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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 [Phys. Rev. A 100, 022514 (2019),https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022514] a King Plotanalysis shows the data to be consistent with linearity below the level ofparts per billion. This observed linearity, which is free of nuclearsystematics, improves the previous isotope-shift based limits of Ca$^+$ forcouplings of a scalar boson beyond the Standard Model to electrons and neutronsby a factor of 3. Our new limit excludes part of the coupling range remainingfor a new physics interpretation after accounting for one higher-order nuclearterm in the nonlinear King plot of Yb/Yb$^+$.

Systematic-free limit on new light scalar bosons via isotope shift spectroscopy in Ca$^+$