Stimulating the production of ultracold molecules with laser pulses

1
Stimulating the production of ultracold molecules
with laser pulses
Subhas Ghosal
Department of Chemistry University of
Durham Durham DH1 3LE UK
2
Feshbach resonances (magnetic)
Formation of ultracold molecules
Photoassociation (optical)

• A Feshbach resonance occurs when an atomic
  scattering state is tuned to degeneracy with a
  bound molecular state

• If the magnetic field is tuned across the
  resonance a pair of tapped atoms can be converted
  into a molecule

R. Grimm et. al., Science 301, 1510 (2003)
3
Schematic representation of the photo association
process

• Two colliding atoms can absorb a photon of right
  frequency and photoassociate to form a bound
  electronically excited molecule

• The molecule thus formed can quickly decay to
  free atoms or a bound ground electronic state
  molecule

• In ultracold temperature the spread of the
  kinetic energy is very less and photoassociation
  takes place in the long range of the molecular
  potential.

• High resolution spectroscopic technique to study
  the high vibrational levels

K. M. Jones et. al. Rev. Mod. Phys. 78, 483 (2006)
4
Collision between Rb and Cs atoms
Rb(5s 2S1/2) Cs (6s 2S1/2) ? RbCs (5s 2S1/2
6p 2P v, J)

• Ground (X 1S) and the two lowest-lying excited
  electronic states (A 1S and b 3?) are considered
  in a simple model

A 1S
b 3?

• Spin-orbit coupling between the two excited
  electronic states are included in the dynamics

Potential Energy Surfaces
X 1S

• Ground state (X 1S)
• Short range Allouche et. al.
• long range Fellows et. al. and Derevianko
  et. al.

• Excited states (A 1S and b 3?) Marinescu et.
  al.

A. R. Allouche et. al. J. Phys. B At. Mol. Opt.
Phys. 33, 2307 (2000)
C. E. Fellows et. al. J. Mol. Spectrosc. 197, 19
(1999)
A. Derevianko et. al. Phys. Rev. A 63, 052704
(2001) M. Marinescu et. al. Phys. Rev. A 59, 390
(1999)
5
Theoretical Methodology

• The dynamics in the ground and excited states
  are described by the time-dependent Schrödinger
  equation (TDSE).
• H?(R, t) ih d/dt ?(R, t)

• The Hamiltonian

• The wave function

• Diagonalization of the Hamiltonian in the
  absence of any electric field gives the
  vibrational energy levels and wave functions
• An initial wavefunction is a scattering state
  on the ground-state potential.
• The excited-state wave packet is made up of a
  superposition of several vibrational levels.

6
Numerical methods

• A large spatial grid is considered (100000 a0)
  to represent the initial continuum state.
• No absorbing boundary - due to large size of the
  grid and very small kinetic energy
• The TDSE is solved by expanding the evolution
  operator in terms of Chebyschev polynomials

• The dynamics of propagation of the wavepacket is
  analyzed by studying the evolution of the
  population on both surfaces.
• Pe(g )(t) lt?e(g)(R,t)?e(g)(R,t)gt
• More detailed information is provided by
  projecting the wavepackets onto the unperturbed
  vibrational states v of the different
  potentials.
• PSv(t) lt?Sv(R)?e,g (R,t)gt2

7
Test Results

• Gaussian pulse

FWHM 2 ps
Detuning 16 cm-1
Max Electric Field 2.512 J/m2
Pulse energy 78.9 nJ
Overall population of the excited molecule

• The maximum of the transferred population occurs
  before the maximum of the pulse

• After the pulse most of the population is going
  back to the initial continuum state and a small
  fraction ( 4e-5) is transferred to the excited
  state

8
Projection of the excited-state wave packet
generated by the pulse onto the vibrational
levels of the ground state.

• many bound levels in the excited states are
  excited during the pulse but levels form v 359
  to v 369 remains populated after the pulse

• Variation of populations of the individual
  vibrational states

9
Time-dependent wave packet dynamics
The wavepacket in different times superimposed on
the excited state potentials
Wave packet propagation
10
The effect of resonant spin-orbit coupling
Avoided crossing in the excited states

• Resonant spin orbit coupling is observed between
  the A 1S and b 3? states due to the avoided
  crossing at R 10 a0

• The excited vibrational eigenfunctions have
  mixed singlet- triplet character

• Very sensitive on the description of the SO
  coupling

• After the pulse the dynamics is studied on the
  two excited surfaces

Diagonal and off-diagonal spin orbit functions

• The stabilization of the ground state molecule
  requires a favourable overlap between the
  vibrational wave functions of both the excited
  and ground molecular state

T Bergeman unpublished since 2007
11
Overlap between the vibrational states

• Franck-Condon overlap with the mixed excited
  states with the vibrational levels of the ground
  state

• The peaks in the rotational constants
• Bv lt1/(2µR2)gt correspond to the levels strongly
  perturbed by resonance coupling

• In order to assure an efficient dump step the
  pump detuning has to be adjusted such that
  resonant excited-state levels are populated

12
Similar study for Rb2

• No of overlapping states are more but the ground
  state vibrational levels are very weakly bound

13
Summary and Conclusion

• The effect of resonant coupling is stronger in
  RbCs than in Rb2
• This occurs because individual states are more
  strongly perturbed, because the density of states
  is much less (R-6 potential instead of R-3)
• Mixed excited levels have good Franck-Condon
  factors with ground state levels with binding
  energies up to 1500 cm-1

Future Plan

• Improve the R-dependent spin-orbit functions in
  order to support our preliminary observations on
  the effect of resonant coupling
• See the effect of positive and negative chirping
  of the laser pulse on the dynamics.
• Extend the three-surface model to six surfaces,
  including all the coupled excited-state
  potentials and the spin-orbit coupling between
  them

14
Acknowledgement
Prof. Jeremy M Hudson
University of Durham
Dr. Christiane P Koch
Freie Universitat Berlin
Dr. Richard J Doyle
15
Thank you......