  We experimentally demonstrate storage and on-demand release of
phase-sensitive, photon-number superposition states of the form $\alpha
|0\rangle + \beta e^{i\theta} |1\rangle$ for an optical quantized oscillator
mode. For this purpose, we introduce a phase-probing mechanism to a storage
system composed of two concatenated optical cavities, which was previously
employed for storage of phase-insensitive single-photon states [Phys. Rev. X 3,
041028 (2013)]. This is the first demonstration of all-optically storing highly
nonclassical and phase-sensitive quantum states of light. The strong
nonclassicality of the states after storage becomes manifest as a negative
region in the corresponding Wigner function shifted away from the origin in
phase space. This negativity is otherwise, without the phase information of the
memory system, unobtainable. While our scheme includes the possibility of
optical storage, on-demand release and synchronization of arbitrary single-rail
qubit states, it is not limited to such states. In fact, our technique is
extendible to more general phase-sensitive states such as multiphoton
superposition or entangled states, and thus it represents a significant step
toward advanced optical quantum information processing, where highly
non-classical states are utilized as resources.
