Progress on a PNC experiment with a single barium ion

This new approach to measuring atomic PNC, first described in Phys. Rev. Lett. 70, 2383 (1993), utilizes the remarkable sensitivity inherent in experiments with a single trapped atomic ion. We have built the first completely solid-state laser system for a trapped barium ion. We have completed key tests to show that a PNC measurement is feasible. We measured lifetimes of the 5D metastable states, studied the 6S -> 5D quadrupole transition at 2.05 um, populated selected magnetic sublevels to create a spin-polarized ion, and demonstrated that long spin relaxation times (>30 s) exist in both the ground and 5D states--absolutely necessary for a PNC experiment.The long-range goal is to measure Ba⁺ PNC to 0.3% or better. Excellent atomic theory of this alkali-like ion would then permit a decisive atomic test of electroweak physics, comparable to that ultimately expected of atomic cesium and complementary to the best high energy accelerator tests.

We have built and tested most of the apparatus for this experiment. A Ba⁺ ion held in an rf electric field trap is Doppler cooled by focused laser beams until the ion reaches mK temperatures and occupies an orbit smaller that 0.1 um at the electric center of the trap, hopefully coinciding with the geometric center of the trap. We will measure PNC by observing the Larmor precession of the electron-spin in the trapped ion using techniques we have already developed.

The experiment

There is high sensitivity inherent in the 6S_1/2 -> 5D_3/2 transition because of the exceptionally long-lived 5D_3/2 excited state. As indicated in the energy level diagram above, this transition acquires a small electric-dipole amplitude E^PNC due to the mixing of nP_1/2 states into the 6S_1/2 state by the internal PNC interaction. The approximate magnitude is :

A specific choice of standing wave fields will produce a shift in the Larmor precession frequency about the z axis for the range of field strengths to be used in the experiment. A major advantage of using the Larmor frequency for measuring the PNC light shift is that the pure quadrupole light shift of the ground state is independent of the direction of the electron spin and hence does not affect the Larmor frequency. Therefore fluctuations in laser field an frequency, and other sources of variation of the pure quadrupole light shift, do not interfere with the PNC measurement.

The sense of the PNC Larmor precession relative to the optical fields reveals the handedness of the interaction, and the behavior under various phase shifts of the optical fields serves to distinguish the PNC light shift from non-PNC shifts. For example, the sense of the PNC Larmor frequncy will be reversed, without in principle inducing any other changes, when the relative sign of E' and E'' is reversed.

To estimate the expected size of the PNC light shift, assume that the PNC amplitude is driven by an optical field E'₀ = 2 x 10⁴ V/cm obtained with a 100-mW intracavity beam focused to a 10-um diameter spot size at the ion. The PNC Larmor shift would be about 0.4 Hz. This shift could be increased by using a larger field E', but the off-resonant dipole coupling to the 6P and 4F levels rapidly becomes important, as discussed in the next section. The field E'' can be made much smaller than E' to reduce any systematic effects associated with the pure quadrupole light shift, so long as it remains much greater than the linewidth of the 2.05-um laser source. For example, E''=E'/300 would generate a pure quadrupole shift of about 20 kHz, common to each m_s=+/-1/2 substate of the 6S level.

A single measurement can determine the PNC light shift to within an uncertainty of about 10^-2 sec^-1; and simultaneous measurements on N atomic systems over a total observation time t > the lifetime of the 5D_3/2 state can yield an accuracy of one part in 2000 in a time t=1 day. We expect other uncertainties, as discussed  below, to prevent reaching this nearly ideal limit.

We will use the method we recently developed for selecting and detecting the spin state of the ion to measure the PNC light shift in a small static magnetic field directed along z. The ion begins a measurement cycle in the ground state with a definite spin orientation (say m_s=+1/2) acquired by using a circularly polarized cooling laser beam at the end of the cooling cycle. The cooling and cleanup beams are then turned off and the interaction of interest is turned on (for example, by adding the PNC laser beam). At the end of the measurement cycle, any change in spin state is determined by the method of "shelving." Circularly polarized light shelves the ion in the long-lived 5D_3/2 state (see energy level diagram above) if the electron spin has changed direction. Shelving prevents the ion from generating the fluorescence normally observed when the cooling and cleanup laser beams are switched back on; the absence of such fluorescence provides detection of a change in spin direction, caused for example by a Zeeman resonance.

A similar method can be used to study spin interactions in the 5D_3/2 state. The figure below shows data using this technique to determine the 5D_3/2 spin relaxation time. It is clear we have achieved excellent sensitivity to the spin direction with a high fractional change in shelving rate when the spin state changes. These data also show very long spin relaxation times in the 5D_3/2 state, comparable to the lifetime of the state itself. We had been concerned that stray electric fields or noise would cause relaxation through coupling to the quadrupole moment of this state, limiting the coherence time for the PNC measurement. Fortunately, the data show that the ion is well isolated from such effects in our trap.

We have used the 2.05-um laser to begin studying the quadrupole transition itself, which is of central interest for PNC. Figure 8 below shows the data, in which the same shelving method described above was used to detect depopulation of the 5S_1/2 state of the ion when the laser is tuned to resonance with the quadrupole transition.

Systematic effects and calibration in the Ba⁺ experiment

Estimating the statistical accuracy of the proposed experiment is reasonably straightforward. Much more difficult is anticipating potential systematic effects. Before undertaking such an ambitious experimental effort as this, we felt it necessary to investigate possible systematic errors in great depth. The main issues are the dipole and quadrupole light shifts induced by the optical fields, and the extent to which imperfections in the apparatus can cause these shifts to look like PNC shifts. Here we summarize the results of our analysis of such effects.

With ideal applied optical fields such as those discussed above, there can be no contribution to the shift in the Larmor precession frequency other than that due to PNC. If the fields deviate from this ideal geometry (as of course they must at some level), then the total light shift will contain terms that can mimic a PNC shift.

At first sight, the most worrisome shift would be caused by the presence of any circular polarization of E', which can indeed mimic PNC at low field strengths. However, at the light intensity to be used in this experiment, the quadratic AC Stark splitting of the 5D_3/2 state virtually eliminates any spurious coupling of circular polarization. This is a most important point concerning systematic errors. If we allow E', which ideally has no gradient at the ion position, to be slightly phase-shifted by an angle f', creating a finite magnitude of the curl of E', and also allow it to point slightly along E'' as a result of misalignment by a small angle q'', then the largest spurious PNC-like resonant quadrupole shift reduces to

An essential part of the final PNC measurement will be calibration of the absolute optical field strengths at the ion location. We will use two independent methods to determine this, both involving purposeful misalignments of the field geometry, in this case by well-known, reproducible amounts. Most directly, we could measure the pure-E2 Larmor shift for known values of f', q'', and q_B. A second, and independent, calibration technique involves the production of a Larmor shift of the ground state due only to the non-resonant E1 dipole mixing due to the PNC optical field. Calibration by this method then requires knowledge of the sum over dipole matrix elements, a significantly different quantity from the E2 matrix element required in method 1; but both these quantities can be calculated as accurately as PNC itself.

In the experiment, the ion itself will be used to set and check the spatial phases and field geometry. Both measurement of absolute E2 transition rates and purposeful misalignment of phases (to induce Larmor-type shifts along various directions) will be useful tools for alignment and for assessment of drift rates. Indeed, in our opinion, this is the major question that still remains. Can the optical fields and phases, and the ion position be stabilized enough to locate the ion properly and carry out the PNC measurement? Our analysis says the answer is yes, but the decisive tests must still be made.