CONTROLLING QUANTUM DYNAMICS WITH ASSISTED ADIABATIC PROCESSES Shumpei Masuda and Stuart A. Rice James Franck Institute, The University of Chicago, Chicago, IL Telluride, 07/14/14

COUNTER-DIABATIC FIELD PROTOCOL If adiabatic transfer of population between states by an applied field is not possible because the necessary field generates unwanted competing processes, or there are internal relaxation processes that compete with the desired transfer of population, can one find a second field (called the counter- diabatic field (CDF)) that, when applied, restores the overall process of adiabatic population transfer between states? The essential concept in the definition of the CDF is the use of time dependent basis states in place of stationary basis states in the representation of the time evolution of a system. Demirplak and Rice have shown that it is possible to find such a field.

Etinski-Uiberacker-Jakubetz 5-level Morse oscillator model

Stimulated Raman Adiabatic Passage (Bergmann et al) |1> |2> |3> Pulsed field intensity profiles

Basic elements of STIRAP Initially Finally = |1> = |3>

Kobrak-Rice 5-level STIRAP |1> |2> |3>|4> |5> |5> Branch state on-resonance Hamiltonian

The Kobrak-Rice 5-level mechanism Null adiabatic eigenstate First node Second node

Transfer of population from thiophosgene state I1> to state I6> via state I5 a > using the composite STIRAP process

M = 3 pulse pairs used to generate I 3> to I5> population transfer in the HCN vibrational manifold

M = 3, I1> to I3> population transfer by composite STIRAP, FWHM = ps

M = 3, I1> to I3> population transfer by composite STIRAP, FWHM = 212.5/3 ps

GLOBAL VIEW OF ACTIVE CONTROL Define the goal of the controlled process Identify the relevant quantum dynamics Construct an active control protocol Examine efficiency of that control protocol Examine realization of the control protocol Examine stability of the control protocol to perturbations to the relevant dynamics

3-level STIRAP with dephasing |1> |2> |3> Dephasing is modeled by stochastic level fluctuations a la the Kubo line shape model

5-level STIRAP applied to Na 2 photo-dissociation Shapiro, Brumer, et al, PRL 76, 2886 Kobrak and Rice, JCP 109, 1

5-level STIRAP with dephasing |1> |2> |3>|4> |5> |5> Dephasing is modeled by stochastic level fluctuations a la the Kubo line shape model

5-level STIRAP with dephasing  P T = 20;  S3 T = 50;  S4 T = 40;  B3 T = 15;  B4 T = 75 = Stokes and Pump pulse widths = T = 2ps; Delay = T ; Correlation time of energy level fluctuations = 8fs P 3 /P 4 = 2.6 with dephasing = 25 without dephasing (not shown) target state |3> target state |4>