arXiv subjects

B. M. Rodríguez-Lara

Publications and source records attributed to B. M. Rodríguez-Lara.

At least 73 records · Page 4Linked to original sources

arXiv2014

Ground state in the finite Dicke model for interacting qubits

We study the ground state of a finite size ensemble of interacting qubits driven by a quantum field. We find a maximally entangled W-state in the ensemble part of the system for a certain coupling parameters region. The area of this region decreases as the ensemble size increases and, in the classical limit, becomes the line in parameter space that defines the phase transition of the system. In the classical limit, we also study the dynamics of the system and its transition from order to disorder for initial energies close to the ground state energy. We find that a critical energy providing this transition is related to the minimum of the projection of the total angular momentum of the quantum system in the $z$-direction.

quant-ph↗

arXiv2014

Phase state and related nonlinear coherents states

We cast the phase state as a $SU(1,1)$ nonlinear coherent state to support the idea that the $SU(1,1)$ representation of the electromagnetic field may be helpful in some instances and to bring forward that it may relate to the phase state problem. We also construct nonlinear coherent states related to the exponential phase operator and provide their corresponding nonlinear annihilation operators. Finally, we discuss the propagation of classical fields through arrays of coupled waveguides that are solved through the use of nonlinear coherent states of $SU(1,1)$ or the exponential phase operator.

quant-ph↗

arXiv2014

Nonlinear coherent state generation in the two-photon Jaynes-Cummings model

We show that the two-photon Jaynes-Cummings model, feasible of experimental realization in cavity or ion-trap quantum electrodynamics, can approximately produce nonlinear coherent states of the field. We introduce these nonlinear coherent states of the field as $2m$-photon added or subtracted coherent states in terms of raising and lowering field operators, also known as London phase operators or Susskind-Glogower operators.

quant-ph↗

arXiv2014

An optical analog of quantum optomechanics

We present a two-dimensional array of nearest-neighbor coupled waveguides that is the optical analog of a quantum optomechanical system. We show that the quantum model predicts the appearance of effective column isolation, diagonal-coupling and other non-trivial couplings in the two-dimensional photonic lattice under a standard approximation from ion-trap cavity electrodynamics. We provide an approximate impulse function for the case of effective column isolation and compare it with exact numerical propagation in the photonic lattice.

physics.optics↗

arXiv2014

Searching for structure beyond parity in the two-qubit Dicke model

We try to classify the spectrum of the two-qubit Dicke model by calculating two quantum information measures of its eigenstates: the Wooters concurrence and the mutual quantum information. We are able to detect four spectral sets in each parity subspace of the model: one set is regular and given by the product of a Fock state of the field times the singlet Bell state of the qubits; the rest are fairly regular and related to the triplet states of the Bell basis. The singlet states become trapping states when we couple the Dicke model to an environment of harmonic oscillators, making them candidates for generating maximally entangled states in experimental realizations of ion trap quantum electrodynamics (QED) and circuit QED. Furthermore, they are robust and survive the inclusion of driving and dipole-dipole interactions, pointing to their use for storing quantum correlations, and it is straightforward to provide a generalization of these trapping states to the Dicke model with even number of qubits.

quant-ph↗

arXiv2014

An intensity-dependent quantum Rabi model: Spectrum, SUSY partner and optical simulation

We study an intensity-dependent quantum Rabi model that can be written in terms of SU(1,1) group elements and is related to the Buck-Sukumar model for the Bargmann parameter $k=1/2$. The spectrum seems to present avoiding crossings for all valid parameter sets and, thus, may be integrable. For a degenerate qubit, the model is soluble and we construct an unbroken supersymmetric parter for it. We discuss the classical simulation of the general model in photonic lattices and show that it presents quasi-periodic reconstruction for a given initial state and parameter set.

quant-ph↗

arXiv2014

Propagation and perfect transmission in three-waveguide axially varying couplers

We study a class of three-waveguide axially varying structures whose dynamics are described by the su(3) algebra. Their analytic propagator can be found based on the corresponding Lie group generators. In particular, we show that the field propagator corresponding to three-waveguide structures that have arbitrarily varying coupling coefficients and identical refractive indices is associated with the orbital angular momentum algebra. The conditions necessary to achieve perfect transmission from the first to the last waveguide element are obtained and particular cases are elucidated analytically.

physics.optics↗

arXiv2013

Propagation of non-classical states of light through one-dimensional photonic lattices

We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal polynomials. We present propagation examples of non-classical states of light: single photon, coherent state, path-entangled state and two-mode squeezed vacuum impinging into two-waveguide couplers and a photonic lattice producing coherent transport.

quant-ph↗

arXiv2013

Jacobi photonic lattices and their SUSY partners

We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the quantum optical analogy. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1,1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.

physics.optics↗

arXiv2013

An introduction to arrays of coupled waveguides

We present the theoretical basis needed to work in the field of photonic lattices. We start by studying the field modes in- and out-side a single waveguide. Then, we use perturbation theory to deal with an array of coupled waveguides and construct mode-coupling theory. Finally, we realize a survey of optical analogues to quantum systems accompanied by an extensive bibliography.

physics.optics↗

arXiv2013

Optical simulation of Majorana physics

We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a bi-chromatic refractive index distribution and nearest neighbor couplings of the type found in Glauber-Fock lattices. This allows us to escape the restriction of staying near the Brillouin zone imposed by the classical simulation of Dirac dynamics with bi-chromatic lattices. Furthermore, it is possible to simulate the evolution of Gaussian wavepackets under the Majorana/Dirac equation with light impinging only into the first waveguide of our bi-chromatic-Glauber-Fock lattice.

physics.optics↗

arXiv2013

Optical Bistability in a cavity with one moving mirror

We analyze the behaviour of a coherent field driving a single mode optical cavity with one perfectly reflecting moving mirror and a partially reflecting fixed mirror, and show that this system's output exhibits optical bistability due to radiation pressure acting over the moving mirror.

quant-ph↗

arXiv2013

The quantum Rabi model for two qubits

We study the two-qubit Rabi model in the most general case where the qubits are different from each other. The spectrum of the system in the ultrastrong-coupling regime is shown to converge to two forced oscillator chains by perturbation theory. An even and odd decomposition of the Hilbert space allows us to calculate the spectra in any given parameter regime; the cases studied confirm our perturbation theory prediction in the ultrastrong-coupling regime and point to crossings in the spectra within each parity subspace in the moderate-coupling regime. The normal modes of the system are calculated by two different methods, the first a linear algebra approach via the parity bases that delivers a four-term recurrence relation for the amplitudes of the proper states and, the second, via Bargmann representation for the field that delivers five-term recurrence relations. Finally, we show some examples of the time evolution of the mean photon number, population inversion, von Neuman entropy and Wootters concurrence under the two-qubit quantum Rabi Hamiltonian by taking advantage of the parity decomposition.

quant-ph↗

arXiv2013

A classical simulation of nonlinear Jaynes--Cummings and Rabi models in photonic lattices

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.

physics.optics↗

arXiv2013

Nondiffracting Accelerating Waves: Weber waves and parabolic momentum

Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a specific class of nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape. They are expressed in an analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solutions of the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic, electromagnetic and elastic waves to surface waves in fluids and membranes.

physics.optics↗

arXiv2013

The exact solution of generalized Dicke models via Susskind-Glogower operators

We show a right unitary transformation approach based on Susskind-Glogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis. This tridiagonal Hamiltonian is diagonalized by a set of orthogonal polynomials satisfying a three-term recurrence relation. Our result is used to deliver a closed form, analytic time evolution for the case of a Jaynes-Cummings-Kerr model and to study the time evolution of the population inversion, reduced field entropy, and Husimi's Q-function of the field for ensembles of interacting two-level systems under a Dicke-Kerr model.

quant-ph↗

arXiv2013

Photon transport in binary photonic lattices

We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where self-energies or couplings are alternated. For didactic reasons, we split the analysis in classical propagation and quantum transport but all methods can be implemented, mutatis mutandis, in any given case. On the classical side, we use coupled mode theory and present an operator approach to Floquet-Bloch theory in order to study the propagation of a classical electromagnetic field in two particular infinite binary lattices. On the quantum side, we study the transport of photons in equivalent finite and infinite binary lattices by couple mode theory and linear algebra methods involving orthogonal polynomials. Curiously the dynamics of finite size binary lattices can be expressed as roots and functions of Fibonacci polynomials.

quant-ph↗

arXiv2013

A photonic crystal realization of a phase driven two-level atom

We propose a set of photonic crystals that realize a nonlinear quantum Rabi model equivalent to a two-level system driven by the phase of a quantized electromagnetic field. The crystals are exactly soluble in the weak-coupling regime and their dispersion relation is discrete. The system is diagonalized by normal modes equivalent to a dressed state basis. In the strong-coupling regime, we use perturbation theory and find that the dispersion relation is continuous and give the normal modes of the crystal in terms of continued fractions. We show that these photonic crystals allow state reconstruction in the form of coherent oscillations in the weak-coupling regime.

quant-ph↗