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We propose a method for measuring parity violation in neutral atoms. It is anadaptation of a seminal work by Fortson [Phys. Rev. Lett. {\bf 70}, 2383(1993)], proposing a scheme for a single trapped ion. In our version, a largesample of neutral atoms should be localised in an optical lattice overlapping agrid of detection sites, all tailored as the single site in Fortson's work. Themethodology is of general applicability, but as an example we estimate theachievable signal in an experiment probing a nuclear spin independent parityviolation on the line$6\mathrm{s}\,^2\mathrm{S}_{1/2}$--$5\mathrm{d}\,^2\mathrm{D}_{3/2}$ in$^{133}$Cs. The projected result is based on realistic parameters and\textit{ab initio} calculations of transition amplitudes, using therelativistic coupled-cluster method. The final result is a predictedspectroscopic signature, evidencing parity violation, of the order of 1 Hz, fora sample of $10^8$ atoms. We show that a total interrogation time of 30000 sshould suffice for achieving a precision of the order of 0.1\% --- surpassingprevious determinations of the weak charge in Cs by at least a factor of five.

An optical lattice based method for precise measurements of atomic parity violation