Introduction

1. This research is sponsored by NSF grant PHY 0902221. Ben Crist was supported by an REU supplement. Looking Inside the Black Box: Deciphering Optimal Control Fields Guan-Yeu Chen, Ben Crist and Wendell. T. Hill III Institute for Physical Science & Technology, Department of Physics, and the Joint Quantum Institute, University of Maryland, College Park, MD 20742 Excited Quasi-bound Bending Motion Control Introduction Unbound Pulse shaping coupled with adaptive feedback provides an experimental knob to control dynamics, to select pathways through transient states and to enhance product yields in quantum systems. Adaptive feedback provides the lacking intelligence to achieve optimization of the field by allowing a concomitant signal that changes in direct proportion with the desired yield, known as the fitness parameter, to be maximized. Generally, the resulting optimal field or optimal pulse shape (OPS) lacks uniqueness and is incomprehensible. The research presented here is a step towards demystification the OPS. In our experiments we control (enhance) specific normal modes of motion and modify decay branching ratios in a simple three-atom system, CO2. We exploit strong-field induced Coulomb explosion imaging to gain a direct view of the structure and dynamics on a time scale limited by the pulse. Feedback for obtaining an OPS is aided by genetic or evolutionary algorithms (GA). In distinction to the more common GA approaches, we employ a geometrical area to filter the image signal as a combined fitness and cost parameter. As will be shown, unique aspects of the OPS and, more importantly, intelligence can be attached to the OPS by comparing GA search results acquires with restricted and unrestricted parameter sets (genes). A better understanding of the OPS will ultimately enable more efficient pulses to be achieved to create qubits, for example. I. Quasi-unrestricted Parameter Set The phase of each spectral element is allowed to change randomly within a predetermined, changeable soft boundary. 32 element gene in ~50 nm range The phase mutation range for each new generation is controlled with a Gaussian boundary centered at the value of the previous phase. Final State Transient State Solutions for Quasi-unrestricted Parameter Set Experiment 50 fsPulse TL Oscillator CPA Shaped Pulse 1st Generation Search solutions generally consist of an intense peak preceded by one or more weaker peaks. Pulse trains are generated by a phase dominated by odd orders, providing insight into what the OPS is doing. Pulse Shaper Pulse Analyzer Camera 42nd Generation Composite Mode Genetic Algorithm II. Restricted Parameter Set Single Shot Mode After a GA solution is found, a fast- frame camera records single-shot explosion events at the laser rep rate. A variety of image correlation techniques are use to extract the molecular dynamics [3-5]. The gene is composed of a spectral phase with four coefficients associated with: Composite Image 4π Image Spectrometer [1,2] The first two orders (0th and 1st) are not specified in our search. The remaining odd orders produce pulse trains with increasing (negative coefficients) or decreasing (positive coefficients) intensity with time. The remaining even orders tend to modify the pulse duration and peak separation. ∑ Solutions for Restricted Parameter Set (222) The solutions again exhibit a pulse train with the last peak having more energy and a wider width (~100 fs) than the preceding peaks. The train produces an explosion signal significantly stronger than an isolated pulse with parameters comparable to that of the final peak. Under our conditions, the early peaks did not produce a detectable signal [6]. Isolated partnersused to extractdynamics [4]. Single frame Explosion partners isolated via Selected Average [3-5] Selected Area (221) Selective Average Images ▲ Two Dimensional Fitness Parameter More complicated areas can be used to distinguish asymmetric explosions. The length of the C2+ lobe is used to identify the amplitude of bending [6]. ♦ 50fs Transform Limited 100fs Transform Limited C2+ O2+ O2+ G.Y. Chen, et al., Phys. Rev. A 79, 011401(R) (2009) Bending Amplitude Branching Ratio Polarization axis Discussion and Interpretation Branching Ratios Control Selected Area Bending Amplitude Fitness Parameter Definition Our interpretation of the OSP is based on theoretical simulations by K. Kono and his group [7,8]. In a series of publications they showed that the large bending amplitude observed in CO2 Coulomb explosion is due to the explosion originating from the lowest excited state of CO22+. This agreed with our experimental analysis of Rc [4]. They further showed that the the curvature of this state is very sensitive to the presence of an external field. C2+ O2+ C2+ Each explosion channel produces a unique image that depends on the charge/mass ratio and the momentum of the constituent ions. Consequently, channels can be discriminated by where the C2+ and O2+ ions are located. To distinguish the (222) and (221) channels, for example, we define two masks to filter the image signal, one for each channel. The fitness parameter is then the ratio of counts associated with each mask. O2+ O2+ O2+ θCM Explosion Partners Strong dipole transitions occur at 800 nm between the two lowest states. Field free, CO22+ is bent in the 1st excited state with a bond angle of ~ 60o. In the presence of a field the surface flattens, and the molecule become more linear. The early peaks in the train are sufficient to populate this state. Several vibrational levels are populated owing to different overlaps at different field strengths and the periodic peak structure of the train. Between peaks when external field is low, bending oscillation is encouraged in response to the surface curvature changing. Consequently, an explosion induced by a train leads to enhanced vibration. Filter for (221) (222) Total Counts = (221) (212) Filter for (222) = (222) (221) (212) Total Counts OPS for bending control Lowest field-free triplet states of CO22+ from H. Kono, et al., Bull. Chem. Soc. Jpn. 2, 196 (2006). Simulation Simulation Simulation Identifying Explosion Channels X X (d) Selective Average [3,5] was performed by scanning the selected area horizontally across the center of the image from left to right (see panels (a) to (c)). The horizontal strips (areas between two white lines) were collected to form a coincidence count map as shown in (d) to (f). The branching ratio between explosion channels is determined from the total ion count within the corresponding islands on the coincidence map. (222) (a) Branching Ratio It is clear that the (222) channel is favored at higher intensity. Thus, lower intensities lead to a trivial enhancement of the (221)/(222) ratio. Two consecutive (nearly) identical peaks produce an enhancement beyond the trivial solution. We suspected the part of the reason involves an inability of a single pulse to Coulomb explode 100% of the population. In distinction to the bending experiment, each peak produces a measurable signal. However, this cannot explain the nearly 30 times enhancement observed. Evidently, the first peak leaves population in excited states, as in the bending experiment, that are more easily ionized by the second peak. The exact mechanism is not yet fully understood. Nevertheless, it is clear that an OPS consisting of a train of identical pulses might lead to a way to enhance “lower order” processes, such a dissociation, over “higher order” processes, such as ionization, that typically dominate as the intensity is raised. Selected area was scanned from left to right (221) (e) (b) (222) Selected Area (222) (f) (c) (212) (221) OPS for branching ratio control The contribution to each channel from each island was determined from fits using multiple Gaussians. (212) (222) Selected Area Results Conclusion The GA solution, which was obtained in the quasi-unrestricted mode, generated a field with a double peak structure. The two peaks were nearly identical with about the same width and energy (fluence). Employing area filters as a combined fitness/cost parameter on velocity maps in feedback-control experiments enables optimal fields to be found from several different perspectives (gene sets). Comparing and contrasting these solutions allows similarities to be determined that can aid in deciphering the pulse. References [5] W. T. Hill III, et al., Progress in Ultrafast Intense Laser Science I, 59 (2006). [6] G. Y. Chen, et al., Phys. Rev. A 79, 011401(R) (2009). [7] Y. Sato, et al., J. Am. Chem. Soc. 125, 8019 (2003). [8] H. Kono. et al., Bull. Chem. Soc. Jpn. 2, 196 (2006). [1] J. Zhu and W. T. Hill III, JOSA B 14, 2212 (1997). [2] K. Zhao,et al., Rev. Sci. Instru. 73, 3044 (2002). [3] K. Zhao, et al., Optics Express 9, 42 (2001). [4] K. Zhao, et al., Phys. Rev. A 68, 063408 (2003).