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We have performed transverse field muon spin rotation measurements of singlecrystals of Ba(Fe$_{0.93}$Co$_{0.07})_2$As$_2$ with the applied magnetic fieldalong the $\hat{c}$ direction. Fourier transforms of the measured spectrareveal an anisotropic lineshape characteristic of an Abrikosov vortex lattice.We have fit the $\mu$SRSR spectra to a microscopic model in terms of thepenetration depth $\lambda$ and the Ginzburg-Landau parameter $\kappa$.  We find that as a function of temperature, the penetration depth varies morerapidly than in standard weak coupled BCS theory. For this reason we first fitthe temperature dependence to a power law where the power varies from 1.6 to2.2 as the field changes from 200G to 1000G. Due to the surprisingly strongfield dependence of the power and the superfluid density we proceeded to fitthe temperature dependence to a two gap model, where the size of the two gapsis field independent. From this model, we obtained gaps of$2\Delta_1=3.7k_BT_c$ and $2\Delta_2=1.6k_BT_c$, corresponding to roughly 6 meVand 3 meV respectively.

Muon Spin Rotation Measurement of the Magnetic Field Penetration Depth in Ba(Fe0.93 Co0.07)2 As2 : Evidence for Multiple Superconducting Gaps