We propose a very sensitive method for measuring the electric dipole moment of the electron using polar molecules embedded in a cryogenic solid matrix of inert-gas atoms. The polar molecules can be oriented in the
-direction by an applied electric field, as has recently been demonstrated by Park et al. The trapped molecules are prepared into a state that has its electron spin perpendicular to
, and a magnetic field along
causes precession of this spin. An electron electric dipole moment
would affect this precession due to the up to 100 GV/cm effective electric field produced by the polar molecule. The large number of polar molecules that can be embedded in a matrix, along with the expected long coherence times for the precession, allows for the possibility of measuring
to an accuracy that surpasses current measurements by many orders of magnitude. Because the matrix can inhibit molecular rotations and lock the orientation of the polar molecules, it may not be necessary to have an electric field present during the precession. The proposed technique can be applied using a variety of polar molecules and inert gases, which, along with other experimental variables, should allow for careful study of systematic uncertainties in the measurement.
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