Unraveling the non-Hermitian skin effect in dissipative systems

Abstract

The non-Hermitian skin effect, i.e., eigenstate condensation at the edges in lattices with open boundaries, is an exotic manifestation of non-Hermitian systems. In Bloch theory, an effective non-Hermitian Hamiltonian is generally used to describe dissipation, which, however, is not norm preserving and neglects quantum jumps.Here it is shown that in a self-consistent description of the dissipative dynamics in a one-band lattice, based on the stochastic Schrödinger equation or Lindblad master equation with a collective jump operator, the skin effect and its dynamical features are washed out. Nevertheless, both short-and long-time relaxation dynamics provide a hidden signature of the skin effect found in the semiclassical limit. In particular, relaxation toward a maximally mixed state with the largest von Neumann entropy in a lattice with open boundaries is a manifestation of the semiclassical skin effect.

Phase transitions in a non-Hermitian Aubry-André-Harper model

“…On the other hand, in an open quantum system we require, after any infinitesimal time step dt, normalization of the wave function, i.e., the state vector |ψ (t ) of the system evolves according to the two-step process |ψ (t + dt ) = exp(−iHdt )|ψ (t ) and |ψ (t + dt ) = |ψ (t + dt )/ ψ (t + dt ) . This two-time-step procedure physically corresponds to the dynamics of postselected quantum trajectories in open quantum systems under continuous measurements where quantum jumps are neglected [55,59,75,76].…”

“…Also, the dynamical phase transition is of first order in the velocity v, since v(V ) turns out to be discontinuous at the critical point. Such results provide important advances to understand the nontrivial interplay between disorder and non-Hermiticity, which is currently a hot area of research [29,[53][54][55][56][57][58][59][60][61]64,67,69,71,73,74]. The kind of non-Hermitian Hamiltonian with asymmetric hopping amplitudes considered in this work could be realized in synthetic matter using, for example, photonic systems [53,64,86,87], topoelectrical circuits [88], mechanical metamaterials [89], or in continuously measured ultracold atom systems with reservoir engineering [55,90].…”

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

“…the state vector |ψ(t) of the system evolves according to the two-step process |ψ(t + dt) = exp(−iHdt)|ψ(t) and |ψ(t + dt ) = |ψ(t + dt )/ ψ(t + dt ) . This two-time step procedure physically corresponds to the dynamics of postselected quantum trajectories in open quantum systems under continuous measurements, where quantum jumps are neglected [55,59,75,76].…”

Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms

“…Within this context, a particularly fascinating phenomenon is the recently discovered non-Hermitian skin effect (NHSE) [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Through what transpires as the nominal bulk eigenstates undergo exponential localization at the open boundaries, the NHSE fundamentally reshapes spectral, band, and dynamic properties of an open system, necessitating a non-Bloch band theory to account for the non-Hermitian topology [10][11][12], and leaving signatures in the dynamics either driven by a non-Hermitian effective Hamiltonian [19,25] or under the master equation [26,27]. While the recent observation of NHSE and its rich consequences have stimulated intense interest [28][29][30][31][32][33], its experimental implementation and characterization in a quantum many-body setting remain an unexplored territory.…”