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S. J. Glaser

Publications and source records attributed to S. J. Glaser.

At least 19 recordsLinked to original sources

Polarization transfer from optically-pumped NV center ensembles to multinuclear spin baths

NV-diamonds have attracted keen interest for nanoscale sensing and spin manipulation. In particular, the non-equilibrium electron spin polarization after optical excitation of single NV centers has successfully been transferred to nuclear spin baths in the surrounding of the defects. However, these experiments need to be extended to NV-ensembles which have promising practical applications in the hyperpolarization of bulk sample volumes for NMR signal enhancement. Here, we use a dense, shallow ensemble of NV-centers to demonstrate polarization transfer to nuclear spins in a well-defined composite diamond sample system. This allows us to address three different types of nuclear spins in different positions with respect to the NV polarization source: from the close proximity of $^{13}$C inside the diamond lattice to the self-assembled molecular system consisting of $^{1}$H and $^{19}$F spins outside the diamond and over multiple interfaces. We show that ensemble NV experiments face problems different from single NV experiments. In particular, using spinlock pulses, the inhomogeneously broadened ESR line of the NV ensemble limits the minimal resonance linewidth with which the transfer protocol can occur. Furthermore, we compare the NV spin-polarization losses and polarization transfer rates to the different nuclear baths and discuss the role of spin-diffusion as detrimentally affecting the direct observation of nuclear polarization build-up within the detection volume of nanoscale NV-NMR experiments.

cond-mat.mes-hall↗

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

quant-ph↗

Purity Speed Limit of Open Quantum Systems from Magic Subspaces

We introduce the concept of Magic Subspaces for the control of dissipative N- level quantum systems whose dynamics are governed by Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so that two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to established bounds and its tightness in the case of a two-level dissipative quantum system. The link between the speed limit and the corresponding time-optimal solution is discussed in the framework of this study. Explicit examples are described for two- and three- level quantum systems.

quant-ph↗

Robust control of a NOT gate by composite pulses

We present a general procedure to implement a NOT gate by composite pulses robust against both offset uncertainties and control field variations. We define different degrees of robustness in this two-parameter space, namely along one, two or all directions. We show that the phases of the composite pulse satisfy a nonlinear system, and can be computed analytically or numerically.

quant-ph↗

Time-optimal selective pulses of two uncoupled spin 1/2 particles

We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the Pontryagin Hamiltonian can be written as a one-dimensional effective Hamiltonian. The optimal fields can be expressed analytically in terms of elliptic integrals. The time-optimal control problem is solved for the selective inversion and excitation processes. A bifurcation in the structure of the control fields occurs for a specific offset threshold. In particular, we show that for small offsets, the optimal solution is the concatenation of regular and singular extremals.

quant-ph↗

Optimal control of an inhomogeneous spin ensemble coupled to a cavity

We apply optimal control techniques to an inhomogeneous spin ensemble coupled to a cavity. A general procedure is proposed for designing the control strategies. We numerically show the extent to which optimal control fields robust against system uncertainties help enhancing the sensitivity of the detection process. The parameters of the numerical simulations are taken from recent Electron Spin Resonance experiments. The low and high cooperativity regimes are explored.

quant-ph↗

Optimizing fingerprinting experiments for parameter identification: Application to spin systems

We introduce the Optimal Fingerprinting Process which is aimed at accurately identifying the parameters which characterize the dynamics of a physical system. A database is first built from the time evolution of an ensemble of dynamical systems driven by a specific field, which is designed by optimal control theory to maximize the efficiency of the recognition process. Curve fitting is then applied to enhance the precision of the identification. As an illustrative example, we consider the estimation of the relaxation parameters of a spin- 1/2 particle. The experimental results are in good accordance with the theoretical computations. We show on this example a physical limit of the estimation process.

quant-ph↗

Optimal control theory for applications in magnetic resonance imaging

We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical limits of the corresponding spin dynamics in the presence of typical experimental imperfections and limitations. We study in this paper two important goals, namely the optimization of image contrast and the maximization of the signal to noise per unit time. We anticipate that the proposed techniques will find practical applications in medical imaging in a near future to help the medical diagnosis.

quant-ph↗

Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond

The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed.

quant-ph↗

Robust optimal control of two-level quantum systems

We investigate the time and the energy minimum optimal solutions for the robust control of two-level quantum systems against offset or control field uncertainties. Using the Pontryagin Maximum Principle, we derive the global optimal pulses for the first robustness orders. We show that the dimension of the control landscape is lower or equal to 2N for a field robust to the N th order, which leads to an estimate of its complexity.

quant-ph↗

A fully efficient time-parallelized quantum optimal control algorithm

We present a time-parallelization method that enables to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver: the computational time is approximately divided by the number of available processors. The control of spin systems, molecular orientation and Bose-Einstein condensates are used as illustrative examples to highlight the wide range of application of this numerical scheme.

math.OC↗

A discrete-pulse optimal control algorithm with an application to spin systems

This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose a generalization of the standard GRAPE algorithm suited to this constraint. We test the validity and the efficiency of this approach for the inversion of an inhomogeneous ensemble of spin systems with different offset frequencies. It is shown that a remarkable efficiency can be achieved even for a very limited number of discrete values. Some applications in Nuclear Magnetic Resonance are discussed.

math.OC↗

Optimal control of the signal to noise ratio per unit time for a spin 1/2 particle

We investigate the maximum signal to noise ratio per unit time that can be achieved for a spin 1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal to noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing use of shaped pulses.

quant-ph↗

Time-optimal control of SU(2) quantum operations

We propose an analysis of the time-optimal control of SU(2) quantum operations. By using the Pontryagin Maximum Principle, we show how to determine the optimal trajectory reaching a given target state. Explicit analytical solutions are given for two specific examples. We discuss the role of the detuning in the construction of the optimal synthesis.

quant-ph↗

Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign

Magnetic Resonance Imaging has become nowadays an indispensable tool with applications ranging from medicine to material science. However, so far the physical limits of the maximum achievable experimental contrast were unknown. We introduce an approach based on principles of optimal control theory to explore these physical limits, providing a benchmark for numerically optimized robust pulse sequences which can take into account experimental imperfections. This approach is demonstrated experimentally using a model system of two spatially separated liquids corresponding to blood in its oxygenated and deoxygenated forms.

physics.med-ph↗

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.

quant-ph↗

Second order gradient ascent pulse engineering

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of quantum systems. These include more accurate gradients, convergence acceleration using the BFGS quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.

quant-ph↗

Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework

For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e. piecewise constant control amplitudes, iteratively into an optimised shape. Here, we present the first comparative study of optimal control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and KROTOV-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. --- Moreover we introduce a novel unifying algorithmic framework, DYNAMO (dynamic optimisation platform) designed to provide the quantum-technology community with a convenient MATLAB-based toolset for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing new proposed algorithms to the state-of-the-art. It allows for a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.

quant-ph↗