arXiv subjects

Dionisis Stefanatos

Publications and source records attributed to Dionisis Stefanatos.

45 records · Page 3Linked to original sources

arXiv2011

Optimal trajectories for efficient atomic transport without final excitation

We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering techniqe based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really harmonic, we keep the relative displacement between the center of mass and the trap center bounded. Under this constraint, optimal protocols are found according to different physical criteria. The minimum time solution has a "bang-bang" form, and the minimum displacement solution is of "bang-off-bang" form. The optimal trajectories for minimizing the transient energy are also discussed.

quant-ph↗

arXiv2011

Minimum-Time Quantum Transport with Bounded Trap Velocity

We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the corresponding optimal control problem and obtain an interesting bang-bang solution. These results are expected to find applications in quantum information processing, where quantum transport between the storage and processing units of a quantum computer is an essential step. They can also be extended to the efficient transport of Bose-Einstein condensates, where the ability to control them is crucial for their potential use as interferometric sensors.

math.OC↗

arXiv2011

The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential

In this article we study the frictionless cooling of atoms trapped in a harmonic potential, while minimizing the transient energy of the system. We show that in the case of unbounded control, this goal is achieved by a singular control, which is also the time-minimal solution for a "dual" problem, where the energy is held fixed. In addition, we examine briefly how the solution is modified when there are bounds on the control. The results presented here have a broad range of applications, from the cooling of a Bose-Einstein condensate confined in a harmonic trap to adiabatic quantum computing and finite time thermodynamic processes.

math.OC↗

arXiv2010

Frictionless atom cooling in harmonic traps: a time-optimal approach

In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for trasient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has "bang-bang" form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.

quant-ph↗

arXiv2010

Optimal Design of Minimum Energy Pulses for Bloch Equations in the case of Dominant Transverse Relaxation

In this report, we apply Optimal Control Theory to design minimum energy $π/2$ and $π$ pulses for Bloch equations, in the case where transverse relaxation rate is much larger than longitudinal so the later can be neglected. Using Pontryagin's Maximum Principle, we derive an optimal feedback law and subsequently use it to obtain analytical expressions for the energy and duration of the optimal pulses.

math.OC↗

arXiv2010

Constrained Minimum-Energy Optimal Control of the Dissipative Bloch Equations

In this letter, we apply optimal control theory to design minimum-energy $π/2$ and $π$ pulses for the Bloch system in the presence of relaxation with constrained control amplitude. We consider a commonly encountered case in which the transverse relaxation rate is much larger than the longitudinal one so that the latter can be neglected. Using the Pontryagin's Maximum Principle, we derive optimal feedback laws which are characterized by the number of switches, depending on the control bound and the coordinates of the desired final state.

math.OC↗

arXiv2009

A Pseudospectral Method for Optimal Control of Open Quantum Systems

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous time optimal control problem, to a finite dimensional constrained nonlinear programming problem. This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in Nuclear Magnetic Resonance (NMR) spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found. We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum energy controls. The method is not restricted to the systems studied in this article but is universal to every open quantum system whose performance is limited by dissipation.

physics.chem-ph↗

arXiv2005

Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems

In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems it is shown that the optimal solution and the reachable set can be found by solving a semidefinite program. In practice, solutions to these problems generate optimal methods for control of quantum mechanical phenomena in presence of dissipation. In the area of coherent spectroscopy, this translates into the maximum signal to noise ratio that can be obtained in a spectroscopy experiment.

math.OC↗

arXiv2005

Relaxation Optimized Transfer of Spin Order in Ising Spin Chains

In this manuscript, we present relaxation optimized methods for transfer of bilinear spin correlations along Ising spin chains. These relaxation optimized methods can be used as a building block for transfer of polarization between distant spins on a spin chain. Compared to standard techniques, significant reduction in relaxation losses is achieved by these optimized methods when transverse relaxation rates are much larger than the longitudinal relaxation rates and comparable to couplings between spins. We derive an upper bound on the efficiency of transfer of spin order along a chain of spins in the presence of relaxation and show that this bound can be approached by relaxation optimized pulse sequences presented in the paper.

quant-ph↗