Quantum optimal control theory and applications

Quantum optimal control theory and applications
Esa Räsänen
Quantum Control and Dynamics Research Group, www.tut.fi/~rasanene/QCAD
Department of Physics, Tampere University of Technology, Finland
Kaj Stenvall, Total control, oil on canvas (2005)
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
Optimal control: Overview
Classical control since 1697
Optimal control: Overview
Classical control since 1697
Learning-loop exp.
since 1960s
Rabitz, Science 288, 824 (2000)
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
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
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, 075008 (2010).
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).
E.R., A. Castro, J. Werschnik,
A. Rubio, and E.K.U. Gross,
PRL 98, 157404 (2007)
Optimization of entanglement
Two electrons in coupled quantum dots + optical field
E.R., T. Blasi, M. F. Borunda, and E. J. Heller, PRB 86, 205308 (2012)
Optimized pulses can be complex...
E.R., T. Blasi, M. F. Borunda, and E. J. Heller, PRB 86, 205308 (2012)
Optimization of local fields
- to be optimized
T. Blasi, M. F. Borunda, E.R., and E. J. Heller, PRB 87, 241303(R) (2013)
Y. Mardoukhi and E.R., Eur. Phys. J. B 87, 144 (2014)
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
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
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)
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)
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, 53001 (2009)
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, 53001 (2009)
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, 53001 (2009)
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, 033426 (2012)
Suppressed ionization (1D hydrogen)
IR regime
E.R. and L.B. Madsen, PRA 86, 033426 (2012)
UV regime
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)
OCT for strong fields: High-harmonic generation
optimized
pulse
desired
harmonic,
cutoff, or/and
yield
HHG spectrum & optimization
1D model atom
HHG spectrum & optimization
OCT constraints: fixed fluence, max freq =
HHG spectrum & optimization
OCT constraints: fixed fluence, max freq =
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)
(www.tddft.org)