Obtaining Atomic Matrix Elements from Vector Tune-Out Wavelengths Using Atom Interferometry

Abstract

Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. Tune-out wavelength measurements to date have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.2 of 12 that of a more easily measured transition. For instance, Herold et al. improved knowledge of the 6P matrix elements in rubidium by a factor of ten by relating them to the better-known 5P elements [4].While these results demonstrate the utility of tune-out spectroscopy, a challenge is that to some degree the frequency of any single response zero depends on all of the accessible states and matrix elements in the atom [2]. To deal with this, theoretical estimates are used for contributions that are not of direct interest. This introduces additional sources of uncertainty and limits the applicability of the measurements to systems where high-quality theoretical estimates are available.We present here a technique to reduce this dependence on theory. Up to now, most studies have centered on the scalar response of the atom, which can be obtained by averaging over the atomic spin states and/or the optical polarization of the light. However, spin-polarized atoms also have a strong vector response, which can be measured by varying the light polarization and the spin orientation. The effect on the tune-out wavelength was measured in a recent study by Schmidt et al. [7] Like the scalar response, the vector response depends on multiple transition matrix elements. However, these elements combine in a different way for the scalar and vector quantities. We show here that by making joint measurements of both responses, different contributions to the electric polarizability can be experimentally resolved. This can lead to improved accuracy and can provide experimental information about matrix elements that cannot easily be observed directly.Of particular significance, it is possible to independently determine the effects of the atomic core and of the infinite manifold of high-lying valence states. The electric polarizability of the ion...

Otto Stern’s Legacy in Quantum Optics: Matter Waves and Deflectometry

“…The nature of the bonding of He 2 [32] was measured via quantum reflection from a grating, since other techniques would have been too invasive to probe the extremely fragile bond. The static polarizability of sodium [33], lithium [34] and other alkali atoms [35] was measured using atom interferometry, and long-range potential properties [36], van der Waals coefficients [37], atomic tune-out wavelengths [38] and transition matrix elements [39,40] as well as surface excitations [41] have all been studied using matter-wave diffraction.…”

Precise control of magnetic fields and optical polarization in a time-orbiting potential trap

“…Our previous experiments [11] took advantage of the rapid bias field reversal in a TOP trap in order to suppress the vector component of the polarizability, which depends sensitively on the polarization of the applied light. For a new experiment [12], we wish to measure the vector polarizability, so it is necessary to characterize both the trap field and the light polarization. Although the discussion is centered on our particular requirements, we believe that the methods presented will be useful for many types of experiments, since it is often necessary to apply well-characterized light to atoms in a well-known magnetic field.…”

Measurement of the 87Rb D-line vector tune-out wavelength

“…For instance, interpreting alkali atom parity violation amplitudes in terms of nuclear physics parameters requires knowledge of the nS 1/2 ↔ nP 1/2 dipole matrix elements [18,19]. Vector tune-out measurements can allow the P 1/2 matrix elements to be constrained separately from the P 3/2 matrix elements, whereas a purely scalar measurement depends jointly on both P 1/2 and P 3/2 elements [20].…”

“…(1) cv = −0.04(4) from Ref. [20]. For the 5P states we use d 5P 1/2 = 4.234 (2) and the ratio d 5P 3/2 /d 5P 1/2 = 1.99217(3) from [11].…”

“…This can be achieved by comparing tune-out measurements near different states, such as the 6P states near λ = 420 nm for Rb. The core and Rydberg contributions have different frequency dependencies, allowing their impact to be resolved [20]. Further, since the J = 1/2 and J = 3/2 states contribute differently to the scalar and vector components of α v in Eqs.…”