Advancing the Fundamentals of

I. Workshop Background

The Workshop was organized in the backdrop of burgeoning activity in the area of controlling quantum phenomena, especially with shaped electromagnetic pulses. The time seemed appropriate to take stock of the field and project ahead from the many successful experiments being performed. In order to appreciate the scope of the Workshop, a brief summary of the history of the field is presented below.^���

Lasers were invented in the early 1960���s with their most evident property being high energy focused into a narrow spectral range. Since energy is a key ingredient for stimulating molecular transformations, a natural proposal (apparently put forth by many scientists simultaneously) at the time was to use lasers as a means for selectively breaking or activating particular chemical bonds, even in complex polyatomic molecules. The narrow bandwidth of the available lasers was understood to likely be a hindrance for this purpose, due to the multispectral nature of the collective transitions in molecules. The high focal intensity of lasers was suggested as a means to overcome this problem through power broadening and multi-photon absorption. Although traditional lasers are capable of depositing sufficient energy to stimulate reactive processes of various types, the desire for a high degree of selectivity amongst competing reactions was not attained in this fashion. Persistent efforts along these lines continued until around 1980, when the community involved generally concluded that an understanding of intramolecular energy transfer would first be required before successful molecular control could be achieved. However, the conceptual breakthroughs and technological advances that opened up the field of quantum control mainly involved developments in other directions.

In the mid-1980���s, molecular control was expressed in terms of manipulating quantum interferences including from a wave packet dynamics perspective. In the late 1980���s and early the 1990���s, the confluence of a number of theoretical tools and technologies rapidly emerged to form the foundations for the field today. In particular, the subject of manipulating quantum dynamics at the atomic and molecular scale was recognized as a control problem subject to much of the same concepts that engineers utilize for managing macroscale processes (e.g., aircraft stabilization, missile guidance, electronic controllers, etc.). Especially important was consideration of the laser as an instrument for optimal design to meet the proposed molecular control objectives. This advance brought to bear the full mathematical machinery of engineering optimal control theory (OCT) including the tools to assess, in principle, to what degree quantum systems could be controlled. Perhaps the most important outcome arising from the introduction of quantum OCT was the finding that optimal laser controls would generally be highly structured broadband pulses. In hindsight, the need for well-orchestrated control pulse structure operating in sync with the multispectral nature of quantum dynamics seems intuitively clear. Initially, the need for complex laser pulses was felt to be a stumbling block towards practical implementation, given that pulse shaping technology was not available at the time. Simultaneously and independently, in the telecommunications industry, laser pulse shaping was being developed, especially wrapped around the Ti:Sapphire laser.

^��� No specific references are sited with this report; however, extensive reviews and primary documents are readily accessible in the literature.

Placing the field of quantum control on firm theoretical ground and having a suitable shapeable laser source available did not immediately lead to successful quantum control experiments. The final advance arose from recognizing that computational optimal pulse design generally would not produce reliable results, given the complexities of quantum dynamics phenomena, even in modest sized molecules. However, considering the high-duty cycle of laser pulse shaping, this problem was circumvented by introducing adaptive learning control techniques. This closed-loop quantum system control procedure can operate in the laboratory with little, and often no, detailed information about the system Hamiltonian. In this fashion, an experiment is performed to test the viability of a new trial control pulse rather than performing numerical simulations of the test. Closed-loop experiments were initiated in 1997 starting with the goal of optimally tailoring the laser pulses themselves and then going onto other objectives including the original one of selective chemical bond breakage. Demonstrations emerged very rapidly showing control over a broad variety of chemical and physical processes ranging from atomic excitation, to high harmonic generation and electron transfer in complex bio-molecules. The numerous laboratory successes and their theoretical underpinnings provide the foundations to expect that virtually any atomic and molecular scale dynamical objective could be subjected to control with the presently available laser tools.

Notwithstanding the many laboratory demonstrations of quantum control, it is still surprising that the experiments work as well as they do, especially considering that quantum mechanical phenomena of diverse spectral character are typically manipulated by a single laser source operating with the controls just lying in a small ~20 nm window centered around 800 nm. There is much room for technological improvement to further enhance the capabilities of quantum control. Additionally, the ease of performing the closed-loop model free laboratory control experiments has outstripped a basic understanding of the chemical and physical events taking place, especially in cases where strong laser fields are involved.

The latter brief history of controlling quantum dynamics phenomena with lasers provides the backdrop for the Workshop whose structure is explained below.

II. Nature of the Workshop

Given the advances in the field of controlling quantum phenomena, in 2005 the time was right for assessing of the field and especially, the issues and challenges ahead to most rapidly advance the subject. With DARPA-ARO support, plans were set forth for a Workshop with a special structure. In recent years, there have been many symposia and workshops on quantum control with all of them having the style of the participants presenting the latest work performed in their laboratories. Given the goals of the Workshop on assessing and projecting the field, a different style was chosen. The Workshop consisted of topical discussions of approximately one hour with each led by a moderator, and only the blackboard was available as a visual aid to the discussions. The participants provided breadth as well as expertise in the general area of controlling quantum phenomena with the aim of having the fullest discussion in the available short time of the Workshop. Thus, participation was limited to twenty one individuals, although there are many more active players in this field worldwide. Prior to arriving in Princeton, the session moderators prepared a list of questions for the participants to consider. The discussions were generally centered on these questions, although in many cases time was also spent on new questions for consideration. The goals of assessing and projecting the field of quantum control was certainly not exhausted, leaving an opportunity to revisit this topic once again in the future.

Below is the Workshop agenda and the list of participants.Agenda (discussion moderators shown in parenthesis)

Participants:

Thomas Baumert, Universit��t Kassel, Kassel, Germany Tammie Borders, Lockheed Martin, Fort Worth, TX Phillip Bucksbaum, University of Michigan, Ann Arbor, MI Gustav Gerber, Universit��t W��rzburg, Jerusalem, Israel Jennifer L. Herek, Institute for Atomic and Molecular Physics, Amsterdam, Netherlands Misha Ivanov, Steacie Institute for Molecular Sciences, Ontario, Canada Henry Kapteyn, University of Colorado, Boulder, CO Ronnie Kosloff, The Hebrew University of Jerusalem, Jerusalem, Israel Robert Kosut, SC Solutions, Sunnyvale, CA Robert J. Levis, Temple University, Philadelphia, PA Hideo Mabuchi, Cal-Tech, Pasadena, CA Luis A. Orozco, University of Maryland, College Park, MD Herschel Rabitz*, Princeton University, Princeton, NJ Robert W. Shaw, Army Research Office, Research Triangle Park, NC Alexei Sokolov, Texas A&M, College Station, TX Gabriel Turinici, CERMICS Institute, Cedex, France Thomas Weinacht, SUNY Stony Brook, NY Ben Whitaker, University of Leeds, Leeds, UK Jean-Pierre Wolf, LASIM, Universit Claude Bernard Lyon, Cedex, France Ludger H. W��ste, Freie Universit��t, Berlin, Germany Marc Vrakking, Institute for Atomic and Molecular Physics, Amsterdam, Netherlands

*Workshop organizer. This report was prepared by the organizer considering advice from the moderators and other Workshop participants.

III. Summary of Workshop Discussions

The summaries below follow the Workshop agenda.

Panel A: Quantum Control Objectives

Quantum control objectives have grown to encompass manipulating nuclear and electron dynamics as well as non-linear optical phenomena. The case of nuclear motion includes isomerization, fragmentation, photo-association, and bio-molecular reactions; control of electron dynamics involves charge transfer and ionization. Non-linear optical phenomena refers to situations where the control pulse induces non-linear processes and where the output signal is often an optical pulse including high harmonic generation, frequency mixing, and spectral transfer from the THz out to the X-ray regimes. The control of electronic and nuclear dynamics, and optical phenomena can also occur simultaneously. Regardless of the objectives, the actual physical systems can range from atoms or small molecules out to complex bio-molecules, nanoparticles, aerosols, color centers in crystals, etc. In addition, the control environment may be isolated molecules in a vacuum out to solutions and trapped particles in solids. Given that a shaped Ti:Sapphire laser pulse centered around 800 nm is commonly employed as the control, most of the applications involve some form of electronic manipulation regardless of the nature of the final desired outcome. Applications in the future will build upon the current successes, as well as consideration of what might open up when suitable new laser sources become available. Potential applications include isotope separation, proto-molecule synthesis and general molecular transformations, the creation of ultra-cold molecules, the manipulation of molecular switches, the creation of tailored light sources at a distance for remote sensing of chemical and biological agents, controlled bio-molecular dynamics, photo-dynamic therapies, tailored deposition or alteration of high value surfaces (i.e., semiconductors), amongst other possibilities. Control applied at the single molecule level may provide the clearest picture of what is physically taking place by eliminating inhomogeneous broadening effects. Looking even further down the road, laser sources of increased energy could allow for manipulating core electron dynamics in atoms and possibly even nuclear reactions.

Many of the objectives being considered are of a fundamental nature aimed at understanding basic quantum dynamical processes. However, other applications may have commercial significance. Business interest in quantum control is now evident suggesting that practical applications may be in the offing soon. Most importantly, when considering any application, the shaped laser pulses acting as controls should be viewed as capable of strongly interacting with matter on par with ordinary reagents. From this perspective, when considering any molecular scale manipulation application the utility of shaped laser pulses (photonic reagents) should be factored in, perhaps in a mix or match scenario with ordinary reagents. Control at the atomic and molecular scale lies at the extreme of a continuum of length and times for control applications. In developing quantum control, its linkages to analogous operations at the nano- and micro-scales should be exploited as well.

Panel B: Control Laser Sources

The broad scale success of the current experiments, in some respects, is surprising, especially given the constraining nature of the commonly used Ti:Sapphire laser source centered in the near infrared with a limited bandwidth. Many experiments operate in the strong field regime and effectively overcome this limitation by utilizing dynamic power broadening. However, ultimately better sources with enhanced spectral characteristics should open up new regimes of control operation (e.g., lower laser intensities) and applications for study. In this regard, bringing pulse shaping to different wavelength regions, ranging from the THz out to the X-ray domains, would be important. Regardless of the nature of the laser source, both pulse-to-pulse and day-to-day stability are essential for reliably performing the control experiments. Although theoretical studies indicate that the closed-loop optimization experiments can overcome many geometrical and intensity aberrations, attaining good stability and uniform intensity over the fully illuminated sample would give more precisely defined control conditions for all the molecules involved. This capability would be especially important for understanding the control mechanisms. It is perhaps ironic that closed-loop techniques are at the heart of the control experiments, yet they are not routinely built into the lasers themselves for their stability. Hopefully, control laser stability will improve with an increasing market size providing the motivation for the laser companies.

There is a need for high power lasers with enhanced repetition rates for a number of applications. Current lasers operating at KHz rates are adequate for many applications, although even higher rates may be important in future domains of study. Another consideration is that a mole of Ti:Sapphire photons consists of ~10⁵ Joules of ~1 eV photons. At a current running cost of approximately one dollar per hour per watt, this corresponds to approximately thirty dollars per mole of photons. Considering that much of the radiation in a shaped laser pulse often passes through the medium without effect, reduction of this cost could be significant for certain practical applications.

Laser pulse shaping technology is functioning well to meet the needs of quantum control, but the opportunities for improvement are significant. For example, routinely shapeable high intensity sources in the mid-IR regime would open up the direct control of vibrational degrees of freedom in molecules without necessarily driving them indirectly (i.e., through electronic transitions). Similarly, sources in the UV out to the X-ray regimes would permit manipulating tightly bound electrons. Free electron laser sources may be valuable in several spectral regimes and much current interest is focused on creating ultra-broad bandwidth sources whose availability would have innumerable applications. Similarly, the ability to readily manipulate high-harmonic or other sources of optical combs opens up new operational regimes including attosecond pulses permitting the control of additional classes of physical and chemical processes. Regardless of the spectral regime, pulse shaping will be necessary to attain the best degrees of quantum control. The current liquid crystal, acousto-optic and deformable mirror techniques each has its own domain of applicability. It is anticipated that new shaping technologies will likely be needed especially at certain wavelengths, pulse energies, or pixel resolutions falling outside of the current technologies. In addition, absolute carrier envelope phase stability will be important for control with attosecond pulses.

Panel C: Detection of Controlled Dynamics Phenomena

All of the current adaptive control experiments operate with a detection signal recorded after the control process is over. This scenario fits most applications where the signal for feedback optimization tests whether the desired ���product��� has been formed. However, detection during the control process with an intermediate signal could both aid the control algorithm to better home in on the target as well as provide information for mechanistic analysis. In principle, any of the ultrafast techniques used for detection could in turn be applied at intermediate times as well. Ultrafast detection techniques include a host of optical probes, and the limit of these techniques certainly has not been reached. Furthermore, in the case of molecular fragmentation being the targeted goal, mass spectrometry is often employed for maximizing the ratio of one mass peak to another for control. But, the full mass spectrum contains a richer amount of information relevant to some applications (e.g., discriminating the presence of one chemical species amongst many similar ones).

Enhancing the product signal-to-noise ratio is important, as noise from the control laser can influence the manipulated dynamics in a complex disruptive fashion, especially in non-linear processes. Theoretical and experimental work indicates that signal-to-noise can be enhanced through suitable control procedures and fast data recording. Also, it would be desirable to go beyond mass spectrometric and optical detection, and in principle, any detection technique sensitive to the product state could be utilized. Examples include photoelectrons, NMR, chromatography (on chips), etc. In the case of controlled molecular fragmentation, observation of the angular and energy distributions of the products should provide valuable information about the dynamics. An important application is control over molecular rearrangement, where structural information for feedback generated during and after the control process would be valuable. Both X-ray and electron diffraction appear feasible for this purpose with temporal resolution down to possibly 10 fs or even better. Coulomb explosion techniques may also be suitable as a means to stop frame identify molecular structures.

When considering any detection technique as a means for providing a feedback control signal, the duty cycle involved is a critical matter. Ideally, the detection process needs to be fast enough to keep up with the rate that the pulse shaper makes control changes in the loop. In turn, choosing detection techniques is also connected with the ability of the associated technology to provide stable probes over a long sequence of experiments. The detection of controlled quantum dynamics is very much technology driven, and advances in allied areas will surely have a continuing impact.

Pane D: Extracting Control Mechanisms

Quantum control mechanism assessment is a topic of basic interest, just as in chemistry as a whole. There are many fundamental issues about mechanism that are not understood at this time, including how to define mechanism in quantum control. The one distinguishing characteristic in this context, beyond traditional mechanistic considerations, is the presence of coherence (at least to some degree) in controlled quantum dynamics. It is anticipated that mechanism within quantum control may be defined a number of ways meeting different needs or levels of mechanistic detail. A general subjective goal is for mechanism to provide ���understanding,��� which can depend on the researcher���s prior experience and perspective. In some cases, mechanism may be described in terms of qualitative dynamical (and even classical) concepts while other cases may call for quantitative measures of the complex evolving wave function amplitudes. Another important issue is the appropriate balance of experiments and computations needed to extract mechanism. Currently, mechanisms have been determined for several control experiments, and in most cases, modeling played an important role. More consideration needs to be given to the flexibility in pulse shaping and high-speed detection for directly extracting mechanistic insights, especially in the most complex situations where modeling is very limited in its capabilities. The control experiments are designed to maximize a target yield, and not to reveal the associated governing mechanisms. However, in favorable cases, mechanism may be extracted from a control experiment utilizing the observed field followed by subsequent detailed quantum dynamics modeling. More information may be generated by employing high-duty cycle pump-probe experiments operating on the neighborhood of the optimal control and specifically tailored to revealing mechanism. Data taken during the control process may be especially valuable.

The fact that the closed-loop experiments operate by learning to control the dynamics through a sequence of trials suggests that mechanistic insights may be extracted from the learning process itself. Although insights can be gained this way, care is needed, as multiple pathways can exist, depending on the learning algorithm employed, producing the same final control field. Furthermore, distinct control fields may also give the same final product yield. A lack of unique control solutions generally implies that multiple mechanisms are expected to exist for meeting the same control objective, although inevitable constraints on the controls may limit the accessible mechanisms in any particular experiment.

In analogy with the descriptive mechanisms often presented for the actions of traditional chemical reagents, it may be possible to identify particular quantum control scenarios such as pump-dump, chirp, two color interference, etc. This descriptive language would be especially valuable if similar types of controls operated successfully with a homologous sequence of samples. As with traditional chemistry, an open question is whether structure and dynamics (function) may be related in the quantum control domain. In terms of the controls themselves, much activity has been focused on deciphering their features in either the time, frequency or joint time-frequency domains. Some success has been achieved in this regard, and the simplicity of such analyses weighs in their favor. In this regard, it is important to remove extraneous pulse features during the control experiments, and simple algorithmic changes can assure such performance. Another simple tool is principal component analysis, which may be applied to various correlation measures of the observed control field. Although valuable insights may be gained from this technique, it is a local analysis tool and may not give broad insights into highly non-linear control processes. Extracting mechanism in strongly driven non-linear processes is perhaps the most challenging dynamical regime to analyze. Regardless of the regime, placing the dynamics in an appropriate representation (i.e., the form and the Hamiltonian or its basis set description) is an important first step towards expressing mechanism in physical terms that are understandable. At this juncture, choosing a representation is largely based on intuition, and a more systematic means would be desirable.

A lack of mechanistic details will generally not stop the performance of control experiments, as already evident from the mounting body of such studies. Nevertheless, attaining mechanistic information is an important intellectual challenge. The ensuing insights could suggest new or improved control experiments and target objectives. As an increasing number of laboratories are performing control experiments (at times with unpublished data), an important resource would be the maintenance of a database of the results for access by the entire community. This database could include successful as well as unsuccessful examples, all of which collectively may begin to provide insights into mechanism.

Panel E: Inverting Control Dynamics Data to Extract Fundamental Molecular Interactions

Hamiltonian information is generally sought after for its value in many contexts, including those outside of quantum control. Another goal with quantum control is to go beyond traditional techniques of extracting Hamiltonians from spectroscopic data, which is typically limited to molecules containing a few atoms for high accuracy results. The opportunity available using controls for this purpose lies in the prospect of performing an optimal experiment which is specifically tailored to the goal of Hamiltonian extraction. The possibility of adaptively altering the control experiments for this purpose contrasts with traditional spectroscopic techniques where few options typically are available except for scanning the source frequency. The field of optimal identification with quantum controls is largely a matter of theoretical analysis and experimental design at this stage.

Traditional spectroscopy operates in the weak field regime under the premise of minimally disturbing the quantum system to determine information about its inherent nature. In the case of quantum control, experiments also could be carried out with weak fields, but the richest controlled dynamics occurs in the strong field regime. Extracting Hamiltonian information in the strong field regime would be most desirable for subsequent control utilization. Regardless of whether weak or strong fields are involved in deducing Hamiltonian information, the choice of a proper representation for the physical system is important, just as for mechanism analysis. An improper choice of representation could easily lead to an intractable data inversion problem and the Hamiltonian being unwieldy to operate with. In addition, ever-present laser and detector noise in the associated ultrafast experiments is an issue to manage.

For the reasons stated above, inverting controlled dynamics data to extract the Hamiltonian and the optical coupling coefficients represents a most challenging task. The promising new feature is the ability to optimally tailor the experiments. This prospect includes the possibility of actively filtering out the control noise, while simultaneously enhancing the sensitivity of the data with respect to the sought after Hamiltonian information. In addition, operating with tailored controls might also open up the possibility of breaking the inversion problem into a hierarchical set, where each member is associated with only a limited portion of the Hamiltonian or dynamics. The latter opportunity is important, as solving Schr��dinger���s equation is an inherent aspect of data inversion, and breaking the computational burden into manageable pieces would be helpful. The computational aspects of controlled data inversion deserves a fresh analysis and assessment of its needs and capabilities, including the possibility of introducing new analytical and numerical techniques that are especially honed to the particular features and options enabled through the use of flexible controls. Some theoretical studies and simulations indicate very positive inversion performance by playing on the power to optimally tune control fields for data inversion, but much more needs to be done to develop practical algorithms and experimental protocols.

When the goal of the inversion exercise is the extraction of a Hamiltonian for subsequent control purposes, the nature of the inversion may substantially alter. In particular, an effective Hamiltonian model may be quite adequate for this purpose. Such models may retain the structure of Schr��dinger���s equation, although the Hamiltonian may not directly resemble its parent multi-particle form. Effective models of this sort are commonly used in engineering control, and pursuits along these lines for quantum control would be most worthwhile. Such effective Hamiltonians in a suitable representation might also provide the basis for understanding control mechanisms as well.

Panel F: Real-Time Feedback Control

The timing of this Workshop largely arose due to the rapidly increasing number of closed-loop adaptive (learning) control experiments opening up the field for wide-scale applications to even complex systems. Closed-loop feedback operations are central to virtually all engineering control applications due to uncertainties of various types entering the picture. Closed-loop quantum adaptive control was introduced for exactly the same reason. However, the form of adaptive control utilized in quantum mechanics is exceptional in engineering applications where real-time feedback control is more commonly performed. Engineering applications can readily operate with real-time feedback control as they work on more comfortable time-scales of seconds or longer, rather than pico- or femtoseconds. Also, often in engineering a single high value object (e.g., a spacecraft) is controlled, in contrast to quantum mechanics where individual systems (e.g., molecules) are very inexpensive and an ensemble of ~10²⁰ may be controlled. Additionally, pulse shapers and detectors in quantum control generally have a very high duty cycle permitting unprecedented numbers of independent control experiments to be carried out in short periods of laboratory time. All of the special features operative for control at the atomic scale with lasers, led to the present widespread use of adaptive feedback control of quantum systems.

Notwithstanding the common use of adaptive feedback control in quantum mechanics, an interesting objective is the application of real-time feedback control in this domain. A number of special issues are of relevance in this regard including the fact that the observation process during the closed-loop experiment will inherently disturb the quantum system, which is not an issue in classical engineering control or adaptive quantum control. Additionally, real-time modeling (i.e., performed at a rate comparable to the quantum system���s timescale) must be carried out during the closed-loop operations in order to process the data from the current experiments and redirect the controls for another excursion around the loop to hopefully achieve a better controlled outcome, etc. The latency time-scale for loop closure, including all operations (i.e., computations and adjustments of the controls), is a key factor to consider for real-time feedback control in relation to the natural time-scales of the system dynamics. The latency period for loop closure should be on the same time-scale of the dynamics, and this criterion will likely limit closed-loop quantum control experiments primarily to physical processes operating in the microsecond regime. Nevertheless, real-time closed-loop quantum control is of fundamental interest, especially with regard to revealing basic issues about observational back action upon the quantum dynamics. Preliminary experiments are already showing the viability of real-time feedback control concepts within quantum mechanics, and further developments will surely come in the years ahead.

Adaptive and real-time feedback control of quantum systems share more common ground than merely their closed-loop nature. The underlying control principles are the same and thus, they share a basic fundamental foundation; the differences lie in the nature of the feedback and its implications for controlling the dynamics. The heavy computational and analysis demands of real-time feedback control are also relevant to the task of Hamiltonian identification, although the latency time-scales involved are less demanding. Both adaptive and real-time feedback control of quantum systems would likely benefit from developments in the other area. Finally, there is the possibility of operating with real-time feedback in the ultrafast pico- and femtosecond regimes by including the measurement and response apparatus directly as a portion of an extended quantum system. This suggestion builds on the notion of finding a quantum analog to the steam engine fly-ball governor.

Panel G: The Roles of Theory and Control Theory

Quantum control theory owes much of its development to borrowing heavily from the groundwork set forth in engineering control. In recent years, the engineering control community also has taken a special interest in the quantum domain, and this enhanced awareness should benefit the future development of quantum control. Control of quantum dynamics is inherently a non-linear (bilinear) problem placing it at the frontier of control theory in general. The familiar engineering issues of system identification, robustness to noise, feedback algorithms, etc., have their own special incarnations in quantum control. Theory, regardless of its origins in either physics, chemistry or engineering, will continue to play central roles in performing better quantum control experiments and assessing their outcomes. Theoretical and computational considerations were a part of all of the other Panel discussions as well.

IV. Recommendations

The Workshop was intense covering many topics in quantum control, but various topics were not discussed due to time constraints. In many cases, the mere questions raised by the moderators and participants were significant stimulation in themselves, and those questions and discussions are blended together in the report summary above. Several specific recommendations follow from the Workshop.

1) Future Workshops. It would be desirable to have a Workshop of this type on a three-year cycle focusing on the state of the field and the projected needs and issues ahead for its advancement. The Workshop would stand out uniquely from all other workshops and symposia in the field.

2) Technical Challenges and Advances.

• Advance broadband stable laser source development including pulse shaping techniques
• Explore the limits on the types and degrees of quantum control that may be achieved
• Go beyond one-off experiments to explore systematic families of controlled samples to reveal the general principles involved
• Push the boundaries of quantum control to manipulating additional classes of atomic, molecular and condensed phase phenomena.
• Establish why quantum control is working so well, while simple intuition would suggest extreme difficulty on many fronts
• Link up the complementary capabilities of quantum control (photonic reagents) with that of ordinary reagents as well as parallel manipulations at the nano and higher length scales
• Explore the capabilities of quantum control to optimally extract system Hamiltonian information.
• Develop viable effective models for quantum control, including with strong fields, to reveal the underlying operational mechanisms

3) Funding. Control at the atomic scale is a frontier field, which is projected to be important for the fundamental insights it provides as well as the practical applications that derive from these efforts. In the US presently there are approximately twenty laboratories actively pursuing quantum control experiments. Outside of the US, more than twice that number of laboratories are involved and growing rapidly. Within the US, no large-scale coordinated efforts are underway to foster the development of this field, while Europe and Japan have such activities. Now that the field of quantum control has established its foundations and demonstrated that its principles are sound, the subject would be most rapidly advanced by a concerted program including appropriate funding. Presently, funding is available on an individual investigator basis through various agencies, and piecemeal progress can continue in this fashion. However, the most rapid advancement of the subject and its applications would occur with a targeted quantum control program. An integral program running for five years would seem best with funding of approximately $10 million per year supporting a group of investigators.