BEC critical exponent near quantum critical point in BaCuSi$_2$O$_6$

BaCuSi$_2$O$_6$ is a spin gap compound comprising coupled square bilayers of vertical dimers. The magnetic ordering transition in applied magnetic fields above the critical magnetic field (H$_{c1}$ = 23.5T) has been interpreted as a condensation of triplons. Proximity to the Quantum Critical point (QCP) can be tuned in this material by changing the particle density via the applied magnetic field (chemical potential.) We present a series of experiments that measure the critical exponent $\nu$ relating the proximity to the QCP, to the ordering temperature (T$_c$) by the power law $T_{c} \alpha (H-H_{c1})^\nu$. Experimental estimates of $\nu$ in this system agree with the theoretical mean field prediction of 2/3 for Bose Condensation of a dilute Bose gas.