arXiv subjects

David Bermudez

Publications and source records attributed to David Bermudez.

At least 19 recordsLinked to original sources

arXiv2026

Backreaction of stimulated Hawking radiation in an optical analogue

Hawking radiation - the emission of quantum particles at the event horizon of a black hole - connects gravity with quantum mechanics and thermodynamics; the Bekenstein-Hawking entropy has been the benchmark for potential quantum theories of gravity. But Hawking radiation has never been observed in astronomy, only in laboratory analogues and the chances of ever observing it in space are astronomically small. The energy of Hawking radiation must come from the gravitational field around the black hole, but how field quanta generate Hawking quanta has been unknown. Here we report on experimental and theoretical evidence for the process that generates Hawking radiation in a fibre-optical analogue of the event horizon. There, as in gravity, it has been believed that Hawking radiation comes from a complicated, cascaded process; here we have found a simple, direct process and measured its backreaction on the field. Our findings suggest an equally direct process for other laboratory analogues and perhaps also for gravitational fields, shedding light on how black holes might radiate.

gr-qc↗

arXiv2026

Analogue Hawking radiation in nonlinear quantum optics

The Hawking effect can be understood as a broad kinematic phenomenon associated with mode behavior near a horizon. While astrophysical black holes produce one specific realization of this radiation, this perspective inspires extensive theoretical and experimental efforts to create event horizons in diverse physical systems to observe the resulting analogue Hawking emission. One of the most successful realizations is the fiber-optical analogue, based on nonlinear quantum optics. In these notes, we introduce and motivate this system while outlining the theoretical concepts underlying the gravitational analogy. Finally, we review key experiments and discuss their impact on the field.

gr-qc↗

arXiv2023

Negative frequencies and negative norms in analogue Hawking radiation systems

In this work, we study the core concepts of Hawking radiation in the astrophysical and analogue systems. We focus on the definitions of negative frequencies and negative norms: their relationship and their role in the particle creation process of the Hawking effect. We characterize the dispersion relation by the signs of the frequency and the norm. We conclude that the most natural frame for studying the Hawking effect is in the frame in which the horizon is static, where the sign of the norm can be made equal to the sign of the Doppler-shifted frequency in that frame. We use as examples the four most successful experimental analogue systems: water waves, Bose-Einstein condensates, polaritons fluids, and optical fibers.

gr-qc↗

arXiv2023

Negative frequencies in pulse propagation equations and the double analytic signal

In recent years, the topic of negative frequencies has resurfaced in optics motivated by the optical analogue of Hawking radiation. We discuss the physical meaning of negative frequencies and the conditions under which they are relevant. We review how negative frequencies are treated in current pulse propagation models based on the electric field and the analytic signal. We focus on experimentally measured signals predicted by the conservation of negative comoving frequency in the nonlinear polarization terms to advance these concepts. We propose a new formalism called the double analytic signal which clearly separates negative frequencies from positive ones. Additionally, we reduce this new formalism to the analytic signal to prove their equivalence. Throughout the paper, we present numerical solutions of the unidirectional pulse propagation equation to illustrate the electric field, analytic signal, and double analytic signal formalisms and to highlight their differences.

physics.optics↗

arXiv2021

Optical analogue of the Schwarzschild-Planck metric

We revisit the connection between trajectories of accelerated mirrors and spacetime metrics. We present the general (1+1)D effective metric that can be obtained with a fibre-optical analogue through the Kerr effect. Then we introduce a new connection between accelerated mirrors and the optical metric. In particular, we connect them for two specific trajectories: The first one is the black mirror that perfectly recreates the Schwarzchild spacetime. The second one is the Schwarzschild-Planck metric that is a regularized version of the Schwarzschild case. The regularization depends on a length scale that has a clear physical interpretation in the fibre-optical analogue system. We study the geometric properties and the Hawking radiation produced in these new analogue metrics.

gr-qc↗

arXiv2021

Frequency and polarization emission properties of a photon-pair source based on a photonic crystal fiber

In this work we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.

quant-ph↗

arXiv2020

Instabilities in an optical black-hole laser

The Hamiltonian of optical fields in a nonlinear dispersive fiber is studied. Quantum field fluctuations are spontaneously created close to an optical event horizon through the analog Hawking effect. The simplest model is considered for an optical black-hole laser, where the Hawking radiation is produced and amplified inside a cavity formed by two horizons: a black hole and a white hole. It is found that resonant Hawking radiation originates from a discrete set of instabilities and tunnels out of the horizons. Finally, the numerical results are compared with the resonance and instability conditions and a phenomenological model is developed to give a clear physical picture.

gr-qc↗

arXiv2020

Hawking radiation in optics and beyond

Hawking radiation was originally proposed in astrophysics, but it has been generalized and extended to other physical systems receiving the name of analogue Hawking radiation. In the last two decades, several attempts have been made to measure it in a laboratory, one of the most successful systems is in optics. Light interacting in a dielectric material causes an analogue Hawking effect, in fact, its stimulated version has already been detected and the search for the spontaneous signal is currently ongoing. We briefly review the general derivation of Hawking radiation, then we focus on the optical analogue and present some novel numerical results. Finally, we call for a generalization of the term Hawking radiation.

gr-qc↗

arXiv2019

Hawking temperature in dispersive media: Analytical and numerical study

In the context of analog gravity the Hawking effect can be generalized to domains outside astrophysics. Arguably, the most successful systems for this analogy have been so far the sonic and the optical ones. However, problems arise in the analog systems as their dispersive effects are too large to be ignored, and this in turn modifies the usual thermal spectrum of Hawking radiation. In this work we perform analytical and numerical studies on how the velocity profile modifies the Hawking temperature in dispersive media, including some with direct experimental application.

gr-qc↗

arXiv2019

Observation of Stimulated Hawking Radiation in Optics

The theory of Hawking radiation can be tested in laboratory analogues of black holes. We use light pulses in nonlinear fiber optics to establish artificial event horizons. Each pulse generates a moving perturbation of the refractive index via the Kerr effect. Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse. We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix.

gr-qc↗

arXiv2018

Resonant Hawking radiation as an instability

We consider a simple model for a black-hole laser: a Bose-Einstein condensate with uniform speed of sound and partially uniform flow, establishing two horizons, a black-hole and a white-hole horizon. Waves confined between the horizons are amplified similar to radiation in a laser cavity. Black-hole lasing appears as an instability with discrete sets of modes given approximately by a round-trip condition. We found that, in addition to the regular Hawking radiation, trans-Planckian radiation does tunnel out of the black-hole laser.

gr-qc↗

arXiv2018

Eigenvalue Determination for Mixed Quantum States using Overlap Statistics

We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends only on the eigenvalues of the mixed state. This allows one to estimate these eigenvalues from the overlap statistics. In the first part of this work, we present explicit results for qutrits, including a discussion of the expected uncertainties in the eigenvalue estimation. In the second part, we assume that the set of available unitary transformations is restricted to $SO(3)$, realized as Wigner $D$-matrices. In that case, the overlap statistics does not depend only on the eigenvalues, but also on the eigenstates of the mixed state under scrutiny. The overlap distribution then shows a complicated pattern, which may be considered as a fingerprint of the mixed state. When using random transformations from the unitary group, the eigenvalues can be determined quite simply from the lower and the upper limit of the overlap statistics. This may still be possible in the $SO(3)$ case, but only at the expense of a finite systematic uncertainty.

quant-ph↗

arXiv2017

The Theory of Optical Black Hole Lasers

The event horizon of black holes and white holes can be achieved in the context of analogue gravity. It was proven for a sonic case that if these two horizons are close to each other their dynamics resemble a laser, a black hole laser, where the analogue of Hawking radiation is trapped and amplified. Optical analogues are also very successful and a similar system can be achieved there. In this work we develop the theory of optical black hole lasers and prove that the amplification is also possible. Then, we study the optical system by determining the forward propagation of modes, obtaining an approximation for the phase difference which governs the amplification, and performing numerical simulations of the pulse propagation of our system.

gr-qc↗

arXiv2017

Dialogues about geometry and light

Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some "new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.

physics.optics↗

arXiv2016

Solutions to the Painlevé V equation through supersymmetric quantum mechanics

In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlevé V (PV) equation, a second-order non-linear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator, while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.

math-ph↗

arXiv2016

Hawking spectrum for a fiber-optical analog of the event horizon

Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the pulse matches the phase velocity of light.

gr-qc↗

arXiv2015

Polynomial Heisenberg algebras and Painlevé equations

We study first the supersymmetric quantum mechanics (SUSY QM), specially the cases of the harmonic and radial oscillators. Then, we obtain a new Wronskian formula for the confluent SUSY transformation and apply the SUSY QM to the inverted oscillator. After that, we present the polynomial Heisenberg algebras (PHA). We study the general systems described by PHA: for zeroth- and first-order we obtain the harmonic and radial oscillators, respectively; for second- and third-order PHA, the potential is determined in terms of solutions to Painlevé IV and V equations ($P_{IV}$ and $P_{V}$), respectively. Later on, we review the six Painlevé equations and we study the cases of $P_{IV}$ and $P_V$. We prove a reduction theorem for $2k$th-order PHA to be reduced to second-order algebras. We also prove an analogous theorem for the $(2k+1)$th-order PHA to be reduced to third-order ones. Through these theorems we find solutions to $P_{IV}$ and $P_V$ given in terms of confluent hypergeometric functions. For some special cases, those can be classified in several solution hierarchies. In this way, we find real solutions with real parameters and complex solutions with real and complex parameters for both equations. Finally, we study the coherent states (CS) for the SUSY partners of the harmonic oscillator that are connected with $P_{IV}$, which we will call Painlevé IV coherent states. Since these systems have third-order ladder operators $l_k^\pm$, we seek first the CS as eigenstates of the annihilation operator $l_k^-$. We also define operators analogous to the displacement operator and we get CS departing from the extremal states in each subspace in which the Hilbert space is decomposed. We conclude our treatment applying a linearization process to the ladder operators in order to define a new displacement operator to obtain CS involving the entire Hilbert space.

math-ph↗

arXiv2015

Wronskian differential formula for k-confluent SUSY QM

The confluent SUSY QM usually involves a second-order SUSY transformation where the two factorization energies converge to a single value. In order to achieve it, one generally needs to solve an indefinite integral, which limits the actual systems to which it can be applied. Nevertheless, not so long ago, an alternative method to achieve this transformation was developed through a Wronskian differential formula [Phys Lett. A 3756 (2012) 692]. In the present work, we consider the k-confluent SUSY transformation, where k factorization energies merge into a single value, and we develop a generalized Wronskian differential formula for this case. Furthermore, we explicitly work out general formulas for the third- and fourth-order cases and we present as examples the free particle and the single-gap Lamé potentials.

math-ph↗