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Author: BLAS MANUEL RODRIGUEZ LARA

The quantum Rabi model for two qubits

BLAS MANUEL RODRIGUEZ LARA (2013)

We study a system composed of two nonidentical qubits coupled to a single mode quantum field. We calculate the spectra of the system in the deepstrong-coupling regime via perturbation theory up to second order corrections, and show that it converges to two forced oscillator chains for cases well into that regime. Our predictions are confirmed by numerical calculation of the spectra using a parity decomposition of the corresponding Hilbert space. The numerical results point to two interesting behaviors in the ultra-strong-coupling regime: the rotating wave approximation is valid for some particular cases and there exist crossings in the spectra within each parity subspace. We also present the normal modes of the system and give an example of the time evolution of the mean photon number, population inversion, von Neuman entropy and Wootters concurrence in the ultra-strong- and deep-strongcoupling regimes.

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Qubits Quantum field Hilbert space CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

Proposal for realization of the Majorana equation in a tabletop experiment

BLAS MANUEL RODRIGUEZ LARA (2013)

We introduce the term Majoranon to describe particles that obey the Majorana equation, which are different from the Majorana fermions widely studied in various physical systems. A general procedure to simulate the corresponding Majoranon dynamics, based on a decomposition of the Majorana equation into two Dirac equations, is described in detail. It allows the simulation of the two-component chiral spinors, the building blocks of modern gauge theories, in the laboratory with current technology. Specifically, a Majoranon in one spatial dimension can be simulated with a single qubit plus a continuous degree of freedom, for example, a single trapped ion. Interestingly, the dynamics of a Majoranon deviates most clearly from that of a Dirac particle in the rest frame, in which the continuous variable is redundant, making a possible laboratory implementation feasible with existing setups.

Article

Proposal Dirac equations Majorana equation CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

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

BLAS MANUEL RODRIGUEZ LARA Héctor Manuel Moya Cessa (2013)

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.

Article

Dicke models Susskind– Glogower operators Tridiagonal Hamiltonia CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

Coherent Quantum Transport in Photonic Lattices

Héctor Manuel Moya Cessa BLAS MANUEL RODRIGUEZ LARA (2013)

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a lattice, thereby demonstrating the general concept of transporting arbitrary quantum information with high fidelity. Coherent transfer over 19 sites is realized by utilizing judiciously designed optical structures consisting of evanescently coupled waveguide elements. We provide unequivocal evidence that such an approach is applicable in the quantum regime, for both bosons and fermions, as well as in the classical limit. Our results illustrate the potential of the perfect state transfer protocol as a promising route towards integrated quantum computing on a chip.

Article

Coherent quantum Transferring quantum CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

Photon transport in binary photonic lattices

BLAS MANUEL RODRIGUEZ LARA Héctor Manuel Moya Cessa (2013)

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 selfenergies 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.

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Mathematical methods Electromagnetic field Binary lattices Photon transport CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

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

BLAS MANUEL RODRIGUEZ LARA FRANCISCO SOTO EGUIBAR ALEJANDRO ZARATE CARDENAS Héctor Manuel Moya Cessa (2013)

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.

Article

Propagation Coupled Resonators Photonic Crystals Quantum Optics Quantum Electrodynamics Guided Wave Applications CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

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

BLAS MANUEL RODRIGUEZ LARA ALEJANDRO ZARATE CARDENAS FRANCISCO SOTO EGUIBAR Héctor Manuel Moya Cessa (2013)

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 solvable in the weak-coupling regime; their dispersion relation is discrete and the system is diagonalized by normal modes similar to a dressed state basis. In the strong-coupling regime, we use perturbation theory and find that the dispersion relation is continuous. We give the normal modes of the crystal in terms of continued fractions that are valid for any given parameter set. We show that these photonic crystals allow state reconstruction in the form of coherent oscillations in the weak-coupling regime. In the strong-coupling regime, the general case allows at most partial reconstruction of single waveguide input states, and non-symmetric coherent oscillations that show partial state reconstruction of particular phase-controlled states.

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Photonic crystals Classical and quantum physics Classical simulation of quantum optics CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA