Atomic parity violation in francium at TRIUMF's ISAC radioactive beam facility

Overview of the Rb work (soon to be replaced by a more general intro into the Fr project)

A programme is currently developed to investigate highly forbidden transitions in laser-cooled Rb and Fr atoms, confined in a magneto-optical trap (MOT). The purpose is to study subtle relativistic effects in atoms and, ultimately, to perform an atomic parity nonconservation (APNC) measurement in an isotopic chain of Fr at TRIUMF's ISAC radioactive beam facility, testing the Standard Model.

The transition {$ns_{1/2} \rightarrow (n\!+\!1) s_{1/2}$} from an alkali's electronic ground state to the first excited {$s$}-state is one of the faintest transitions observed in atoms; it is electric-dipole (E1) forbidden, and in the non-relativistic limit, the magnetic-dipole (M1) amplitude also vanishes. Relativistic effects and the hyperfine (HF) interaction with the nuclear spin give rise to an extremely weak M1 transition with tiny oscillator strength {$f$} (e.g. {$10^{-13}$} in Cs --- allowed E1 transitions have {$f\!\approx\!1$}), which has attracted a lot of interest. First, the exact mechanism giving rise to the relativistic M1 amplitude has been unclear for a long time, and it is considered the most sensitive electromagnetic transition to the accuracy of the relativistic description of an atomic system [1]. Second, the {$6s_{1/2} \rightarrow 7s_{1/2}$} transition in Cs has been the basis of the landmark APNC measurements carried out by Wieman et al.~[2]: the parity-violating Z-boson exchange between the valence electron and the nucleons mixes states of opposite parity and leads to an E1 amplitude {$A_{\rm PNC}$} ({$f \approx 10^{-22}$} in Cs). The significant difficulties in observing such weak lines have so far prevented experiments other than in Cs.

The 5s - 6s Transition in Rb

Savukov et al.~[1] have recently shown the importance of including negative-energy states (NES), i.e.~the effect of electron-positron pairs, in the relativistic computation of the M1 amplitude and discovered surprisingly large NES contributions. In case of Rb, they found a cancellation between the no-pair and the NES amplitude, reducing the predicted total M1 amplitude by a factor of 8, providing the best opportunity for an experimental test of electron-positron pair contributions in atomic structure. We propose to measure {$A_{\rm M1}$} by observing the {$A_{\rm Stark} A_{\rm M1}$} interference in Rb [3]. The Stark-interference technique was proposed by Bouchiat [4] and used by Wieman for APNC. The {$ns_{1/2}\! \rightarrow\! (n\!\!+\!\!1) s_{1/2}$} transition is excited with laser light in the presence of an external homogeneous electric field {$E$} of {$\approx 1$} kV/cm. The resulting Stark-mixing of states of opposite parity leads (in an appropriate geometry) to an E1 amplitude {$A_{\rm Stark} \approx \beta E$}, where {$\beta$} is the tensor transition polarizability. The total transition rate is {$R \propto |A_{\rm Stark} + A_{\rm M1} + A_{\rm PNC}|^2$}. For {$A_{\rm Stark} \gg A_{M1}, A_{\rm PNC}$}, the rate reduces to
{$R \propto |A_{\rm Stark}|^2 \pm 2 A_{\rm Stark} A_{M1} \pm 2 A_{\rm Stark} A_{\rm PNC}$} (simplified). The signs of the interference terms change under reversals of the electric field, magnetic field, and the {$m$}-substate. {$R$} is measured by observing the fluorescence from the decay of the excited {$s$} state via a cascade of two allowed E1 transitions (see Fig.~1). The relative change in fluorescence under field reversals, {$\Delta R/R = 4 A_{M1(PNC)}/\beta E$} is a measure of {$A_{M1} (A_{\rm PNC})$}, once {$\beta$} and {$E$} are known. Compared to a direct observation of {$|A_{M1 (PNC)}|^2$}, the Stark-interference method effectively amplifies the signature by a factor {$A_{\rm Stark}/A_{M1 (PNC)}$}. In Rb, the M1 signal is increased roughly by a factor of 500, and the PNC signal in Fr by a factor of {$10^4$}.

Instead of a massive thermal beam (Cs: {$10^{15}$} s{$^{-1}$}cm{$^{-2}$}), we plan to use the new route of using cold, trapped atoms to maximize the signal. A beam works for Rb, but an important milestone is to demonstrate highly efficient and robust techniques off-line, applicable on-line to short-lived Fr isotopes at ISAC. In the MOT, a sample density of {$5\times10^{10}$} cm{$^{-3}$} can readily be achieved, with {$5\times10^{7}$} atoms in the trap. Trapping periods are interleaved with measurement periods of a few ms duration, during which the MOT is turned off. The trapped atoms are optically pumped into a specific m-state of the lower HF ground state and exposed to the {$5s - 6s$} laser. An electric field of 3 kV/cm leads to {$\approx 5\times10^{8}$} excitations per second in the trap. Spontaneous decay via {$5p$} returns more than half back into the previously depleted upper HF ground state. They are probed by a short laser pulse of {$5s - 5p_{3/2}$} light, producing tens of 780 nm photons per {$6s$}-excited atom, yielding {$> 5\times10^8$} photons/s in a detector with 10 \% efficiency (internal and solid angle). In Rb, {$\Delta R/R \approx 2\times 10^{-4}$} for {$\Delta F=0$} transitions (NES sensitive), where {$F$} is the HF quantum number. In a shot-noise limited measurement, the Stark-M1 interference can be detected within a few seconds (intensity fluctuations and scattered light must be highly optimized).

In a first step, the transition has to be found at 496 nm. Using our precision wavemeter with 200 MHz absolute accuracy, the laser can be tuned to the correct frequency. The faint fluorescence radiation from the forbidden transition is very hard to detect, and for a first identification and characterization of the transition, it is best to work with a dense atomic vapor in a cell exposed to a kV/cm level Stark mixing field, and using lock-in detection techniques. With this setup, the transition can be found and the Stark mixing can be quantified. However, a E1-M1 interference measurement is only possible with resolved {$m$}-states, as the interference term vanishes when summed over all magnetic sublevels.

An On-Line Fr Trap at ISAC

There is strong interest in an APNC measurement in Fr (see e.g. [5]), where the effect is predicted to be {$18\times$} larger than in Cs. The expected flux of several Fr isotopes at ISAC will be sufficient to load a MOT with a number of atoms exceeding that in the interaction region in the Cs beam work. First, {$A_{\rm M1}$} in Fr is measured. It is predicted to be 500 times larger than in Rb, but is insensitive to NES. A determination of the M1 contribution induced by the HF interaction is a powerful way to determine the polarizability {$\beta$} in Fr, a quantity not easily measurable otherwise, but essential in the interpretation of APNC. With the experience gained, the measurement of the parity-nonconserving amplitude {$A_{\rm PNC}$} can be contemplated. In this case, a standing-wave laser beam configuration is chosen, which eliminates the {$A_{\rm Stark} A_{\rm M1}$} interference term, but not the {$A_{\rm Stark} A_{\rm PNC}$} contribution. The latter leads to {$\approx \Delta R/R = 10^{-4}$} under field reversals.

References:

[1] I. M. Savukov, A. Derevianko, H. G. Berry, and W. R. Johnson. Phys. Rev. Lett. 83, 2914 (1999).

[2] C. S. Wood, S. C. Bennett, D. Cho, B. P. Masterson, J. L. Roberts, C. E. Tanner, and C. E. Wieman. Science 275, 1759 (1997).

[3] S. L. Gilbert, R. N. Watts, and C.  E. Wieman. Phys. Rev. A 29, 137 (1984).

[4] M. A. Bouchiat and C. Bouchiat. J. Phys. (Paris) 35, 899 (1974).

[5] S. Sanguinetti, J. Guena, M. Lintz, P. Jacquier, A. Wasan, and M. A. Bouchiat. Eur. Phys. J. D 25, 3 (2003).

[6] G. Gwinner, E. Gomez, L.A. Orozco, A. Perez Galvan, D. Sheng, Y. Zhao, G.D. Sprouse, J.A. Behr, K.P. Jackson, M.R. Pearson, et al. Hyperfine Interactions 172, 45 (2006).