Borromean Supercounterfluidity.

We demonstrate microscopically the existence of a new superfluid state of matter in a three-component Bose mixture trapped in an optical lattice. The superfluid transport involving coflow of all three components is arrested in that state, while counterflows between any pair of components are dissipationless. The presence of three components allows for three different types of counterflows with only two independent superfluid degrees of freedom.

Dissipationless Vector Drag-Superfluid Spin Hall Effect.

Dissipationless flows in single-component superfluids have a significant degree of universality. In ^{4}He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear.

Comment on "Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates".

In a recent Letter [Phys. Rev. Lett.

Time Crystal Behavior of Excited Eigenstates.

In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Wilczek, spontaneous breaking of time translation symmetry cannot be observed if one starts with the ground state.