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

We report on the search for a $CPT$- and Lorentz-invariance-violating coupling of the ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ nuclear spins (each largely determined by a valence neutron) to posited background tensor fields that permeate the Universe. Our experimental approach is to measure the free precession of nuclear spin polarized ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ atoms in a homogeneous magnetic guiding field of about 400 nT using ${\mathrm{LT}}_C$ SQUIDs as low-noise magnetic flux detectors. As the laboratory reference frame rotates with respect to distant stars, we look for a sidereal modulation of the Larmor frequencies of the colocated spin samples. As a result we obtain an upper limit on the equatorial component of the background field interacting with the spin of the bound neutron ${\tilde{b}}_{\perp }^{\mathrm{n}}<8.4\times {10}^{-34}\mathrm{GeV}$ (68% C.L.). Our result improves our previous limit (data measured in 2009) by a factor of 30 and the world’s best limit by a factor of 4.

Figure 1

(a) Weighted phase difference $\mathrm{\Delta }\mathrm{\Phi }$ (data bin: 320 s) after subtraction of the linear terms $\mathrm{\Delta }{\mathrm{\Phi }}_{\mathrm{lin}}$ in Eq. (9). The remaining parabolic shaped structure is the contribution of the RBS shift (in particular the self-shift). (b) Phase residuals after subtraction of the entire fit model $\mathrm{\Delta }{\mathrm{\Phi }}_c$ according to Eqs. (8) and (9). The time evolution of the phase noise is caused by the exponential decay of the signal amplitudes. Note that the phase noise is much less than the symbol size in (a).

Figure 2

Allan Standard Deviations (ASD) of the residual phase noise of a single run ($j=6$). The total observation time was $T=90000\mathrm{s}$. With increasing integration times $\tau$ the uncertainty in phase decreases as $\propto {\tau }^{-(1/2)}$ indicating the presence of white phase noise.