Searcharxiv⌕ Search

arXiv subjects

H. Moya-Cessa

Publications and source records attributed to H. Moya-Cessa.

At least 19 recordsLinked to original sources
arXiv2025

Unitary transformation approach to the paraxial wave equation

We present a framework for the paraxial wave equation based on propagation-dependent unitary transformations closely related to the Lewis-Ermakov invariant. This approach establishes a formal equivalence between free-space propagation and the dynamics in a quadratic gradient index (GRIN) medium. In this context, the dynamical invariant and the free-space Hamiltonian do not commute at the initial propagation stage due to Gaussian modulation, which imposes an effective quadratic confinement. Exact commutativity would only be possible for an infinitely wide, nonsquare-integrable optical field; therefore, any finite-energy beam propagates as if it were subject to a quadratic GRIN-like potential. The unitary transformation approach reveals how the Gaussian envelope of physical beams leads to effective harmonic confinement and connects the propagation dynamics to oscillator-like invariants. This method enables the derivation of stationary solutions in different coordinate systems by mapping to an effective quadratic-like medium and establishes a direct link to the zero-frequency Ermakov equation and the Lewis-Ermakov invariants.

physics.optics↗
arXiv2017

Multiphoton processes by conditional measurements in the atom-field interaction

We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e., adding or subtracting several photons from the cavity field.

quant-ph↗
arXiv2013

Intrinsic decoherence in the interaction of two fields with a two-level atom

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. Then we solve a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment.

quant-ph↗
arXiv2013

Quantum derivation of Manley Rowe type relations

The Ermakov Lewis quantum invariant for the time dependent harmonic oscillator is expressed in terms of number and phase operators. The identification of these variables is made in accordance with the correspondence principle and the amplitude and phase representation of the classical orthogonal functions invariant. The relationship between the number and phase operators is established through this invariant as the system evolves from one frequency to another. In the specific case where the excitations represent the photon number, these relations are equivalent to the power density transport equations derived in nonlinear optical processes.

quant-ph↗
arXiv2013

NOON states in trapped ions

We show how NOON states may be generated in ion traps. We use the individual interaction of light with each of two vibrational modes of the ion to entangle them. This allows us to generate NOON states with N=8.

quant-ph↗
arXiv2013

Generalized qubits of the vibrational motion of a trapped ion

We present a method to generate qubits of the vibrational motion of an ion. The method is developed in the non-rotating wave approximation regime, therefore we consider regimes where the dynamics has not been studied. Because the solutions are valid for a more extended range of parameters we call them generalized qubits.

quant-ph↗
arXiv2013

Mirror-field-atom interaction: Hamiltonian diagonalization

We show that the interaction between a movable mirror with a quantized field that interacts with a two-level atom may be simplified via a transformation that involves Susskind-Glogower operators (SGO). By using this transformation it is easy to show that we can cast the Hamiltonian, after a series of small rotations, into an effective Hamiltonian that may be solved. We would like to stress that the transformation in terms of SGO already simplifies enough the Hamiltonian in the sense that, in an exact way, it "eliminates" one of the three-subsystems, namely the quantized field.

quant-ph↗
arXiv2013

Entropy operator and associated Wigner function

We show how the entropy operators for two subsystems may be calculated. In the case of the atom-field interaction we obtain the associated Wigner function for the entropy operator for the quantized field.

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↗
arXiv2011

Alternative analysis to perturbation theory

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function, additionally we can analyze the time evolution of the system. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.

quant-ph↗
arXiv2011

Solution to the Landau-Zener problem via Susskind-Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.

quant-ph↗
arXiv2010

Exact solution of the ion-laser interaction in all regimes

We show that in the trapped ion-laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb-Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.

quant-ph↗
arXiv2009

Sudden death and long-lived entanglement of two three-level trapped ions

The dynamical properties of quantum entanglement in two three-level trapped ions interacting with a laser field are studied in terms of the negative eigenvalues of the partial transposition of the density operator. In contrast to the usual belief that destroying the entanglement can be observed due to the environment, it is found that the Stark shift can also produce sudden death of entanglement and long-lived entanglement between the qubits that are prepared initially in separable states or mixed states.

quant-ph↗