Why investigating ultracold molecules in electric fields?

Over the past decade investigations of ultracold quantum gases have been revealing a wealth of intriguing phenomena. In particular, ultracold molecular systems represent a paradigm including molecular Bose-Einstein condensates. External fields on the other hand are equally important for the preparation and control of ultracold systems. They are used for cooling and trapping as well as for quantum state preparation or the tuning of atomic/molecular interactions. Due to their permanent electric dipole moments, heteronuclear polar dimers deserve a special focus. They open up the possibility to create dipolar quantum gases with long-ranged interactions which introduces exceptional properties for the corresponding quantum systems. Electric fields play here an important role due to their immediate impact on polar systems which leads for isolated molecules amongst others to rotational orientation and alignment.

Further applications:

• manipulation of rovibrational spectra and transitions
• ultracold state-to-state chemical reaction dynamics
• collisional spin relaxation in cold molecules
• molecular quantum computing

What we do

We investigate the steric as well as the radiative properties of heteronuclear dimers exposed to strong static electric fields. We go beyond the so-called rigid rotor approximation by solving the full Schrödinger equation including both the rotational and the vibrational degree of freedom. This allows us to use an electronic dipole moment function depending on the internuclear distance of the molecule, thus coupling the the angular and radial motion nonlinearly. By doing so, we calculate the influence of the electric field on the rovibrational spectrum and dynamics as well as on the radiative properties of heteronuclear dimers. Furthermore, by extending the theoretical framework to unbound molecular states, it is possible to describe the advantages of an external electric field for the formation process of ultracold heteronuclear molecules via stimulated photoassociation.

Some illustrative results at a glance

The following pictures show how the external electric field alters the rotational properties of the LiCs molecule: Low lying rotational states are severly affected by the field and possess a strong hybridization and orientation along the field axis.
Left: Steric properties of the first few rotational states of the LiCs molecule exposed to an electric field F=10^-4 a.u.
Right: Cascade of the fully angular-momentum-polarized states in the presence of the same field.

Spontaneous radiative transitions between rotational states are changed by the interaction with the external field as well: The restrictive selection rules for field-free molecules loose, resulting in a reduction of the otherwise tremendously long (in the range of days) radiative lifetimes. However, the decay path of fully angular-momentum-polarized states (J=M) remains unique (see picture on the right above) and therefore offers a valuable tool to control the orientation of the molecules, e.g., via stimulated absorption and emission processes.

Latest developments

As mentioned above, the quest for polar molecular quantum gases attracts a lot of attention. One very promising way to achieve such ultracold ground-state heteronuclear molecular gases is the photoassociation scheme, as depicted in the picture below. Also in this case, the application of an external electric field is favourable since then the direct production of s-wave molecules is possible.


Figure: Schematics of the one-photon association process followed by a radiative deexcitation cascade (not to scale). The electronic potential energy curve and dipole moment function of the electronic ground state of the LiCs molecule are also shown.

However, this technique results in highly excited vibrational molecular states and subsequently a radiative deexcitation cascade will occur. Again, field-free selection rules will be lifted by electric fields, consequently making purely vibrational decays favourable. This results in a much narrower rotational state distribution in the vibrational ground level compared to the field-free case:
Left: Population distribution of the vibrational ground state for the decay cascade starting from the (v=44,J=1,M=0) state in the absence of the electric field.
Right: The same with (v=44,J=M=0) as initial state and for F=4*10^-5a.u.

Literature

R. Gonzalez and P. Schmelcher:
Rovibrational Spectra of Diatomic Molecules in Strong Electric Fields: The Adiabatic Regime
Physical Review A 69, 023402 (2004)

R. Gonzalez and P. Schmelcher
Electric Field-Induced Adiabaticity in the Rovibrational Dynamics of Heteronuclear Diatomic Molecules
Physical Review A  71, 033416 (2005)

R. Gonzalez-Ferez and P. Schmelcher
Electric Field-Induced Rovibrational Mixing in Heteronuclear Dimers
Europhysics Letters 72, 555 (2005)

R. Gonzalez-Ferez, M. Mayle and P. Schmelcher
Rovibrational Dynamics of LiCs Dimers in Strong Electric Fields
Chemical Physics 329, 203 (2006)

M. Mayle, R. Gonzalez-Ferez and P. Schmelcher
Controlling Molecular Orientation through Radiative Rotational Transitions in Strong Static Electric Fields
Physical Review A 75, 013421 (2007)