Molecular Deceleration Georgios Vasilakis

Outline  Why cold molecules are important  Cooling techniques  Molecular deceleration  Principle  Theory  Experiment  Results  Summary

Applications of cold molecules Molecules can be polar !(unlike atoms) EDM experiments Time reversal symmetry violation Parity-violating interaction in chiral molecules Lifetime measurements Cold colisions Quantum chemistry New quantum phases of matter Quantum computing

Various cooling techniques Laser cooling. Unlike atoms, molecules have complex energy spectrum! No simple closed-level systems can be found Indirect cooling (form molecules from pre-cooled atoms) photoassociation Feshbach resonances Buffer gas cooling Molecular deceleration

Principle Energy of a dipole in Electric field: U=-p·E The behavior of a dipole depends on the orientation of p (state of the molecule) with respect to E  Low and high-field seeking states Time varying inhomogeneous electric fields can cause deceleration Etot=K+U Gain of potential energy is compensated by loss of kinetic energy

Stark shift Molecular state: |ΛΣ>|JMΩ>|v> (within Born-Oppenheimer approximation): |JMΩ> and |JM-Ω> have the same energy but small splitting since the separation of electronic and nuclear motion is not exact An applied electric field causes mixing between states of opposite parity: Stark shift=potential energy of the molecule

Typical Stark Shifts For the maximum electric fields in the laboratory typical Stark shifts a few cm -1 Kinetic energy of molecules in the beams typically on the order of 100cm -1 ⇒ Need to use multiple pulsed electric fields!

Decelerating low field seekers  Series of stages.  Each stage consists of two parallel cylindrical metal rods  Typical dimensions: radius,rod spacing,stage spacing~ a few mm  Alternating stages are connected to each other  One of the rods is connected to a positive and the other to a negative switchable high-voltage power supply (typically ~10KV, generating maximum electric fields ~100KV/cm)  When at one stage the high voltage is on, the neighboring stages are grounded.  When the voltage at a stage is switched off, the next stage simultaneously is switched on.

Importance of phase stability The energy a molecule loses per stage depends on the its position at the time the fields are being switched!! Switch on the voltage at the correct time. ⇒ Switch on the voltage at the correct time. For equal spacing between stages, that means that the time intervals after which the electric fields are being switched should be gradually increased (because the molecules are being decelerated).  From the initial molecular beam only those molecules that have a certain velocity and a certain spatial extent will be decelerated.

Focusing in transverse directions Molecules spread in the transverse directions ⇒ Importance of focusing Solution:  Successive stages are orientated orthogonally to each other to provide guiding of the molecular beam in both transverse dimensions  Hexapole electrostatic lens

Experimental setup (low field seekers) First experiment to perform molecular deceleration! They used metastable (τ=3.7msec) CO molecule (dipole moment 1.37 Debye). CO molecules can be prepared in single quantum state at a well-defined position and time, and their velocity distribution can readily be measured. A UV laser prepares the system in the metastable state. 63 equidistant electric field stages. Velocity distribution determined by recording time of flight.

Experimental results Demonstrated slowing down from 225m/s to 98m/s. As they increase the number of stages the deceleration is increased!

High Field seekers The problem arises because of the difficulty in transverse confinement. Maxwell’s equations do not allow for a maximum of the electric field in free space. If the same geometry for electrodes is used then the high-field-seeking states have the tendency to crash into the electrodes. This difficulty can be overcome by using Alternate Gradient (AG) focusing lenses. (one lens converging and the other diverging, if both lenses have equal focal lengths and certain spacing then the total focal length is positive). The rotational ground state of any molecule is always lowered in energy by an external perturbation ⇒ it is a high-field seeking state. By letting the molecules fly out of, instead of into, the region of a high electric field we can in principle decelerate the molecules.

Summary Molecular (Stark) decelaration is a powerful technique to cool down molecules. It involves the use of properly time varying electric fields. It opens new possibilities in the field of cold molecules