Quantum optimal control theory and applications
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1 Quantum optimal control theory and applications Esa Räsänen Quantum Control and Dynamics Research Group, Department of Physics, Tampere University of Technology, Finland Kaj Stenvall, Total control, oil on canvas (2005)
2 Outline Principles of quantum optimal control theory (OCT) Examples of OCT in solid-state physics Optimization of entanglement Optimization of local fields Optimization of quantum revival OCT for strong-field applications Enhancement of ionization Suppression of ionization Control of high-harmonic generation
3 Optimal control: Overview Classical control since 1697
4 Optimal control: Overview Classical control since 1697 Learning-loop exp. since 1960s Rabitz, Science 288, 824 (2000)
5 Optimal control: Overview Classical control since 1697 Learning-loop exp. since 1960s Quantum OCT since 1980s Laarmann et al. (2007) Recently: applications in chemistry and condensed matter & solid state physics M. Inguscio, LENS Delft Qubit Project
6 Quantum optimal control theory (OCT) Key question: What is the external time-dependent field that drives the system into a predefined goal? control functions Usually the control function is an electric field (laser pulse) Most commonly the objective is to maximize the transition probability to a target state
7 Formulation of OCT Find the extremal points of the functional target functional field constraint fulfillment of the TD-SE => control equations to be solved iteratively (various algorithms) For useful reviews, see J. Werschnik and E.K.U. Gross, J. Phys. B 40, R175 (2007); C. Brif, R. Chakrabarti, and H. Rabitz, New J. Phys. 12, (2010).
8 Control equations Forward propagation for Backward propagation for Solution field: with These self-consistent equations are solved iteratively (various algorithms). For a review, see J. Werschnik and E.K.U. Gross, J. Phys. B: At. Mol. Opt. Phys. 40, R175-R211 (2007).
9 E.R., A. Castro, J. Werschnik, A. Rubio, and E.K.U. Gross, PRL 98, (2007)
10 Optimization of entanglement Two electrons in coupled quantum dots + optical field E.R., T. Blasi, M. F. Borunda, and E. J. Heller, PRB 86, (2012)
11 Optimized pulses can be complex... E.R., T. Blasi, M. F. Borunda, and E. J. Heller, PRB 86, (2012)
12 Optimization of local fields - to be optimized T. Blasi, M. F. Borunda, E.R., and E. J. Heller, PRB 87, (R) (2013) Y. Mardoukhi and E.R., Eur. Phys. J. B 87, 144 (2014)
13 Optimization of quantum revival 2D Gaussian wave packet propagated (and revived) in three systems: clean distorted distorted + controlled 97% 71% clean E.R. and E. J. Heller, Eur. J. B 86, 17 (2013) distorted controlled
14 OCT in strong-field and ultrafast regime What is a strong field? - One definition: electric fields corresponding to intensities - Realization: (i) collision of charged particles, (ii) laser fields
15 OCT in strong-field and ultrafast regime What is an ultrafast field? - One definition: pulse lengths below one femtosecond are ultrafast... or more precisely: for electrons, nuclei, and solid-state devices, ultrafast time scales are as, fs, and ps, respectively - Current world record: 67 as (Univ. of Central Florida, 2012) Streaking spectrogram for neon 2p photoelectrons (A. Assion et al., Laser Focus World, (2008)
16 Femtosecond pulse shaping Synthesized Light Transients A. Wirth et al., Science 334, 195 (2011) Control knobs for NIR, VIS, and VIS-UV, respectively: chirp CEP delay energy (beam size)
17 OCT for strong fields: Enhanced ionization Target operator: System: (in 3D) Initial pulse: OCT constraints: fixed fluence max freq = A. Castro, E.R., A. Rubio, and E.K.U. Gross, Europhys. Lett. 87, (2009)
18 OCT for strong fields: Enhanced ionization Target operator: System: (in 3D) Initial pulse: OCT constraints: fixed fluence max freq = A. Castro, E.R., A. Rubio, and E.K.U. Gross, Europhys. Lett. 87, (2009)
19 OCT for strong fields: Enhanced ionization Target operator: System: (in 3D) Initial pulse: Ionization probabilities: A. Castro, E.R., A. Rubio, and E.K.U. Gross, Europhys. Lett. 87, (2009)
20 OCT for strong fields: Suppressed ionization Motivation: undesired ionization restricts controlled dissociation or HHG Control target: ground-state occupation at the end of the pulse Example: 1D hydrogen E.R. and L.B. Madsen, PRA 86, (2012)
21 Suppressed ionization (1D hydrogen) IR regime E.R. and L.B. Madsen, PRA 86, (2012) UV regime
22 Suppressed ionization in 3D (fixed nuclei) tunneling regime multiphoton regime ionization: 35% ionization: 70% N. I. Shvetsov-Shilovsky, L. B. Madsen, and E.R., Phys. Rev. A (in print)
23 OCT for strong fields: High-harmonic generation optimized pulse desired harmonic, cutoff, or/and yield
24 HHG spectrum & optimization 1D model atom
25 HHG spectrum & optimization OCT constraints: fixed fluence, max freq =
26 HHG spectrum & optimization OCT constraints: fixed fluence, max freq =
27 Acknowledgements Janne Solanpää and Nikolay Shvetshov-Shilovski (Tampere Univ. of Tech.) Jorge Budagosky and Alberto Castro (Univ. of Zaragoza) Angel Rubio (UPV/EHU San Sebastian) Hardy Gross (MPI Halle) Lars Madsen (Aarhus Univ.) Eric Heller (Harvard Univ.) Mario Borunda (Oklahoma State Univ.) Thomas Blasi (TU Munich) OCTOPUS code (GPL) (
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