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We performed a search for a Lorentz-invariance- and CPT-violating coupling ofthe $^3$He and $^{129}$Xe nuclear spins to posited background fields. Ourexperimental approach is to measure the free precession of nuclear spinpolarized $^3$He and $^{129}$Xe atoms using SQUID detectors. As the laboratoryreference frame rotates with respect to distant stars, we look for a siderealmodulation of the Larmor frequencies of the co-located spin samples. As aresult we obtain an upper limit on the equatorial component of the backgroundfield $\tilde{b}^n_{\bot}< 8.4 \cdot 10^{-34}$ GeV (68\% C.L.). Furthermore,this technique was modified to search for an electric dipole moment (EDM) of$^{129}$Xe.

Limit on Lorentz-Invariance- and CPT-Violating Neutron Spin Interactions Using a $^3$He-$^{129}$Xe Comagnetometer