## CP Violation Experiment | Romalis Group Home |

A permanent electric dipole moment of a fundamental particle or an atom directly violates time-reversal symmetry and by the CPT theorem violates CP. While CP symmetry is violated at a small level in the Standard Model, this violation is insufficient to explain the observed asymmetry between matter and anti-matter in the universe. Furthermore, the amount of CP violation in the Standard Model yields permanent EDMs several orders of magnitude smaller than current experimental limits. Many natural extensions to the Standard Model such as supersymmetry, necessary for electroweak symmetry breaking, produce EDMs well within current experimental limits. Thus, the search for a permanent EDM of a fundamental particle or an atom is viewed as a background free test of physics beyond the Standard Model.

Using the method of spin exchange
optical pumping it is possible to obtain a large sample of highly polarized
liquid ^{129}Xe. Liquid Xe is a unique substance which has all
properties necessary for a nuclear EDM experiment:

- Long transverse spin relaxation time (>1300 s)
- Large density (~10
^{22}/cm^{3}) - High electric field breakdown strength (~400 kV/cm)

Thus the shot noise limit for our experiment is

$${ \delta d={\displaystyle \frac{\hbar}{2E\sqrt{2NT_{2}t}}}\approx10^{-36}\text{e-cm} }$$for an
integration time of one day.Of
course, we expect to be limited by a number of other factors such as magnetic
field noise created by the magnetic shields and noise in the high T_{c}
SQUID detectors. A more realistic
limit is probably about 10^{-31} to 10^{-32} e-cm before going
to superconducting magnetic shields and low T_{c} SQUID detectors.

To detect the
nuclear spin precession in our low magnetic field of 10 mG we use a pair of
commercially available high T_{c} SQUID detectors to detect the
magnetic field created by the ^{129}Xe nuclei, completely avoiding the
usual penalty in signal to noise of traditional NMR experiments in low field
environments. A simple dewar
constructed of G11 fiberglass filled with LN_{2} cools the SQUIDs. The temperature of the liquid xenon cell
is controlled by a column of warm (-100 C) nitrogen vapor running through the
liquid nitrogen bath. A CCD camera
monitors the height of liquid xenon in the cell as it condenses via a fiber
optic bundle.

To search for an electric dipole moment one merely needs to create a region with a uniform magnetic field and opposing electric fields and look for a phase difference between the two SQUID signals

In preparation for such an experiment, we have been exploring the low magnetic field behavior of this system with no applied electric field. In a uniformly polarized spherical sample, because of the Pauli exclusion principle, the magnetic field felt by a particular atom due to all other atoms averages to zero. However, due to the slow diffusion in a liquid, in the presence of an applied magnetic field gradient the transverse components of the magnetization develop gradients. A simple model taking into account only first order gradients yields analytic predictions in excellent quantitative agreement with the data. First order gradients of the magnetization create their own magnetic field gradients further influencing the evolution of the magnetization. For tip angles greater than 35 degrees we find that the magnetization gradients grow exponentially. The figure below shows data following a 90 degree pulse. The model begins to deviate from the data when the magnetization has decayed appreciably and is no longer well approximated by a linear gradient.

For a tip angle of 35 degrees, the self interaction effects turn off and the gradients of the magnetization grow linearly in time. Thus, for large tip angles the sensitivity to magnetic field gradients in the self interacting system is enhanced exponentially relative to the non self-interacting system. In principle the gain may be quite large (the exponential growth can occur with time constants > 1 s). In practice we have observed gains in sensitivity by a factor of 10 over the non self-interacting system, given by the ratio of the circles to diamonds in the figure above. The dipolar fields act as a built in amplifier, exponentially enhancing the effects of applied magnetic field gradients!

For tip angles less than 35 degrees, the magnetization gradients oscillate. Instead of a rapid decay of the transverse magnetization in a large gradient, the free induction decay time is substantially increased. Both the frequency of phase oscillations for small angle pulses and the time constant for the exponential growth are in good agreement with the model with errors dominated by uncertainty in the geometry.

The simple linear
model does not explain the free induction decay time for small angle pulses or
the asymmetry in the SQUID signals, nor does it explain the decay of the phase
oscillations, which occur too fast to be explained by diffusion.Extending the model to take into account
higher order gradients of the magnetization and solving numerically a sytem of
coupled differential equations reproduces the asymmetry in the SQUID signals
and improves the accuracy of the prediction for the frequency of the phase
oscillations, but the higher order terms grow rapidly and hence the model
cannot be followed long enough to obtain a quantitative prediction of either T_{2}*
or the decay time of the phase oscillations. Relaxation of the steady state gradients
due to diffusion may play a role in determining T_{2}^{*}. In
the absence of applied field gradients we have obtained FID signals with a T_{2}^{*}
in excess of 800 seconds.

We are currently exploring the effects of deformations of the cell, prototyping the design of a cell that will be used in the actual EDM experiment, developing methods to suppress the sensitivity of the system to unwanted gradients and developing more sophisticated numerical methods for modeling the behavior of this non-linear, self-interacting system. More to come soon!

- M. P. Ledbetter, I. M. Savukov, and M. V. Romalis. "Nonlinear Amplification of Small Spin Precession Using Long-Range Dipolar Interactions."
*Phys. Rev. Lett.***94**, 060801 (2005). - M. P. Ledbetter, I. M. Savukov, L.-S. Bouchard, and M. V. Romalis, "Numerical and experimental studies of long-range magnetic dipolar interactions", J. Chem. Phys.
**121**(3), 1454 (2004). [Copyright AIP] - M. P. Ledbetter and M. V. Romalis, "Nonlinear Effects from Dipolar Interactions in Hyperpolarized Liquid
^{129}Xe", Phys. Rev. Lett.**89**, 287601 (2002). - M. V. Romalis and M. P. Ledbetter, "Transverse Spin Relaxation in Liquid
^{129}Xe in the presence of Large Dipolar Fields," Phys. Rev. Lett.**87**, 67601 (2001).

- M. Ledbetter, "Low Field NMR of Liquid
^{129}Xe: Progress Towards a Search for a Permanent EDM." Presented at DAMOP 2002. - M. V. Romalis, "Limits on CP Violation from Searches for Electric Dipole Moments." Presented at DAMOP 2002.
- M. V. Romalis, "Constraints on CP Violation from Searches for Nuclear Electric Dipole Moments." Presented at the University of Illinois at Urbana-Champaign.