Stimulated Raman Adiabatic Passage into continuum

Andon Rangelov (Sofia University, Bulgaria)

Nikolay Vitanov (Sofia University, Bulgaria)

Ennio Arimondo (Pisa University, Italy)

Palermo, 2 June 2007

Control of Quantum Dynamics of Atoms, Molecules and Ensembles by Light

(TOK)

Engineering, Manipulation and Characterization of Quantum

States of Matter and Light (RTN)

Outline

3. How to optimize the ionization ?

• Three-level atom - configuration• Hamiltonian, dark state, counterintuitive scheme

2. What is Laser Induced Continuum Structure (LICS) ?

1. What is Stimulated Raman Adiabatic Passage (STIRAP) ?

• LICS configuration• Fano autoionization configuration• STIRAP via the continuum

• Direct ionization into continuum, Ionization via intermediate state: REMPI, STIRAP • STIRAP into continuum with LICS scheme• Hamiltonian, pulse sequence, quasi-dark state

0 0

( ) 220 0

p

p s

s

H t

Hamiltonian In Rotating Wave Approximation (RWA)

1 2 3( ) sin ( )cos ( ) sin ( ) cos ( )cos ( )t t t t t t

1 2 3( ) sin ( )sin ( ) cos ( ) sin ( )cos ( )t t t t t t

diabatic basis1 2 3, ,

adiabatic basis (eigenvectors of H(t) )0( ), ( ), ( )t t t

Three level atom- configuration

Pump

Stokes

3

2

( )tan ( )

( )p

s

tt

t

2 2( ) ( )tan 2 ( )

p st tt

1

- dark state0 1 3( ) cos ( ) sin ( )t t t

STIRAP in configuration

Conditions: Adiabatic evolution & Counterintuitive order of pulses

Result: Highly efficient population transfer

-dark state0 3( ) ( ) / 2

-dark state0 1( ) ( ) 0

- dark state0 1 3( ) cos ( ) sin ( )t t t Explanation:

tan ( ) ( ) / ( )p st t t

Laser Induced Continuum Structure (LICS)

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.

1 2.con

1

2

.con

controllaser

pumplaser

LICS Fano autoionization

1

2

.con

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:

2

T

1 . 1 2con

STIRAP via the continuum

1

3

.con

Stokeslaserpump

laser

Stokeslaser

Conditions for STIRAP via a continuum:1) Adiabatic evolution2) Counterintuitive order of pulses3) 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)

How to optimize the ionization

We consider ionization of atom 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 coherent superposition of discrete states.

Stokes

Pump

Stokes

Can we use STIRAP with LICS to optimize ionization?

STIRAP into continuum

Stokes

Pump

Control

laser-induced continuum structure (LICS)

Pump

STIRAP into continuum with LICS

Stokes

Hamiltonian, pulse sequence, quasi-dark state

Pump

Control

STIRAP into continuum with LICS

Adiabatic elimination of the continuum states

2 2 2

3 3 3

0 01

2 ( )20 ( ) 2

P

P S Q

S Q

H i i q i

q i i

detuning between and P pump Rabi frequency

1 22

Fano parameterq

decay rate from 2

Stokes

2 2 2 2P S Q

3 3 3 3P S Q 2 3

Ionization widths of states and

2 2 2 2P S Q

2 3

Stark shifts of states and

3 3 3 3P S Q

2

1

3

Continuum

Hamiltonian, pulse sequence, quasi dark state

Pump

Control

STIRAP into continuum with LICS

Hamiltonian matrix is non-Hermitian

2

3

0 01

2 ( )20 ( ) 2

P

P S S Q

S Q Q

H i i q i

q i i

detuning between and P pump Rabi frequency

1 22

Fano parameterq

decay rate from 2

Stokes

2 3

Ionization widths of states and

2 2S

S 2 33 3

QQ

2

1

3

Continuum

, could be incorporated in the detunings

Hamiltonian, pulse sequence, quasi dark state

Pump

Control

STIRAP into continuum with LICS

Hamiltonian matrix is non-Hermitian

2

3

0 01

2 ( )20 ( ) 2

P

P S S Q

S Q Q

H i i q i

q i i

Stokes

2

1

3

Continuum

Less population in : Stokes before pumpMaximum ionization: Stokes before controlTo have LICS: control close to the pump

2Pulse ordering:

This means that in the beginning

of the evolution: P S Q

We want to find analytically populations , signal from and the ionization

1 2 3, ,P P P S2 1 2 31I P P P S

Schrödinger equation in adiabatic basis:

adiabatic diagonal Hamiltonian

If the time evolution is slow we can neglect the nonadiabatic coupling

dynamics is determined by the initial conditions on the adiabatic states

addi B H Bdt

����������������������������

1 1ad dH R HR iR R

dt where

10

0 0

0 0

0 0

R HR

1 diR Rd

( ) ( )exp 't

B t B i dt

where,0,

Then

( )B

Instead of the complicated adiabatic states we make the approximation P S Q

gives the connection between adiabatic and diabatic bases

R

nonadiabatic coupling

0, ,B B B B ��������������

Quasi-dark state of Hamiltonian:

~ ~2 22

0 ~ ~ ~ ~ ~ ~2 2 2 2

4 2( ) 1 , ,

2( 4 ) 4 4

T

S S PP P

S S S

t

0 ( )t

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

0 ~0 2

( )tan ( )

( )P

S

tt

t

( )S S Qq i

~

2 ( ) / 2Si i

~

3 / 2Qi Also:

p is assumed to be small parameter ( )

2

0 2( ) 1 ,0,

2P P

SS

t

P S Q

Initially only the quasi-dark state is populated. In the adiabatic limit the populations are

numerical simulations for Gaussian pulse shapes of Stokes,pump,control

2

0( ) expP P

tt

T

2

0( ) exp SS S

S

tt

T

2

0( ) exp QQ Q

Q

tt

T

2~

2 22

1 ~ ~2 2

4( ) 1

2 ( 4 )

SP

S

P t A

2~

2 ~ ~2

2( )

4

P

S

P t A

2

3 ~ ~2

( )4

S P

S

P t A

2~

~ ~2

( ')exp '

( ') 4

tP

S

tA i dt

t

where

Hamiltonian

2

3

0 01

2 ( )20 ( ) 2

P

P S S Q

S Q Q

H i i q i

q i i

An important difference between LICS-STIRAP and STIRAP:

The control pulse plays a important role in achieving a high ionization rate.

12

13

10 0

0

10

50P S

S

T

T

T

T

12

10 0

0

50

0.5

P S

S

Q

T

T

T

T

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

12

13

10

10

10

0

10

50

50

50

0.5

3

P

S

Q

Q

T

T

T

T

T

T

q

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

2

12

13

0 0

0 0

0

10

0.5

3

P Q

S Q

Q

S

T

T

T

T

q

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

Summary

• An interesting analytic prediction, for an optimal population transfer into continuum was presented

A. Rangelov, N. Vitanov, E. Arimondo, submitted to PRA

• 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.