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We report a precise measurement of the isotope shifts in the $4^2$S$_{1/2}\rightarrow 3^2$D$_{3/2}$ electric quadrupole transition at 732~nm in $^{40 -42,44,48}$Ca$^+$ via high-resolution laser spectroscopy of co-trapped ions,finding measured shifts of 2,775,392,374.8(6.0), 5,347,679,835.1(5.9), and10,003,129,115.1(5.7) Hz between $^{42,44,48}$Ca$^+$and $^{40}$Ca$^+$,respectively. When combined with prior measurements on the $4^2$S$_{1/2}\rightarrow 3^2$D$_{5/2}$ transition [PhysRevA.100.022514 (2019)] a King Plotanalysis shows the data to be consistent with linearity at the level of$\sim$8~Hz, setting new isotope-shift-based limits on couplings betweenelectrons and neutrons due to beyond-Standard-Model bosons.

New limit on isotope-shift-based bounds for beyond Standard Model light Bosons via King's linearity in Ca$^+$