Magnetic field-induced modification of superfluid density and interplane spectral weight in YBa$_2$Cu$_3$O$_y$

We report on the interlayer infrared response of YBa$_2$Cu$_3$O$_y$ in an applied magnetic field. This study explores both the underdoped ($y$ = 6.67 and 6.75) and optimally doped ($y$ = 6.95) regions of the phase diagram, and includes data for fields applied both parallel to the $c$ axis and to the CuO$_2$ planes in this anisotropic superconductor. A sum rule analysis reveals that magnetic fields $H \parallel c$ eliminate the high-frequency contribution to the superfluid density, returning the system to a more BCS-like energy scale [1]. For fields $H \parallel$ CuO$_2$, however, the high-energy component scales with the superfluid density, and the anomalous scheme of condenstate formation is maintained, at least in underdoped $y$=6.67 and 6.75 samples. This behavior is discussed in relation to the change of electronic kinetic energy and the suppression of interplane phase coherence. [1] A. D. LaForge \emph{et al.}, Phys. Rev. Lett. \textbf{101}, 097008 (2008).