arXiv subjects

Sofía Martínez-Garaot

Publications and source records attributed to Sofía Martínez-Garaot.

6 recordsLinked to original sources

arXiv2026

Quasiparticle projection method for dynamically unstable Bose-Einstein condensates

We present a general formalism for performing a time-dependent Bogoliubov analysis of a dynamically unstable Bose-Einstein condensate, which extends the quasiparticle projection method of Morgan et al. [Phys. Rev. A 57, 3818 (1998)] to cases with a complex spectrum. By introducing the proper left eigenvectors associated with each regime, we construct a biorthogonal basis. While the usual Bogoliubov normalization $\langle u | u \rangle - \langle v | v \rangle = 1$ may not hold in this basis, it still allows for a complete mode decomposition and an accurate reconstruction of arbitrary perturbations over time. This approach extends the applicability of the Bogoliubov framework beyond the stable regime, providing a consistent analysis of the time evolution of unstable condensates. As a proof of concept, we apply the method to a one-dimensional condensate with attractive interactions, which is dynamically unstable and evolves into nonstationary localized structures seeded by small perturbations. Overall, the present method provides a complete and robust mode expansion that remains meaningful beyond the linear regime and useful for characterizing the macroscopic development of instabilities.

cond-mat.quant-gas↗

arXiv2026

Numerically Optimizing Shortcuts to Adiabaticity: A Hybrid Control Strategy

Achieving fast, excitation-free quantum control is a vital challenge in modern quantum technologies. In many cases, shortcuts to adiabaticity enable fast adiabatic-like protocols, yet determining control parameters that satisfy practical constraints is often challenging in complex systems. Here, we combine an analytical shortcut to adiabaticity approach with several numerical optimization methods to boost the performance of the protocol. As a proof-of-principle for this hybrid approach, we study a particularly intricate control problem, the separation of two trapped ions. We show that this analytical-numerical approach, along with the physical insight gained through the variety of suboptimal solutions, leads to the exploration of new solutions in a complex landscape that yield improvements of up to 3 orders of magnitude. Moreover, this improvement comes with no additional cost from an experimental point of view.

quant-ph↗

arXiv2025

Impact of Force Noise on the Visibility of STA-Based Atom Interferometers

In a previous work, we designed a compact atom interferometer to measure homogeneous constant forces guiding the arms via shortcuts to adiabatic paths. Within this scheme we drive the atom by moving spin-dependent traps, and design a force $f(t)$ to compensate inertial terms in the moving frame. In this paper we analyze how robust our interferometer is against some realistic noisy deviation from the unperturbed value of the force $f(t)$. The complex overlap of the atom wave functions for each arm of the interferometer at the final time of the process is calculated. We demonstrate that the measure of the unknown force will not be affected, as there will be no contribution of the error in the phase difference of the overlap. Nevertheless, the visibility will be reduced as the modulus will no longer be one. In addition we find the optimal trajectories minimizing the effect of the noise in the visibility while keeping the sensitivity of the interferometer.

quant-ph↗

arXiv2020

Shortcut-to-adiabaticity-like techniques for parameter estimation in quantum metrology

Quantum metrology makes use of quantum mechanics to improve precision measurements and measurement sensitivities. It is usually formulated for time-independent Hamiltonians but time-dependent Hamiltonians may offer advantages, such as a $T^4$ time dependence of the Fisher information which cannot be reached with a time-independent Hamiltonian. In Optimal adaptive control for quantum metrology with time-dependent Hamiltonians (Nature Communications 8, 2017), Shengshi Pang and Andrew N. Jordan put forward a Shortcut-to-adiabaticity (STA)-like method, specifically an approach formally similar to the "counterdiabatic approach", adding a control term to the original Hamiltonian to reach the upper bound of the Fisher information. We revisit this work from the point of view of STA to set the relations and differences between STA-like methods in metrology and ordinary STA. This analysis paves the way for the application of other STA-like techniques in parameter estimation. In particular we explore the use of physical unitary transformations to propose alternative time-dependent Hamiltonians which may be easier to implement in the laboratory.

quant-ph↗

arXiv2020

Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity

We find the noise sensitivities (i.e., the quadratic terms of the energy with respect to the perturbation of the noise) of a particle shuttled by an optical lattice that moves according to a shortcut-to-adiabaticity transport protocol. Noises affecting different optical lattice parameters, trap depth, position, and lattice periodicity, are considered. We find generic expressions of the sensitivities for arbitrary noise spectra but focus on the white-noise limit as a basic reference, and on Ornstein-Uhlenbeck noise to account for the effect of non-zero correlation times.

quant-ph↗

arXiv2018

Non-linear mixing of Bogoliubov modes in a bosonic Josephson junction

We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.

cond-mat.quant-gas↗