1. Stimulated Raman Adiabatic Passage into continuum
Andon Rangelov
(Sofia University, Bulgaria)
Nikolay Vitanov
Ennio Arimondo
(Pisa University, Italy)
Control of Quantum Dynamics of Atoms, Molecules and Ensembles by Light (TOK)
Engineering, Manipulation and Characterization of Quantum States of Matter and Light (RTN)
Palermo, 2 June 2007

2. Outline 1. What is Stimulated Raman Adiabatic Passage (STIRAP) ?
Three-level atom -  configuration
Hamiltonian, dark state, counterintuitive scheme
2. What is Laser Induced Continuum Structure (LICS) ?
LICS configuration
Fano autoionization configuration
STIRAP via the continuum
3. How to optimize the ionization ?
Direct ionization into continuum, Ionization via intermediate state: REMPI, STIRAP
STIRAP into continuum with LICS scheme
Hamiltonian, pulse sequence, quasi-dark state

3. Three level atom-  configuration
Hamiltonian In
Rotating Wave Approximation (RWA)
Stokes
Pump
diabatic basis 1 y
adiabatic basis (eigenvectors of H(t) )
- dark state

4. STIRAP in  configuration
Conditions: Adiabatic evolution & Counterintuitive order of pulses
Result: Highly efficient population transfer
- dark state
Explanation:
-dark state
-dark state

5. Laser Induced Continuum Structure (LICS)
Fano autoionization 1 y
Discrete state is embedded in the continuum via the interaction T. A laser of frequency (which is weak in the original Fano work) induces the following transitions:
control
laser
pump
laser 1 y
Two discrete states , are coupled to continuum states with pump and control lasers. If control laser is strong, a structure occurs in the otherwise flat continuum.

6. STIRAP via the continuum
Conditions for STIRAP via a continuum:
1) Adiabatic evolution
2) Counterintuitive order of pulses
3) Two-photon detuning
pump
laser
Stokes
laser
Stokes
laser
For purely bound states -these conditions can be easily fulfilled.
When involving continuum states -high laser intensities are required to fulfill the condition of adiabaticity. 1 y
T.Peters, L.P.Yatsenko, and T.Halfmann, Phys. Rev. Lett. 95, (2005)

7. How to optimize the ionization
We consider ionization of atom initially in ground state
Stokes
Pump
1) Direct ionization: it requires a very strong pulse with a short wave length.
2) Ionization via intermediate state: REMPI (resonantly-enhanced multiphoton ionization) works, if small decay form the intermediate state
3) Ionization via intermediate (which decay with large rate): naturally leads to counterintuitive pulse ordering, as in STIRAP.
It is not really STIRAP, because of continuum, which does not allow the formation of a dark state, which is a coherent superposition of discrete states.

8. Can we use STIRAP with LICS to optimize ionization?
STIRAP into continuum with LICS
STIRAP into continuum
laser-induced continuum structure (LICS)
Pump
Control
Stokes
Stokes
Pump

9. Hamiltonian, pulse sequence, quasi-dark state
STIRAP into continuum with LICS
Adiabatic elimination of the continuum states
Control
Continuum
Stokes
Fano parameter
pump Rabi frequency
detuning between and
decay rate from
Pump
Stark shifts of states and
Ionization widths of states and

10. Hamiltonian, pulse sequence, quasi dark state
STIRAP into continuum with LICS
Hamiltonian matrix is non-Hermitian
Control
Continuum
Stokes
Fano parameter
pump Rabi frequency
detuning between and
decay rate from
Pump
, could be incorporated
in the detunings
Ionization widths of states and

11. Hamiltonian, pulse sequence, quasi dark state
STIRAP into continuum with LICS
Hamiltonian matrix is non-Hermitian
Control
Continuum
Stokes
Pulse ordering:
Less population in : Stokes before pump
Maximum ionization: Stokes before control
To have LICS: control close to the pump
This means that in the beginning
of the evolution:
Pump
We want to find analytically populations , signal from and the ionization

12. Schrödinger equation in adiabatic basis:
gives the connection between
adiabatic and diabatic bases
where
adiabatic
diagonal Hamiltonian
nonadiabatic
coupling
If the time evolution is slow we can neglect the nonadiabatic coupling
Then
where
dynamics is determined by the initial conditions on the adiabatic states
Instead of the complicated adiabatic states we make the approximation

13. Quasi-dark state of Hamiltonian:
is assumed to be small parameter ( )
Also:
If is stable ( ) and at two-photon resonance ( ) , the quasi-dark state turns into the well-known dark state written for small values of angle

14. Initially only the quasi-dark state is populated
Initially only the quasi-dark state is populated. In the adiabatic limit the populations are
where
numerical simulations for Gaussian pulse shapes of Stokes,pump,control
Hamiltonian

15. An important difference between LICS-STIRAP and STIRAP:
The control pulse plays a important role in achieving a high ionization rate.

16. An important difference between LICS-STIRAP and STIRAP:
The control pulse plays a important role in achieving a high ionization rate.

17. An important difference between the scheme that we proposed and STIRAP:
In STIRAP the arrival and the departure of the pulses should be in the proper time window, while in our technique it is only important how the pulses arrive but not what is the order of their departures

18. There is a laser intensity for which the ionization rate reach it maximal value and after that is saturated (regime of the adiabaticity)

19. A. Rangelov, N. Vitanov, E. Arimondo, submitted to PRA
Summary
An interesting analytic prediction, for an optimal population transfer into continuum was presented
The control pulse plays a very important role in achieving a high ionization rate
The pulse ordering is important for how the pulses arrive but not what is the order of their departures
Applications: Rydberg atom ionization efficiency close to unity with negligible population into discrete states and efficient photoionization of a Bose-Einstein condensate.
A. Rangelov, N. Vitanov, E. Arimondo, submitted to PRA