arXiv subjects

D. Sugny

Publications and source records attributed to D. Sugny.

At least 19 recordsLinked to original sources

arXiv2025

Energy shortcut of N-level quantum protocols by optimal control

We introduce an energetically-optimal method inspired from Shortcut-To-Adiabaticity (STA) processes, named Quantum-Optimal-Shortcut-To-Energetics (QOSTE). QOSTE produces the same transformation as STA for a given protocol used in quantum technologies or thermodynamics, but at the lowest possible energy cost. In the general case of a N- level quantum system, we derive the QOSTE controls using geometrical and optimal control tools, and show that the minimal energy cost is determined by the length of the geodesic in the rotating frame given by the original protocol. For long control times, the scaling of the ratio between the two energy costs of STA and QOSTE is quadratic in time. We benchmark our results with the Landau-Zener protocol for qubits and STIRAP for three-level systems. We observe a drastic reduction in energy with respect to standard STA methods. Finally, using gradient-based optimization algorithms and highlighting the emerging trade-off between robustness and energy cost, we design robust QOSTE outperforming STA both in robustness and energy efficiency.

quant-ph↗

arXiv2025

Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems

We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This reduction leads to a complete analytical derivation of the optimal solution in terms of elliptic functions and elliptic integrals. Necessary optimality conditions are then obtained for the original system. These conditions are verified numerically and lead to the optimal control protocol. Various examples, ranging from state-to-state transfer to the generation of a Not gate, illustrate this study. The connection with other geometric optimization approaches that have been used to solve this problem is also discussed.

quant-ph↗

arXiv2025

Unitary Transformations using Robust Optimal Control on a Cold Atom Qudit

In this paper, we design and experimentally implement various robust quantum unitary transformations (gates) acting on $d$-dimensional vectors (qudits) by tuning a single control parameter using optimal control theory. The quantum state is represented by the momentum components of a Bose-Einstein condensate (BEC) placed in an optical lattice, with the lattice position varying over a fixed duration serving as the control parameter. To evaluate the quality of these transformations, we employ standard quantum process tomography. In addition, we show how controlled unitary transformations can be used to extend state stabilization to global stabilization within a controlled vector subspace. Finally, we apply them to state tomography, showing how the information about the relative phase between distant momentum components can be extracted by inducing an interference process.

quant-ph↗

arXiv2025

Characterization of P-divisibility in two-level open quantum systems

We study different characterizations of P-divisibility in two-level open quantum systems whose dynamics are governed by a time-local master equation with time-dependent relaxation rates. Necessary and sufficient conditions for the P-divisibility of the dynamical map are given in terms of inequalities on such relaxation rates. The equivalence between several P-divisibility characterizations existing in the literature is explicitly proven. The connection to the Breuer-Laine-Piilo measure of non-Markovianity is also established. As an application of such characterizations, we study the open dynamics of a qubit interacting with a bosonic mode. More precisely, we characterize the properties of the local map on the qubit generated by its interaction with the bosonic mode, playing the role of an extremely reduced bath. Interesting observations are made, opening perspectives for a deeper physical understanding of CP-divisibility, P-divisibility, and BLP measure.

quant-ph↗

arXiv2024

Optimal control of a Bose-Eintein Condensate in an optical lattice: The non-linear and two-dimensional cases

We numerically study the optimal control of an atomic Bose-Einstein condensate in an optical lattice. We present two generalizations of the gradient-based algorithm, GRAPE, in the non-linear case and for a two-dimensional lattice. We show how to construct such algorithms from Pontryagin's maximum principle. A wide variety of target states can be achieved with high precision by varying only the laser phases setting the lattice position. We discuss the physical relevance of the different results and the future directions of this work.

quant-ph↗

arXiv2024

Optimal Floquet Engineering for Large Scale Atom Interferometers

The effective control of atomic coherence with cold atoms has made atom interferometry an essential tool for quantum sensors and precision measurements. The performance of these interferometers is closely related to the operation of large wave packet separations. We present here a novel approach for atomic beam splitters based on the stroboscopic stabilization of quantum states in an accelerated optical lattice. The corresponding Floquet state is generated by optimal control protocols. In this way, we demonstrate an unprecedented Large Momentum Transfer (LMT) interferometer, with a momentum separation of 600 photon recoils ($600\hbar k$) between its two arms. Each LMT beam splitter is realized in a remarkably short time (2 ms) and is highly robust against the initial velocity dispersion of the wave packet and lattice depth fluctuations. Our study shows that Floquet engineering is a promising tool for exploring new frontiers in quantum physics at large scales, with applications in quantum sensing and testing fundamental physics.

physics.atom-ph↗

arXiv2024

Introduction to Theoretical and Experimental aspects of Quantum Optimal Control

Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.

quant-ph↗

arXiv2023

A $\texttt{SPIRED}$ code for the reconstruction of spin distribution

In Nuclear Magnetic Resonance (NMR), it is of crucial importance to have an accurate knowledge of the sample probability distribution corresponding to inhomogeneities of the magnetic fields. An accurate identification of the sample distribution requires a set of experimental data that is sufficiently rich to extract all fundamental information. These data depend strongly on the control fields (and their number) used experimentally. In this work, we present and analyze a greedy reconstruction algorithm, and provide the corresponding $\texttt{SPIRED}$ code, for the computation of a set of control functions allowing the generation of data that are appropriate for the accurate reconstruction of a sample distribution. In particular, the focus is on NMR and the Bloch system with inhomogeneities in the magnetic fields in all spatial directions. Numerical examples illustrate this general study.

physics.comp-ph↗

arXiv2023

Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system

We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the time-dependent relaxation rates to ensure complete positivity and positivity of the dynamical map. We discuss their relations with the non-Markovian behavior of the open system. We also analyze the long-time asymptotic behavior of the dynamics as a function of the rates. We show under which conditions on the rates the system tends to the equilibrium state. Different examples illustrate this general study.

quant-ph↗

arXiv2023

Reply to the comment on the letter "Geometric Origin of the Tennis Racket Effect"

The author of the comment~[arXiv:2302.04190] criticizes our published results in Phys. Rev. Lett. \textbf{125}, 064301 (2020) about the Tennis Racket Effect (TRE). The TRE is a geometric effect which occurs in the free rotation of any asymmetric rigid body. We explain why the criticism of this comment is not valid.

physics.class-ph↗

arXiv2023

Characterization of a driven two-level quantum system by Supervised Learning

We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.

quant-ph↗

arXiv2023

Signatures of physical constraints in rotating rigid bodies

We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery Phase and in the Tennis Racket Effect.

physics.class-ph↗

arXiv2023

Chattering Phenomenon in Quantum Optimal Control

We present a quantum optimal control problem which exhibits a chattering phenomenon. This is the first instance of such a process in quantum control. Using the Pontryagin Maximum Principle and a general procedure due to V. F. Borisov and M. I. Zelikin, we characterize the local optimal synthesis, which is then globalized by a suitable numerical algorithm. We illustrate the importance of detecting chattering phenomena because of their impact on the efficiency of numerical optimization procedures.

quant-ph↗

arXiv2022

Time-optimal control of two-level quantum systems by piecewise constant pulses

We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases with one and two controls. Exact quantum speed limits are established as a function of the sampling period. We observe numerically an exponential convergence towards the minimum time in the continuous limit when this period goes to zero. We show that this convergence is only polynomial for a linearized quantum system. We discuss the experimental impact of this result.

quant-ph↗

arXiv2022

Simultaneous field-free molecular orientation and planar delocalization by THz laser pulses

This study shows the unexpected and counter-intuitive possibility of simultaneously orienting a molecule while delocalizing its molecular axis in a plane in field-free conditions. The corresponding quantum states are characterized and different control strategies using shaped THz laser pulses are proposed to reach such states at zero and nonzero temperatures. The robustness against temperature effects of a simple control procedure combining a laser and a THz pulse is shown. Such control strategies can be applied not only to linear molecules but also to symmetric top molecules.

quant-ph↗

arXiv2022

Phase-space distributions of Bose-Einstein condensates in an optical lattice: Optimal shaping and reconstruction

We apply quantum optimal control to shape the phase-space distribution of Bose-Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.

cond-mat.quant-gas↗

arXiv2021

Hamiltonian Monodromy via spectral Lax pairs

Hamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a neighborhood of a focus-focus singularity by a spectral Lax pair approach. From the Lax pair, we derive a Riemann surface which allows us to compute in a straightforward way the corresponding Monodromy matrix. The general results are applied to the Jaynes-Cummings model and the spherical pendulum.

math-ph↗

arXiv2021

Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control

Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin Maximum Principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The tutorial covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The connection between the Pontryagin Maximum Principle and gradient-based optimization algorithms used for high-dimensional quantum systems is described. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.

quant-ph↗