Abstract
The wake following a vessel in water is a signature interference effect of moving bodies, and, as described by Lord Kelvin, is contained within a constant universal angle. However, wakes may accompany different kinds of moving disturbances in other situations and even in lattice systems. Here, we investigate the effect of moving disturbances on a Fermi lattice gas of ultracold atoms and analyze the novel types of wake patterns that may occur. We show how at half-filling, the wake angles are dominated by the ratio of the hopping energy to the velocity of the disturbance and on the angle of motion relative to the lattice direction. Moreover, we study the difference between wakes left behind a moving particle detector versus that of a moving potential or a moving particle extractor. We show that these scenarios exhibit dramatically different behavior at half-filling, with the ``measurement wake'' following an idealized detector vanishing, though the motion of the detector does still leaves a trace through a ``fluctuation wake.'' Finally, we discuss the experimental requirements to observe our predictions in ultracold fermionic atoms in optical lattices.
Highlights
Many signature effects of classical hydrodynamics have counterparts in quantum systems and serve to provide intuition as well as a spectacular source for interesting new physical situations
Due to the absence of internal scale in hydrodynamics, it can be applied for physical scenarios of vastly different scales
Another interesting example of a hydrodynamics-inspired study is the investigation of wake waves produced as a response to a moving potential interacting with a twodimensional electron gas, recently described in Ref. [4]
Summary
Many signature effects of classical hydrodynamics have counterparts in quantum systems and serve to provide intuition as well as a spectacular source for interesting new physical situations. Due to the scale inherent in the lattice structure, our wakes depend explicitly on the time τ characterizing the effective speed of the moving tip, compared to the hopping energy thop of the fermions in a tight-binding lattice To describe these effects of dynamics in many-particle quantum systems we use the nonequilibrium framework derived in Ref. This approach allows the buildup of tractable nonequilibrium problems utilizing combinations of four elementary operations: detection, particle injection, particle extraction, and free evolution While some of these ideas have been applied to problems in one dimension (e.g., driven and dissipative X X spin chains [32] and steady states of a driven hopping model [30]), here we study an essential twodimensional (2D) problem: the emergence of wakes behind moving objects interacting with a Fermi sea. We suggest an experimental setup to directly observe the wake patterns
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