Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays

Bartels, Randy A.; Backus, Sterling; Zeek, E.; Misoguti, Lino; Vdovin, Gleb; Christov, Ivan P.; Murnane, Margaret M.; Kapteyn, Henry C.

doi:10.1038/35018029

Cited by 682 publications

(368 citation statements)

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“…The results suggest that under such circumstances, controlling complex quantum systems with many degrees of freedom should be no more difficult than controlling simple systems. Evidently the same conclusion applies to performing OCE for various objectives, where the search effort appears to be essentially the same regardless of the system complexity when operating with physically appropriate controls [20,25,28,30]. The next section will address the relationship between the observed trends in search effort and the underlying control landscape structure.…”

Section: The |1 → |N Transitionmentioning

confidence: 99%

“…The collective OCT literature, however, suggests that the required search effort to find an optimal control is generally on the order of ∼ 10 2 iterations, [2,3,9,13,15,17,, and systematic optimization of P i→f using kinematic control variables indicates that the search effort scales at most very slowly with N [61]. Successful OCE studies ranging from control of atoms [20,25] to complex protein molecules [28,30] further suggest a practical level of invariance of search effort to system complexity. Based on these collective findings, we performed optimization of P i→f on a broad sampling of systems ranging from N =5 to N =100 in order to determine whether scaling invariance to N can be demonstrated systematically using dynamical control variables.…”

Section: Search Effort and System Complexitymentioning

confidence: 99%

“…OCT simulations have successfully controlled a variety of objectives, including state preparation [2,6,7], molecular isomerization [8][9][10][11][12], dissociation [13][14][15][16], and orientation/alignment [17][18][19]. OCE using ultrafast tailored laser pulses have achieved control over many processes including state preparation [20,21], selective molecular dissociation [22][23][24], generation of high order optical harmonics [25][26][27], and energy transfer and isomerization in large biomolecules [28][29][30]. Simulation models consider from 2 to ∼ 10 2 or more states, and the atoms/molecules used in OCE often have much larger numbers of accessible states.…”

Section: Introductionmentioning

confidence: 99%

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Exploring quantum control landscapes: Topology, features, and optimization scaling

2011

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Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states N ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of sub-optimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9% upon careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension N . This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as N increases.

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Section: The |1 → |N Transitionmentioning

confidence: 99%

Section: Search Effort and System Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring quantum control landscapes: Topology, features, and optimization scaling

2011

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“…Using ideas that derive from the seminal paper by Rabitz on "teaching lasers to control molecules" [3], many examples currently exist where shaped laser pulses have been optimized by a genetic or evolutionary algorithm in order to accomplish a desired task or to optimize a desired end result (see, e.g., [4][5][6][7][8]). The remarkable success of these experiments can be understood from the fact that feedbackcontrolled optimization drives quantum systems to perfect control, provided that no constraints are placed on the controls [9].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary optimization of rotational population transfer

et al. 2011

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We present experimental and numerical studies on control of rotational population transfer of NO(J = 1/2) molecules to higher rotational states. We are able to transfer 57% of the population to the J = 5/2 state and 46% to J = 9/2, in good agreement with quantum mechanical simulations. The optimal pulse shapes are composed of pulse sequences with delays corresponding to the beat frequencies of states on the rotational ladder. The evolutionary algorithm is limited by experimental constraints such as volume averaging and the finite laser intensity used, the latter to circumvent ionization. Without these constraints, near-perfect control (>98%) is possible. In addition, we show that downward control, moving molecules from high to low rotational states, is also possible.

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“…A more general approach is provided by "optimal control," a well established procedure in which H C (t) is parameterized by a set of control variables, and a numerical search performed to optimize the fidelity with which the control objective is achieved [2]. The application of optimal control to quantum systems originated in NMR [1] and physical chemistry [2], and has expanded to include ultrafast physics [6], cold atoms [7,8], biomolecules [9], condensed matter spins [10], and superconducting circuits [11].…”

mentioning

confidence: 99%

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

et al. 2015

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Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant inputoutput maps are unitary transformations, and the fundamental challenge becomes how to implement these with high fidelity in the presence of experimental imperfections and decoherence. For two-level systems (qubits) most aspects of unitary control are well understood, but for systems with Hilbert space dimension d>2 (qudits), many questions remain regarding the optimal design of control Hamiltonians 1 and the feasibility of robust implementation 2,3 . Here we show that arbitrary, randomly chosen unitary transformations can be efficiently designed and implemented in a large dimensional Hilbert space (d=16) associated with the electronic ground state of atomic 133 Cs, 4 achieving fidelities above 0.98 as measured by randomized benchmarking 5 . Generalizing the concepts of inhomogeneous control 6 and dynamical decoupling 7 to d>2 systems, we further demonstrate that these qudit unitary maps can be made robust to both static and dynamic perturbations. Potential applications include improved fault-tolerance in universal quantum computation 8 , nonclassical state preparation for high-precision metrology 9 , implementation of quantum simulations 10 , and the study of fundamental physics related to open quantum systems and quantum chaos 11 .The goal of quantum control is to perform a desired transformation through dynamical evolution driven by a control Hamiltonian H C (t) . For example, one common objective is to evolve the system from a known initial state to a desired final state. If the control task is simple or special symmetries are present, it is sometimes possible to find a high-performing control Hamiltonian through intuition, or to construct one using group theoretic methods 12 . In this letter we explore the use of "optimal control" 1 to design control Hamiltonians for tasks of varying complexity, from state-to-state maps to unitary maps on the entire accessible Hilbert space. The basic procedure is well established: the Hamiltonian H C (t) is parameterized by a set of control variables, and a numerical search is performed to find values that optimize the fidelity with which the control objective is achieved. The application of optimal control to quantum systems originated in NMR 13 and physical chemistry 1 , and has since expanded to include, e. g., ultrafast physics 14 , cold atoms 15,16 , biological molecules 17 , spins in condensed matter 18 , and superconducting circuits 19 .We study the efficacy of numerical design and the performance of the resulting control Hamiltonians using a well developed testbed consisting of the electron and nuclear spins of individual 133 Cs atoms driven by radiofrequency (rf) and microwave (µw) magnetic fields (Fig. 1) 16 . Our experiments show that the optimal control strategy is adaptable to a wide range of control tasks, and that it can generate control Hamiltonians with excellent performance even in the prese...

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Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays

Cited by 682 publications

References 30 publications

Exploring quantum control landscapes: Topology, features, and optimization scaling

Exploring quantum control landscapes: Topology, features, and optimization scaling

Evolutionary optimization of rotational population transfer

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

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