Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case

The objective of this article is to complete preliminary results concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by Lindblad equations. The extremal system is described by a 3D-Hamiltonian depending upon three parameters. We combine geometric techniques with numerical simulations to deduce the optimal solutions.Comment: 24 pages, 16 figures. submitted to IEEE transactions on automatic contro

Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.Comment: 30 pages, 13 figur

Energy minimization problem in two-level dissipative quantum control: meridian case

International audienceWe analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky-Lindblad equation. According to the Pontryagin Maximum Principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis concerning 2D solutions in the case where the Hamiltonian dynamics are integrable

Nuclear DFT electromagnetic moments of intruder configurations calculated in heavy deformed open-shell odd nuclei with 63<=Z<=82 and 82<=N<=126

Within the nuclear DFT approach, we determined the magnetic dipole and electric quadrupole moments for paired nuclear states corresponding to the proton (neutron) quasiparticles blocked in the p11/2- (n13/2+) intruder configurations. We performed calculations for all deformed open-shell odd nuclei with 63<=Z<=82 and 82<=N<=126. Time-reversal symmetry was broken in the intrinsic reference frame and self-consistent shape and spin core polarizations were established. We determined spectroscopic moments of angular-momentum-projected wave functions and compared them with available experimental data. We obtained good agreement with data without using effective g-factors or effective charges in the dipole or quadrupole operators, respectively. We also showed that the intrinsic magnetic dipole moments, or those obtained for conserved intrinsic time-reversal symmetry, do not represent viable approximations of the spectroscopic ones.Comment: 11 RevTex pages, 9 figure

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using band-pass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.Comment: 16 pages, 4 figures. To appear in Physical Review

The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO(3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface and the conjugate points of this metric are evaluated using recent work [4] on surfaces of revolution

Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity

We analytically determine the minimal time and the optimal control laws required for the realization, up to an assigned fidelity and with a fixed energy available, of entangling quantum gates ($\mathrm{CNOT}$) between indirectly coupled qubits of a trilinear Ising chain. The control is coherent and open loop, and it is represented by a local and continuous magnetic field acting on the intermediate qubit. The time cost of this local quantum operation is not restricted to be zero. When the matching with the target gate is perfect (fidelity equal to one) we provide exact solutions for the case of equal Ising coupling. For the more general case when some error is tolerated (fidelity smaller than one) we give perturbative solutions for unequal couplings. Comparison with previous numerical solutions for the minimal time to generate the same gates with the same Ising Hamiltonian but with instantaneous local controls shows that the latter are not time-optimal.Comment: 11 pages, no figure

Automatically tracking feeding behavior in populations of foraging worms

C. elegans feeds on bacteria and other small microorganisms which it ingests using its pharynx, a neuromuscular pump. Currently, measuring feeding behavior requires tracking a single animal, indirectly estimating food intake from population-level metrics, or using restrained animals. Therefore, to enable large throughput feeding measurements of unrestrained, crawling worms on agarose plates, we developed an imaging protocol and a complementary image analysis tool called PharaGlow. We image up to 50 freely moving worms simultaneously and extract locomotion and feeding behaviors. Our tool reliably detects pharyngeal pumping in adult worms with a maximum deviation of 5% in the number of pumps compared to an expert annotator. We demonstrate the tool's robustness and highthroughput capabilities by measuring feeding in different use-case scenarios. This includes tracing pharyngeal dynamics during development, revealing their highly conserved nature throughout all life cycle stages. We also observed pumping after food deprivation, corroborating previous studies in which starvation time strongly influences pumping. Finally, we further validated our behavioral tracker by exploring two previously characterized pumping defective mutants: unc-31 and eat-18. Remarkably, our analysis of eat-18 mutants identified unreported defects in pumping and overall locomotion regulation, highlighting the potential of this toolkit. Pharaglow therefore enables the observation and analysis of the temporal dynamics of food intake with high-throughput and precision in a user-friendly system

Automatically tracking feeding behavior in populations of foraging C. elegans

Caenorhabditis elegans feeds on bacteria and other small microorganisms which it ingests using its pharynx, a neuromuscular pump. Currently, measuring feeding behavior requires tracking a single animal, indirectly estimating food intake from population-level metrics, or using restrained animals. To enable large throughput feeding measurements of unrestrained, crawling worms on agarose plates at a single worm resolution, we developed an imaging protocol and a complementary image analysis tool called PharaGlow. We image up to 50 unrestrained crawling worms simultaneously and extract locomotion and feeding behaviors. We demonstrate the tool’s robustness and high-throughput capabilities by measuring feeding in different use-case scenarios, such as through development, with genetic and chemical perturbations that result in faster and slower pumping, and in the presence or absence of food. Finally, we demonstrate that our tool is capable of long-term imaging by showing behavioral dynamics of mating animals and worms with different genetic backgrounds. The low-resolution fluorescence microscopes required are readily available in C. elegans laboratories, and in combination with our python-based analysis workflow makes this methodology easily accessible. PharaGlow therefore enables the observation and analysis of the temporal dynamics of feeding and locomotory behaviors with high-throughput and precision in a user-friendly system.eLife digest: A small worm called C. elegans is constantly hungry. It spends all its time looking for food or eating. Hunger and environmental factors, like light, influence its feeding behavior. Studying these worms has helped scientists learn how feeding affects health, longevity, and aging. Feeding studies might also help scientists learn how the nervous system works and how it controls feeding. Most studies have used one of two approaches. Scientists may measure how much food a group of C. elegans eat by measuring food before and after it is offered to the worms. Or they restrain individual worms and measure the movement of a tube-like muscle, called the pharynx, which the animals use to vacuum up food. Restraining the worms can alter their behavior or brain activity, and studying group feeding habits may miss individual differences, so neither is optimal. Ideally, scientists could measure the feeding activity of many free-ranging worms, but because the movements of the pharynx are small, that too can be a challenge. Bonnard, Liu et al. developed a software tool that automatically detects and measures feeding behavior in a group of about 30 free-ranging C. elegans simultaneously. In the experiments, Bonnard, Liu et al. genetically engineered worms expressing a fluorescent protein in their pharynx, making it possible to measure its movements with a microscope. They used the microscope to capture images of 30-50 animals at a time as they foraged for food in a dish. Then, they used the software to analyze the data they collected. Over three days and five imaging sessions, Bonnard and Liu et al. tracked the feeding behavior of about 1,000 animals under different conditions. The experiments show that the pharynx grows rapidly during early worm development when the worms quadruple their length, but the rate of pharynx muscle contractions stays the same. They also showed the technique could measure feeding behaviors in animals with different genetic backgrounds, ages, or those engaged in behaviors like mating. The tool allows for larger and longer-term studies of worm feeding behaviors than previous approaches. Bonnard, Liu et al. made their software, called PharaGlow, available for use by other researchers. The tool may make feeding measurements a routine part of C. elegans studies. It will allow scientists to gain new insights into the role of feeding in a range of processes, including aging, fitness, mating, and overall health. Follow-up studies could determine if these findings are general strategies that also apply to other animals