Sti mulated R aman A diabatic P assage into continuum

1. Stimulated Raman Adiabatic Passage into continuum Andon Rangelov (Sofia University, Bulgaria) Nikolay Vitanov (Sofia University, Bulgaria) Ennio Arimondo (Pisa University, Italy) Engineering, Manipulation andCharacterizationof QuantumStates ofMatterand Light(RTN) Controlof Quantum Dynamics ofAtoms, Molecules and EnsemblesbyLight(TOK) 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 • STIRAPvia the continuum 3. Howto optimize the ionization ? • Direct ionization into continuum, Ionization via intermediate state: REMPI, STIRAP • STIRAP into continuum withLICS scheme • Hamiltonian, pulse sequence, quasi-dark state

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

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

5. Fano autoionization y y 1 1 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: Laser Induced Continuum Structure (LICS) LICS control laser pump laser 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. Stokes laser Stokes laser pump laser y 1 STIRAP via the continuum Conditions for STIRAP via a continuum: 1) Adiabatic evolution 2) Counterintuitive order of pulses 3) Two-photon detuning 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. T.Peters, L.P.Yatsenko, and T.Halfmann, Phys. Rev. Lett. 95, 103601 (2005)

7. Stokes Stokes Pump Howto optimize the ionization We consider ionization ofatom initially in ground state 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 coherentsuperposition of discrete states.

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

9. Control Hamiltonian, pulse sequence, quasi-dark state STIRAP into continuum with LICS Adiabatic elimination of the continuum states 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. Control Hamiltonian, pulse sequence, quasi dark state STIRAP into continuum with LICS Hamiltonian matrix is non-Hermitian 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. Control We want to find analytically populations , signal from and the ionization Hamiltonian, pulse sequence, quasi dark state STIRAP into continuum with LICS Hamiltonian matrix is non-Hermitian 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

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 statewritten for small values of angle

14. 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. 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