Observation of Floquet erratic non-Hermitian skin effect in photonic mesh lattice

Abstract

In ordered, translationally invariant non-Hermitian systems, the skin effect is understood as a boundary phenomenon: nonreciprocal hopping drives an extensive accumulation of eigenstates towards the edges, whereas the periodic-boundary spectrum remains Bloch extended. Here we experimentally reveal the opposite limit -- a disorder-enabled, boundary-independent, and intrinsically bulk form of skin localization -- the recently predicted erratic non-Hermitian skin effect (ENHSE), realized in a driven photonic platform. Using a time-multiplexed photonic mesh lattice with programmable gain, loss, and phase modulation, we engineer spatially fluctuating imaginary gauge fields and realize a Floquet non-Hermitian lattice whose global reciprocity can be tuned independently of strong local nonreciprocity. We observe a disorder-driven non-Hermitian topological transition between two oppositely directed disordered skin phases through a critical point of global reciprocity. At this transition, boundary skin accumulation disappears, yet the wave dynamics self-organizes into bulk-localized patterns without any interface, providing direct evidence of ENHSE. The measured localization profiles agree with simulations and exhibit the defining feature that distinct eigenstates share a common bulk-localized envelope determined by the disordered imaginary gauge fields. By further introducing controllable on-site disorder, we reveal the competition between ENHSE and Anderson localization, and show how increasing scattering progressively suppresses erratic skin dynamics. Our results help establish ENHSE as a unique disorder-induced non-Hermitian phenomenon and open a route to engineering localization, transport, and topology beyond conventional Bloch and boundary-based paradigms.

Figures (4)

• Figure 1: Erratic non-Hermitian skin effect as a non-Hermitian phase transition featuring bulk localization.a. Schematic of a one-dimensional Hatano-Nelson lattice (top) with nonreciprocal left- and right-hopping amplitudes $J_n^{L}\propto\exp(-h_n)$ and $J_n^{R}\propto\exp(h_n)$ that can be described by disordered imaginary gauge fields $\{h_n\}$. A Floquet realization (bottom), based on a time-multiplexed quantum walk in a photonic mesh lattice, encodes the disorder in the time-varying gain and loss (shaded gray arrows) in the conditioned translation (red and blue arrows) b. The normalized sum of disordered imaginary gauge fields $X_n=\frac{1}{N-1}\sum_{l=1}^{n-1}{h_l}$ ($X_1\equiv0$). c. Real-space winding number $W$ versus the average imaginary gauge fields $\bar{h}$. A non-Hermitian topological phase transition occurs around $\bar{h}=0$, where $W$ switches from 1 to -1 through $W=0$. d. Complex energy spectra under PBC (black) and OBC (colored) for three cases: $\bar{h}<0$, $\bar{h}=0$, and $\bar{h}>0$. e. Spatial distributions of localized OBC eigenstates for different $\bar{h}$ corresponding to d. For $\bar{h}<0$ and $\bar{h}>0$, the states are localized near opposite boundaries, corresponding to winding numbers $w=\pm1$. For $\bar{h}=0$, all the OBC eigenstates localize around the same position in the bulk.
• Figure 2: Experimental setup and disordered modulation waveforms.a. A photonic mesh lattice setup showing two fiber loops of different lengths coupled by a beam splitter. Both loops contain erbium-doped fiber amplifiers (EDFAs) to compensate for the insertion loss. The disordered imaginary gauge fields are introduced via the three amplitude modulators (AMs). The phase modulator (PM) allows for the control of real on-site potentials. b. Example transmittance modulation sequence of the three AMs. c. Example phase modulation of the PM. $\Delta t$ is half of the round-trip time difference of pulse propagation inside the two loops.
• Figure 3: Floquet dynamics of erratic non-Hermitian skin effect.a. Disordered non-Hermitian skin effect (DNHSE) under global nonreciprocity $\bar{h}<0$. b-d. Three examples of erratic non-Hermitian skin effect under global reciprocity $\bar{h}=0$, which exhibit a defining feature of bulk localization without the need for an interface. e. Disordered non-Hermitian skin effect under global nonreciprocity $\bar{h}>0$. Top: Summed modulus-squared eigenstate distribution; middle: simulated dynamics; bottom: measured dynamics.
• Figure 4: Floquet dynamics shaped by disordered imaginary gauge fields and disordered on-site potential.a. Ballistic spreading of wavefunction under weak on-site disorder with $\phi_{\mathrm{max}}=0.1\pi$. b. Evident ENHSE in the presence of the weak on-site disorder (a). c. Anderson localization under strong on-site disorder with $\phi_{\mathrm{max}}=\pi$. d. Suppressed ENHSE in the presence of the strong on-site disorder (c). The AM modulations in (b) and (d) are configured in the same way as those in \ref{['fig:3']}(b). Top: simulated dynamics; bottom: measured dynamics.