Dynamically encircling an exceptional point for asymmetric mode switching

Abstract

Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise [1][2][3][4][5][6] . Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly 7,8 , like a state-flip or the accumulation of a geometric phase 9,10 . Experiments dedicated to this issue could already successfully explore the topological structure of exceptional points [11][12][13] , but a full dynamical encircling and the breakdown of adiabaticity inevitably associated with it 14-21 remained out of reach of any measurement so far. Here we

Floquet exceptional points and chirality in non-Hermitian Hamiltonians

“…selection of a different final state when the system is repeatedly and slowly cycled in opposite directions of parameter space. To conclude, it is worth commenting similarities and differences between the chiral behavior induced by a Floquet EP, studied in this work, and the chirality observed when a static EP is encircled, a well-known phenomenon which has been investigated in several recent works [18,27,40,41,42,44,47]. In both cases chirality arises because asymmetry in nonadiabatic effects observed when the circulation direction of the loop is reversed, a typical signature of non-Hermitian dynamics.…”

“…a different final state is selected when dynamically encircling an EP in clockwise or counter-clockwise directions. Recent experiments [18,27] demonstrated chirality of EP cycling, originally predicted in Refs. [41,42], and raised a great interest owing to potential applications of EPs to topological energy transport [27], asymmetric mode switching [18,33] and polarization control of light [40].…”

“…They have been predicted and observed in a wide variety of physical systems, including atomic and molecular systems [13,14,15], microwave cavities and waveguides [16,17,18], electronic circuits [19], optical structures [20,21], Bose-Einstein condensates [22,23], acoustic cavities [24], non-Hermitian Bose-Hubbard models [25], exciton-polariton billiards [26], opto-mechanical systems [27] and many others. Besides of their theoretical interest, EPs can find important applications, for example in the design and realization of unidirectionally invisible media [28,29,30,31,32], for asymmetric mode switching [18,33] and topological energy transport [27], for the design of novel laser devices [34,35,36,37,38], for optical sensing [39] and polarization mode conversion [40]. The dynamical properties associated to the encircling of an EP and the chirality of EPs arising from breakdown of the adiabatic theorem have received a great attention in recent years [16,17,18,27,40,41,42,43,44,45].…”

“…Besides of their theoretical interest, EPs can find important applications, for example in the design and realization of unidirectionally invisible media [28,29,30,31,32], for asymmetric mode switching [18,33] and topological energy transport [27], for the design of novel laser devices [34,35,36,37,38], for optical sensing [39] and polarization mode conversion [40]. The dynamical properties associated to the encircling of an EP and the chirality of EPs arising from breakdown of the adiabatic theorem have received a great attention in recent years [16,17,18,27,40,41,42,43,44,45]. A remarkable property observed when encircling an EP is a topological-robust state-flip for quasi-static cycling [15,17,46], and the chiral behavior associated to breakdown of adiabaticity for dynamical circling [18,27,40,41,42,44].…”

“…The dynamical properties associated to the encircling of an EP and the chirality of EPs arising from breakdown of the adiabatic theorem have received a great attention in recent years [16,17,18,27,40,41,42,43,44,45]. A remarkable property observed when encircling an EP is a topological-robust state-flip for quasi-static cycling [15,17,46], and the chiral behavior associated to breakdown of adiabaticity for dynamical circling [18,27,40,41,42,44]. In the former case state flip arises from to the branch point character of the degeneracy that causes a gradual transition between the intersecting complex Riemann sheets.…”