J. M. Geremia

Incorporating physical implementation concerns into closed loop quantum control experiments

In quantum control experiments, it is desirable to build features into the field that address physical concerns such as simplicity, robustness, dynamical coherence, power expenditure, etc. With a judicious choice for the cost functional, it is possible to incorporate such secondary features into the field, often without altering the experimental procedure or apparatus. Through simulated closed-loop population transfer experiments, we demonstrate the benefit of carefully designed cost functionals. As specific examples, we address two common physical concerns: removing extraneous structure from the control pulse and finding robust fields. Removing unnecessary field components is critical if information about the mechanism is to be interpreted from the structure of the optimal pulse. Robust fields produce a stable outcome despite noise in the field and, perhaps, environmental inhomogeneities in the quantum system as is typical of condensed phase experiments.

Coherent learning control of vibrational motion in room temperature molecular gases

An evolutionary learning algorithm in conjunction with an ultrafast optical pulse shaper was used to control vibrational motion in molecular gases at room temperature and high pressures. We demonstrate mode suppression and enhancement in sulfur hexafluoride and mode selective excitation in carbon dioxide. Analysis of optimized pulses discovered by the algorithm has allowed for an understanding of the control mechanism.

Optimal Hamiltonian identification: The synthesis of quantum optimal control and quantum inversion

We introduce optimal identification (OI), a collaborative laboratory/computational algorithm for extracting quantum Hamiltonians from experimental data specifically sought to minimize the inversion error. OI incorporates the components of quantum control and inversion by combining ultrafast pulse shaping technology and high throughput experiments with global inversion techniques to actively identify quantum Hamiltonians from tailored observations. The OI concept rests on the general notion that optimal data can be measured under the influence of suitable controls to minimize uncertainty in the extracted Hamiltonian despite data limitations such as finite resolution and noise. As an illustration of the operating principles of OI, the transition dipole moments of a multilevel quantum Hamiltonian are extracted from simulated population transfer experiments. The OI algorithm revealed a simple optimal experiment that determined the Hamiltonian matrix elements to an accuracy two orders of magnitude better than ...

Achieving the laboratory control of quantum dynamics phenomena using nonlinear functional maps

Abstract This paper introduces a new algorithm for achieving closed-loop laboratory control of quantum dynamics phenomena. The procedure makes use of nonlinear functional maps to exploit laboratory control data for revealing the relationship between control fields and their effect on the observables of interest. Control is achieved by (1) constructing the maps by performing laboratory experiments during an initial learning phase and then (2) searching the maps for fields that drive the system to the desired target during a separate, offline optimization stage. Once the map is learned, additional laboratory experiments are not necessarily required if the control target is changed. Maps also help to determine the control mechanism and assess the robustness of the outcome to fluctuations in the field since they explicitly measure the nonlinear response of the observable to field variations. To demonstrate the operation of the proposed map based control algorithm, two illustrations involving simulated population transfer experiments are performed.

Efficient chemical kinetic modeling through neural network maps

An approach to modeling nonlinear chemical kinetics using neural networks is introduced. It is found that neural networks based on a simple multivariate polynomial architecture are useful in approximating a wide variety of chemical kinetic systems. The accuracy and efficiency of these ridge polynomial networks (RPNs) are demonstrated by modeling the kinetics of H(2) bromination, formaldehyde oxidation, and H(2)+O(2) combustion. RPN kinetic modeling has a broad range of applications, including kinetic parameter inversion, simulation of reactor dynamics, and atmospheric modeling.

Constructing global functional maps between molecular potentials and quantum observables

The relationships that connect potential energy surfaces to quantum observables can be complex and nonlinear. In this paper, an approach toward globally representing and exploring potential-observable relationships using a functional mapping procedure is developed. Based on selected solutions of the Schrodinger equation, it is demonstrated that an observable’s behavior can be learned as a function of the potential and any other variables needed to specify the quantum system. Once such a map for the observable is in hand, it is available for use in a host of future applications without further need for solving the Schrodinger equation. As formulated here, maps provide explicit information about the global response of the observable to the potential. In this paper, we develop the mapping concept, estimate its scaling behavior (measured as the number of times the Schrodinger equation must be solved during the learning process), and numerically illustrate the technique’s globality and nonlinearity using well-...

The Ar–HCl potential energy surface from a global map-facilitated inversion of state-to-state rotationally resolved differential scattering cross sections and rovibrational spectral data

A recently developed global, nonlinear map-facilitated quantum inversion procedure is used to obtain the interaction potential for Ar–HCl(v=0) based on the rotationally resolved state-to-state inelastic cross sections of Lorenz, Westley, and Chandler [Phys. Chem. Chem. Phys. 2, 481 (2000)] as well as rovibrational spectral data. The algorithm adopted here makes use of nonlinear potential→observable maps to reveal the complete family of surfaces that reproduce the observed scattering and spectral data to within its experimental error. A nonlinear analysis is performed on the error propagation from the measured data to the recovered family of potentials. The family of potentials extracted from the inversion data is compared to the Hutson H6(4,3,0) surface [Phys. Chem. 96, 4237 (1992)], which was unable to fully account for the inelastic scattering data [Phys. Chem. Chem. Phys. 2, 481 (2000)]. There is excellent agreement with H6(4,3,0) in the attractive well, where Hutson’s surface is considered most reliab...

Quantum optimal quantum control field design using logarithmic maps

A mapping technique is introduced to expand the capabilities of current control field design procedures. The maps relate the control field to the logarithm of the time evolution operator. Over the dynamic range of the maps, which begins at the sudden limit and extends beyond, they are found to be more accurate than field → observable maps. The maps may be used as part of an iterative computational algorithm for field design. This process is illustrated for the design of a field to meet a population transfer objective.

Closed-loop quantum control utilizing time domain maps

Abstract Closed-loop laser control of quantum dynamics phenomena may be accomplished through frequency domain manipulations in the laboratory guided by a learning algorithm. This paper presents an alternative method based on the use of nonlinear input→output maps generated in the time domain, although the actual experiments and control optimization are carried out in the frequency domain. The procedure first involves the construction of input→output maps relating the field structure to the observed control performance. These maps are utilized as a substitute for actual experiments in the subsequent optimization stage in order to find the field that drives the system to a specified target. This closed-loop learning process is repeated with a sufficient number of maps until a control field is found that yields the target observable as best as possible. The overall algorithm is simulated with two model quantum systems. It is shown that excellent quality control can be achieved through this sequential learning procedure, even with individual maps that have only modest global accuracy.