This paper proposes a way to generalize the non-Hermitian skin effect into the genuine time dimension and to treat space and time on equal footing. The non-Hermitian skin effect (NHSE) is a phenomenon where many bulk states pile up at the edges of a system when some form of loss or gain and directional coupling are present. The authors show, in theory, how a single engineered “parent” skin effect can be made to appear either as a spatial piling up or as a time-domain counterpart, using a ring of ultracold atoms under periodic driving.

The idea uses Floquet engineering, which means shaping the system by periodic driving. Atoms trapped in a ring are made to rotate and are driven by time-periodic, state-dependent perturbations. By focusing on slow components of the motion and working in a frame where time acts like an extra space (the Floquet phase space), the authors build an effective lattice that mixes real space and time. In that lattice a carefully designed driving pattern creates a zigzag ladder of sites, built-in effective boundaries, and direction-dependent hopping between sites.

Two ingredients produce the nonreciprocity needed for the skin effect. First, a two-tone phase shaking gives rise to geometric phases (sometimes called Peierls phases) that are different for clockwise and counterclockwise motion on the ladder. Second, one internal atomic state is made lossy (dissipative). The combination of chiral geometric phases and state-selective loss makes hopping stronger in one direction than the other. Under the engineered boundary in the Floquet phase space, this drives a skin effect that can be seen as either a spatial accumulation or a time-domain funneling of probability.

The spatial projection is notable because it produces NHSE while the atoms are still on a ring with periodic boundary conditions. That means the skin location can be tuned arbitrarily by changing drive phases, without cutting the ring or making a physical edge. The temporal projection leads to time-domain nonreciprocity and a periodic temporal funneling that is consistent with causality. In short, the same engineered dynamics show up as a spatial NHSE or as a novel, causality-safe temporal NHSE when viewed in the appropriate frame.