Observation of Anderson localization beyond the spectrum of the disorder

Abstract

Anderson localization predicts that transport in one-dimensional uncorrelated disordered systems comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wave packets whose spectral extent resides within the region of the wave number span of the disorder. Here, we show experimentally that Anderson localization can occur and even be dominant for wave packets residing entirely outside the spectral extent of the disorder. We study the evolution of wave packets in synthetic photonic lattices containing bandwidth-limited (correlated) disorder and observe strong localization for wave packets centered at twice the mean wave number of the disorder spectral extent and at low wave numbers, both far beyond the spectrum of the disorder. Our results shed light on fundamental aspects of disordered systems and offer avenues for using spectrally shaped disorder for controlling transport.

A Perspective on Synthetic Dimensions in Photonics

“…These advantages are complemented by outstanding flexibility: Active amplitude-and phase modulation serve to imprint real as well as imaginary on-site terms in the corresponding Hamiltonian, which can be dynamically adjusted for each site in synthetic space and time. By virtue of these remarkable capabilities, photonic time-division multiplexing schemes have been used to emulate a wide range of phenomena in synthetic (1+1)D lattices, including Anderson localization, [51,52] geometrical pumping, [49] and topological phases [53,54] or nonlinear effects [55,56] and neural networks [57] as well as non-Hermitian phenomena such as ones related to Parity-Time (PT) symmetry, [48] stochastic dissipation, [58] constant intensity waves, [59] and non-Hermitian topology. [50,60] Moreover, the feasibility of two synthetic spatial dimensions has been demonstrated for single photons [61,62] and classical light, [63][64][65] paving the way toward even higher dimensions.…”

Observation of Generalized Dynamic Localizations in Arbitrary‐Wave Driven Synthetic Temporal Lattices

“…To start, we consider the synthetic temporal lattice constructed by mapping from two coupled fiber loops with slightly different lengths. [26][27][28][29][30][31][32][33][34][35][36][37][38] As shown in Figure 1a, the fiber-loop circuit is fed with an optical pulse from the longer loop generated from a laser diode. Upon entering the circuit and passing through the central coupler, the injected pulse will be split into two parts and enter two different loops.…”

“…To circumvent the drawbacks of high loss and poor tunability of spatial waveguide lattices, one may construct an artificial lattice using synthetic dimensions for realizing generalized DLs. Synthetic lattices, formed by coupling a set of discrete photonic modes with equally spaced frequency, [17][18][19][20][21][22][23][24][25] time, [26][27][28][29][30][31][32][33][34][35][36][37][38] and orbital angular momentum, [39][40][41][42] have attracted intensive recent attention in emulating many fundamental lattice dynamics for photons. Benefiting from the convenient controllability and reconfigurability of lattice parameters, a lot of physical concepts that are difficult to realize in spatial lattices have been demonstrated in synthetic lattices, such as parity-time symmetry, [27][28][29] topological windings, [24] and non-Hermitian skin effect.…”

Simulating topological materials with photonic synthetic dimensions in cavities

“…By engineering the skin effect and edges along the temporal lattice, one can synthesize a topological light funnel [67]. In addition, this system can also be used to study physics in disorder [68], and time crystals [69].…”