On deflection fields, weak-focusing and strong-focusing storage rings for polar molecules

In this paper, we analyze electric deflection fields for polar molecules in terms of a multipole expansion and derive a simple but rather insightful expression for the force on the molecules. Ideally, a deflection field exerts a strong, constant force in one direction, while the force in the other directions is zero. We show how, by a proper choice of the expansion coefficients, this ideal can be best approximated. We present a design for a practical electrode geometry based on this analysis. By bending such a deflection field into a circle, a simple storage ring can be created; the direct analog of a weak-focusing cyclotron for charged particles. We show that for realistic parameters a weak-focusing ring is only stable for molecules with a very low velocity. A strong-focusing (alternating-gradient) storage ring can be created by arranging many straight deflection fields in a circle and by alternating the sign of the hexapole term between adjacent deflection fields. The acceptance of this ring is numerically calculated for realistic parameters. Such a storage might prove useful in experiments looking for an EDM of elementary particles.Comment: 8 pages, 5 figure

Efficient Stark deceleration of cold polar molecules

Stark deceleration has been utilized for slowing and trapping several species of neutral, ground-state polar molecules generated in a supersonic beam expansion. Due to the finite physical dimension of the electrode array and practical limitations of the applicable electric fields, only molecules within a specific range of velocities and positions can be efficiently slowed and trapped. These constraints result in a restricted phase space acceptance of the decelerator in directions both transverse and parallel to the molecular beam axis; hence, careful modeling is required for understanding and achieving efficient Stark decelerator operation. We present work on slowing of the hydroxyl radical (OH) elucidating the physics controlling the evolution of the molecular phase space packets both with experimental results and model calculations. From these results we deduce experimental conditions necessary for efficient operation of a Stark decelerator.Comment: 8 pages, 9 figure

Stark deceleration of CaF molecules in strong- and weak-field seeking states

We report the Stark deceleration of CaF molecules in the strong-field seeking ground state and in a weak-field seeking component of a rotationally-excited state. We use two types of decelerator, a conventional Stark decelerator for the weak-field seekers, and an alternating gradient decelerator for the strong-field seekers, and we compare their relative merits. We also consider the application of laser cooling to increase the phase-space density of decelerated molecules.Comment: 10 pages, 8 figure

Ramsey-type microwave spectroscopy on CO (a3Πa^3\Pi)

Using a Ramsey-type setup, the lambda-doublet transition in the $J=1,\, \Omega=1$ level of the $a^3\Pi$ state of CO was measured to be 394 064 870(10) Hz. In our molecular beam apparatus, a beam of metastable CO is prepared in a single quantum level by expanding CO into vacuum and exciting the molecules using a narrow-band UV laser system. After passing two microwave zones that are separated by 50 cm, the molecules are state-selectively deflected and detected 1 meter downstream on a position sensitive detector. In order to keep the molecules in a single $m_J^B$ level, a magnetic bias field is applied. We find the field-free transition frequency by taking the average of the $m_J^B = +1 \rightarrow m_J^B = +1$ and $m_J^B = -1 \rightarrow m_J^B = -1$ transitions, which have an almost equal but opposite Zeeman shift. The accuracy of this proof-of-principle experiment is a factor of 100 more accurate than the previous best value obtained for this transition

Sensitivity of rotational transitions in CH and CD to a possible variation of fundamental constants

The sensitivity of rotational transitions in CH and CD to a possible variation of fundamental constants has been investigated. Largely enhanced sensitivity coefficients are found for specific transitions which are due to accidental degeneracies between the different fine-structure manifolds. These degeneracies occur when the spin-orbit coupling constant is close to four times the rotational constant. CH and particularly CD match this condition closely. Unfortunately, an analysis of the transition strengths shows that the same condition that leads to an enhanced sensitivity suppresses the transition strength, making these transitions too weak to be of relevance for testing the variation of fundamental constants over cosmological time scales. We propose a test in CH based on the comparison between the rotational transitions between the e and f components of the Omega'=1/2,J=1/2 and Omega'=3/2,J=3/2 levels at 532 and 536 GHz and other rotational or Lambda-doublet transitions in CH involving the same absorbing ground levels. Such a test, to be performed by radioastronomy of highly redshifted objects, is robust against systematic effects

Feasibility of a storage ring for polar molecules in strong-field-seeking states

We show, through modeling and simulation, that it is feasible to construct a storage ring that will store dense bunches of strong-field-seeking polar molecules at 30 m/s (kinetic energy of 2K) and hold them, for several minutes, against losses due to defocusing, oscillations, and diffusion. The ring, 3 m in diameter, has straight sections that afford access to the stored molecules and a lattice structure that may be adapted for evaporative cooling. Simulation is done using a newly-developed code that tracks the particles, in time, through 400 turns; it accounts for longitudinal velocity changes as a function of external electric field, focusing and deflection nonlinearities, and the effects of gravity. An injector, decelerator, and source are included and intensities are calculated.Comment: 6 pages 5 figures, 3 table

UV frequency metrology on CO (a3Pi); isotope effects and sensitivity to a variation of the proton-to-electron mass ratio

UV frequency metrology has been performed on the a3Pi - X1Sigma+ (0,0) band of various isotopologues of CO using a frequency-quadrupled injection-seeded narrow-band pulsed Titanium:Sapphire laser referenced to a frequency comb laser. The band origin is determined with an accuracy of 5 MHz (delta \nu / \nu = 3 * 10^-9), while the energy differences between rotational levels in the a3Pi state are determined with an accuracy of 500 kHz. From these measurements, in combination with previously published radiofrequency and microwave data, a new set of molecular constants is obtained that describes the level structure of the a3Pi state of 12C16O and 13C16O with improved accuracy. Transitions in the different isotopologues are well reproduced by scaling the molecular constants of 12C16O via the common mass-scaling rules. Only the value of the band origin could not be scaled, indicative of a breakdown of the Born-Oppenheimer approximation. Our analysis confirms the extreme sensitivity of two-photon microwave transitions between nearly-degenerate rotational levels of different Omega-manifolds for probing a possible variation of the proton-to-electron mass ratio, \mu=m_p/m_e, on a laboratory time scale

Traveling-wave deceleration of SrF molecules

We report on the production, deceleration and detection of a SrF molecular beam. The molecules are captured from a supersonic expansion and are decelerated in the X$^2\Sigma^+ (v=0, N=1)$ state. We demonstrate the removal of up to 40% of the kinetic energy with a 2 meter long modular traveling-wave decelerator. Our results demonstrate a crucial step towards the preparation of ultracold gases of heavy diatomic molecules for precision spectroscopy

Field-linked States of Ultracold Polar Molecules

We explore the character of a novel set of ``field-linked'' states that were predicted in [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasi-bound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the 2-D Schrodinger equation to find bound states, whose energies correlate well with resonance features found in fully-converged multichannel scattering calculations

Slowing heavy, ground-state molecules using an alternating gradient decelerator

Cold supersonic beams of molecules can be slowed down using a switched sequence of electrostatic field gradients. The energy to be removed is proportional to the mass of the molecules. Here we report deceleration of YbF, which is 7 times heavier than any molecule previously decelerated. We use an alternating gradient structure to decelerate and focus the molecules in their ground state. We show that the decelerator exhibits the axial and transverse stability required to bring these molecules to rest. Our work significantly extends the range of molecules amenable to this powerful method of cooling and trapping.Comment: 4 pages, 5 figure