Momentum-space non-Hermitian skin effect in an exciton-polariton system

Localization of a macroscopic number of eigenstates on a real-space boundary, known as the non-Hermitian skin effect, is one of the striking topological features emerging from non-Hermiticity. Realizing this effect typically requires periodic (lattice) systems with asymmetry of intersite coupling, which is not readily available in many physical platforms. Instead, it is meticulously engineered, e.g., in photonics, which results in complex structures requiring precise fabrication steps. Here, we propose a simpler mechanism: introducing an asymmetric, purely imaginary potential in a topologically trivial system induces momentum-space localization akin to the skin effect. We experimentally demonstrate this localization using exciton polaritons, hybrid light-matter quasi-particles in a simple engineered `round box’ trap, pumped by a laser pump offset from the trap center. The effect disappears if the pump is concentric with the trap. The localization persists and becomes stronger at higher densities of polaritons, when a non-equilibrium Bose-Einstein condensate is formed and the system becomes nonlinear. Our approach offers a new route to realizing skin effects in continuous, non-periodic systems and exploring the interplay of non-Hermiticity, topology, and nonlinearity in macroscopic quantum states.

💡 Research Summary

This paper, titled “Momentum-space non-Hermitian skin effect in an exciton-polariton system,” introduces and experimentally demonstrates a novel mechanism for realizing the non-Hermitian skin effect (NHSE) in a continuous, non-periodic system, shifting the paradigm from real-space to momentum-space localization.

The NHSE, where a macroscopic number of eigenstates localize at a physical boundary, is a hallmark topological phenomenon in non-Hermitian physics. Traditionally, it requires carefully engineered periodic lattice systems with asymmetric coupling between sites, posing significant fabrication challenges. This work proposes a significantly simpler alternative: introducing an asymmetric, purely imaginary potential into a topologically trivial, continuous system can induce a skin-effect-like localization in momentum space.

The theoretical foundation rests on the concept of an imaginary vector potential. The authors consider a model, such as a quantum harmonic oscillator with a linear imaginary potential, V(x) = mω²(x² - iξx)/2. When reformulated in momentum space, the Hamiltonian takes a form where the imaginary term iξ/2 acts as an imaginary vector potential for momentum. This effectively introduces asymmetric nearest-neighbor coupling in a discretized momentum lattice, directly analogous to the Hatano-Nelson model—the quintessential model for the real-space NHSE. The eigenstates become skewed in momentum space, described by ψ_n(p) ∝ e^{-ξp/2ℏ} ψ_n^(0)(p). The topological nature of this effect is confirmed by the dramatic sensitivity of the system’s spectrum to boundary conditions: the unconfined spectrum (analogous to periodic boundary conditions) forms a closed loop with a non-zero topological winding number in the complex energy plane, while the confined spectrum (analogous to open boundary conditions) consists of real-valued discrete points.

The experimental demonstration utilizes an exciton-polariton system. Polaritons are hybrid light-matter quasiparticles in a semiconductor microcavity, featuring a very small effective mass, inherent non-Hermiticity due to their finite lifetime, and strong nonlinear interactions. A trapping potential for polaritons is created using a circular mesa structure. The key control parameter is an off-resonant laser pump, whose position relative to the trap center is precisely adjustable. This pump creates an exciton reservoir, which provides a complex-valued potential for polaritons: a repulsive real potential and a gain/loss imaginary potential. By offsetting the pump from the trap center, the researchers create the necessary spatial asymmetry in the imaginary part of the potential.

The experimental results clearly validate the theory. When the pump is concentric with the trap (symmetric imaginary potential), the polariton momentum distribution is symmetric. However, when the pump is offset, the photoluminescence emission—which maps the momentum distribution—shows a clear skew towards one direction in momentum space. This momentum-space localization is observed across multiple energy states within the trap. Crucially, the effect not only persists but becomes enhanced when the pump power is increased above the threshold for non-equilibrium Bose-Einstein condensation. In this regime, polariton interactions (nonlinearities) become significant, demonstrating the robustness and interplay of the momentum-space NHSE with many-body physics.

In conclusion, this work provides a new and accessible route to realizing skin effects without the need for intricate periodic structures. By generalizing the NHSE to momentum space in a continuous system and demonstrating its control via a simple pump geometry, it opens new avenues for exploring the rich interplay between non-Hermitian topology, wave dynamics in momentum space, and nonlinear phenomena in quantum systems.