magnetic fields. The emitter's lifetime is a discontinuous function of $|{\bf B}|$, which is a direct consequence of the occurrence of discrete Landau levels in graphene. We demonstrate that, in the near-field regime, the magnetic field enables an unprecedented control of the decay pathways into which the photon/polariton can be emitted. Our findings strongly suggest that a magnetic field could act as an efficient agent for on-demand, active control of light-matter interactions in graphene at the quantum level.

cond-mat.mes-hall↗

arXiv2015

The influence of a surface in the non-retarded interaction between two atoms

In this work we obtain analytical expressions for the non-additivity effects in the dispersive interaction between two atoms and perfectly conducting surface of arbitrary shape in the non-retarded regime. We show that this three bodies quantum-mechanical problem can be solved by mapping it into a two-bodies electrostatic one. We apply the general formulas developed in this paper in several examples. Firstly we re-derive the London interaction as a particular case of our formalism. Then we treat two atoms in the presence of a plane, re-obtained the result displayed in the literature. After we add some new examples. A particularly interesting one is two atoms inside a plate capacitor, a situation where non-additivity is very manifest since the plates lead to the exponentially suppression of the interaction of the atoms, provided the atoms are separated by a distance of the order of the distance between the plates or greater. Our results holds even in the presence of other atoms inside the plate capacitor. As a last example we deal with two atoms in the presence of a sphere, both grounded and isolated. We show that for realistic experimental parameters the non-additivity may be relevant for the force in each atom.

quant-ph↗

arXiv2014

Circular polarization in the optical afterglow of GRB 121024A

Gamma-ray bursts (GRBs) are most probably powered by collimated relativistic outflows (jets) from accreting black holes at cosmological distances. Bright afterglows are produced when the outflow collides with the ambient medium. Afterglow polarization directly probes the magnetic properties of the jet, when measured minutes after the burst, and the geometric properties of the jet and the ambient medium when measured hours to days after the burst. High values of optical polarization detected minutes after burst in GRB 120308A indicate the presence of large-scale ordered magnetic fields originating from the central engine (the power source of the GRB). Theoretical models predict low degrees of linear polarization and negligable circular polarization at late times, when the energy in the original ejecta is quickly transferred to the ambient medium and propagates farther into the medium as a blastwave. Here we report the detection of circularly polarized optical light in the afterglow of GRB 121024A, measured 0.15 days after the burst. We show that the circular polarization is intrinsic to the afterglow and unlikely to be produced by dust scattering or plasma propagation effects. A possible explanation is to invoke anisotropic (rather than the commonly assumed isotropic) electron pitch angle distributions, and we suggest that new models are required to produce the complex microphysics of realistic shocks in relativistic jets.

astro-ph.HE↗

arXiv2014

Tuning quantum fluctuations with an external magnetic field: Casimir-Polder interaction between an atom and a graphene sheet

We investigate the dispersive Casimir-Polder interaction between a Rubidium atom and a suspended graphene sheet subjected to an external magnetic field B. We demonstrate that this concrete physical system allows for an unprecedented control of dispersive interactions at micro and nanoscales. Indeed, we show that the application of an external magnetic field can induce a 80% reduction of the Casimir-Polder energy relative to its value without the field. We also show that sharp discontinuities emerge in the Casimir-Polder interaction energy for certain values of the applied magnetic field at low temperatures. Moreover, for sufficiently large distances these discontinuities show up as a plateau-like pattern with a quantized Casimir-Polder interaction energy, in a phenomenon that can be explained in terms of the quantum Hall effect. In addition, we point out the importance of thermal effects in the Casimir-Polder interaction, which we show that must be taken into account even for considerably short distances. In this case, the discontinuities in the atom-graphene dispersive interaction do not occur, which by no means prevents the tuning of the interaction in ~50% by the application of the external magnetic field.

quant-ph↗

arXiv2014

New signatures of the dynamical Casimir effect in a superconducting circuit

We found new signatures of the dynamical Casimir effect (DCE) in the context of superconducting circuits. We show that if the recent experiment made by Wilson {\it et al}, which brought the DCE into reality for the first time, is repeated with slight modifications (for instance, different values for the capacitance of the SQUID), three remarkable results will show up, namely: {\it (i)} a quite different spectral distribution for the created particles, deviating from the typical parabolic shape; {\it (ii)} an enhancement by a factor of approximately $5 \times 10^3 $ in the number of created particles with half driven frequency of the effective moving mirror and {\it (iii)} an enhancement by a factor of $3 \times 10^2$ in the particle creation rate. These results may guide the experimentalists in their search for alternative routes to observe the DCE in future experiments.

quant-ph↗

arXiv2014

A Trio of GRB-SNe: GRB 120729A, GRB 130215A / SN 2013ez and GRB 130831A / SN 2013fu

We present optical and near-infrared (NIR) photometry for three gamma-ray burst supernovae (GRB-SNe): GRB 120729A, GRB 130215A / SN 2013ez and GRB 130831A / SN 2013fu. In the case of GRB 130215A / SN 2013ez, we also present optical spectroscopy at t-t0=16.1 d, which covers rest-frame 3000-6250 Angstroms. Based on Fe II (5169) and Si (II) (6355), our spectrum indicates an unusually low expansion velocity of 4000-6350 km/s, the lowest ever measured for a GRB-SN. Additionally, we determined the brightness and shape of each accompanying SN relative to a template supernova (SN 1998bw), which were used to estimate the amount of nickel produced via nucleosynthesis during each explosion. We find that our derived nickel masses are typical of other GRB-SNe, and greater than those of SNe Ibc that are not associated with GRBs. For GRB 130831A / SN 2013fu, we use our well-sampled R-band light curve (LC) to estimate the amount of ejecta mass and the kinetic energy of the SN, finding that these too are similar to other GRB-SNe. For GRB 130215A, we take advantage of contemporaneous optical/NIR observations to construct an optical/NIR bolometric LC of the afterglow. We fit the bolometric LC with the millisecond magnetar model of Zhang & Meszaros (2001), which considers dipole radiation as a source of energy injection to the forward shock powering the optical/NIR afterglow. Using this model we derive an initial spin period of P=12 ms and a magnetic field of B=1.1 x 10^15 G, which are commensurate with those found for proposed magnetar central engines of other long-duration GRBs.

astro-ph.HE↗