Supersolid and the Non-uniform Condensate

We construct a model of non-uniform condensate having a spatially modulated complex order parameter that makes it kinematically an x-ray solid, i.e., a real mass density wave, but one admitting an associated superfluid flow. Intrinsic to this state is a non-classical translational inertia which we derive for the case of a potential flow. Connection to the non-classical rotational inertia observed in recent experiments on solid helium-4 is discussed. Our semi-phenomenological treatment suggests a flow-induced supersolid-to-superfluid transition. Recent experiments of Kim and Chan [1,2] on solid helium-4 at very low temperatures have strikingly revealed a non-classical rotational inertia that seems intrinsic to it, much as it is in the case for superfluid He II. Such a supersolid was indeed predicted much earlier on theoretical grounds as a plausible concomitant of a quantum crystal with delocalized defects, or of a Bose-Einstein condensate [3-5], and had motivated years of research [6]. The non-classical inertial effect was, however, estimated to be very small, and direct tests were therefore suggested [5]. Thus, the question " can a solid be superfluid? " , raised some 35 years ago [5] has now been finally answered in the affirmative. In this work we explicitly construct a complex order-parameter that underlies a real mass density wave modeling the supersolid, and demonstrate analytically its necessarily non-classical inertia − the signature of a supersolid. We also predict a flow-induced supersolid-to-superfluid transition.