Non-Hermitian topology makes directional amplification robust against disorder
The authors show that due to its underlying non-trivial non-Hermitian topology directional amplification is robust against any kind of disorder as long as it is smaller than the size of the point gap of the system, i.e. the minimal separation between the spectrum under periodic boundary conditions and the origin.
One of the most exciting properties of systems featuring non-trivial (Hermitian) topology is robustness against disorder. In recent years, studies have been extended to systems that experience gain and loss, i.e. to systems described by a non-Hermitian, rather than a Hermitian, matrix. Indeed, the same authors have shown that a non-trivial (non-Hermitian) winding number corresponds to directional amplification (Nat Commun 11, 3149 (2020)) which is potentially a key resource for quantum information processing. It has however remained unclear if systems featuring non-trivial non-Hermitian topology enjoy the same level of robustness against disorder as their Hermitian counterparts.
Writing in Physical Review Letters, an international team answers this question in the affirmative. They show analytically that the transport properties associated with non-trivial non-Hermitian topology are robust against any kind of bounded disorder. This can be understood well graphically: Bounded disorder leads to eigenvalues within an annular region around the disorderless spectrum whose width is given by the disorder strength (green region). As soon as the annular region touches the origin, the disordered system may - with some probability - be topologically trivial and directional amplification is lost. We see directional amplification is robust as long as disorder does not close the point gap. Furthermore, it is also shown that non-reciprocity, i.e. suppression of the transmission in the reverse direction, which is a highly sought-after property, is robust against any local (even arbitrarily strong) disorder.
Clara C. Wanjura, Matteo Brunelli, and Andreas Nunnenkamp. Correspondence between non-Hermitian topology and directional amplification in the presence of disorder. Physical Review Letters 127, 213601 (2021).