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

Abstract

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.

Figures (4)

• Figure 1: Continuous non-Hermitian skin effect (NHSE).a, Localized real-space eigenstates of a one-dimensional quantum harmonic oscillator with the $x$-component of the imaginary vector potential $(\nabla A)_x = A_0$. Black solid curve is the real-space potential V(x). b, Localized momentum-space eigenstates arising from a harmonic potential with a linear imaginary potential $V(x) = m\omega^2 (x^2 - i\xi x)/2$. c, Same as b but for a particle in a box-like potential with an offset imaginary Gaussian potential defined in Eq.(\ref{['anharmonic']}) and plotted in e. Black solid lines in b,c represent the kinetic energy part of the Hamiltonian, $p^2/(2m)$. d, Spectrum of eigenvalues corresponding to a and b for open (dotted) and periodic (solid) boundary conditions. e, Potential and f, spectrum of eigenvalues corresponding to the model displaying momentum-space skin effect in c. Solid curve and dots in f correspond to the effective periodic and open boundary conditions, respectively. The imaginary part in e is magnified 10 times.
• Figure 2: Experimental momentum-space localization of polaritons in a trap with a controllable imaginary potential.a, Sketch of the optical microcavity formed by distributed Bragg reflectors with embedded exciton-hosting quantum wells (QWs) and a microstructured mesa defining the trapping potential for polaritons. The angle of cavity photoluminescence emission, which determines the measured momentum ($p \propto \sin(\theta)$, see text). b, Schematics of the microstructured potential and the optically induced reservoir that controls the imaginary potential. c--e, Momentum (top) and position (bottom) resolved spectra of polaritons for three positions (see inset) of the pump laser. f, Momentum and g, position space profiles of four selected energy states ($E_1 = 1.5800$ eV, $E_2 = 1.5808$ eV, $E_3 = 1.5816$ eV, $E_4 = 1.5824$ eV) marked with the arrows in c--e (green/blue/purple for positive/zero/negative pump asymmetry in real space).
• Figure 3: Condensation of momentum-space localized polaritons.a,c, Schematics of pump configuration and corresponding b,d, real-space distribution of the condensed mode. e,h, Angle-resolved PL below to above threshold for the two pump configurations. i,j, Normalized (with respect to maximum) momentum-space profile of the mode as a function of pump power. k, Center-of-mass momentum (or emission angle) of the condensing mode as a function of pump power.
• Figure 4: Ground-state condensation of momentum-space localized polaritons in a tight trap.a,b, Two pumping configurations. c,d, Ground-state angle-resolved distribution and e, experimental momentum-space COM as a function of pump power. f, Simulated COM as a function of pump power. g,h, Experimental g and simulated h condensate energy as a function of pump power.