arXiv subjects

D. Martínez-Tibaduiza

Publications and source records attributed to D. Martínez-Tibaduiza.

5 recordsLinked to original sources

arXiv2026

All-optical saddle trap as a platform for mesoscopic quantum experiments

We investigate the quantum dynamics of a levitated nanoparticle in a structured light rotating saddle-like optical potential consisting of a superposition of Gaussian and Laguerre-Gauss modes with detuned frequencies. This rotating saddle trap offers unique opportunities for quantum experiments, such as reduced decoherence due to photon recoil and absorption, the possibility of large delocalization of the particle's center-of-mass motion, particle recovery protocols, the generation of motional entanglement and momentum squeezing. As an application, we show that this saddle-trap architecture enables force detection with sensitivity in the zepto-Newton regime.

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arXiv2025

$\texttt{Symdyn}$: an automated algebraic solution for high-order quantum systems

Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\hat{H}(t)=\sum_{l=1}^{L}η_{l}(t)\hat{g}_{l}$. The Wei-Norman method provides a framework for determining the coefficients of the corresponding time evolution operator in its factorized representation, $\hat{U}(t) = \prod_{l=1}^{L} e^{ Λ_{l}(t)\hat{g}_{l}}$. This work introduces $\texttt{Symdyn}$, a Python library that automates the application of this method. The library efficiently computes similarity transformations and the nonlinear differential equations intrinsic to derive Baker-Campbell-Hausdorff-like relations and the time evolution of high-order quantum systems ($L\geq 6$). We demonstrate its robustness by deriving the time evolution operator for a system of two time-dependent coupled harmonic oscillators. Additionally, we specialize the library to the Lie group $\textit{SU}(N)$, showing its versatility with $\textit{SU}(2)$, $\textit{SU}(3)$ and $\textit{SU}(4)$ examples, relevant to quantum computing.

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arXiv2023

Quantum-based solution of time-dependent complex Riccati equations

Using the Wei-Norman theory we obtain a time-dependent complex Riccati equation (TDCRE) as the solution of the time evolution operator (TEO) of quantum systems described by time-dependent (TD) Hamiltonians that are linear combinations of the generators of the $\mathfrak{su}(1,1)$, $\mathfrak{su}(2)$ and $\mathfrak{so}(2,1)$ Lie algebras. Using a recently developed solution for the time evolution of these quantum systems we solve the TDCRE recursively as generalized continued fractions, which are optimal for numerical implementations, and establish the necessary and sufficient conditions for the unitarity of the TEO in the factorized representation. The inherited symmetries of quantum systems can be recognized by a simple inspection of the TDCRE, allowing effective quantum Hamiltonians to be associated with it, as we show for the Bloch-Riccati equation whose Hamiltonian corresponds to that of a generic TD system of the Lie algebra $\mathfrak{su}(2)$. As an application, but also as a consistency test, we compare our solution with the analytic one for the Bloch-Riccati equation considering the Rabi frequency driven by a complex hyperbolic secant pulse generating spin inversion, showing an excellent agreement.

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arXiv2022

Algebraic approach to a two-qubit quantum thermal machine

Algebraic methods for solving time dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled q-bits, performing an Otto cycle. The thermal interaction occurs with two baths at different temperatures, while work is associated with the interaction with an arbitrary time-dependent magnetic field that varies in intensity and direction. For the coupling, we consider the 1-d isotropic Heisenberg model, which allows us to describe the system by means of the irreducible representation of the $\mathfrak{su}(2)$ Lie algebra within the triplet subspace. We inspect different settings of the temperatures and frequencies of the cycle and investigate the corresponding operation regimes of the engine. Finally, we numerically investigate the engine efficiency under a time varying Rabi frequency, interpolating the abrupt and adiabatic limits.

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arXiv2021

Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

In this work, we provide an answer to the question: how sudden or adiabatic is a change in the frequency of a quantum harmonic oscillator (HO)? To do this, we investigate the behavior of a HO, initially in its fundamental state, by making a frequency transition that we can control how fast it occurs. The resulting state of the system is shown to be a vacuum squeezed state in two bases related by Bogoliubov transformations. We characterize the time evolution of the squeezing parameter in both bases and discuss its relation with adiabaticity by changing the rate of the frequency transition from sudden to adiabatic. Finally, we obtain an analytical approximate expression that relates squeezing to the transition rate as well as the initial and final frequencies. Our results shed some light on subtleties and common inaccuracies in the literature related to the interpretation of the adiabatic theorem for this system.

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