Dynamical Superfluid and Bose-Insulator Phases in Quantized Polariton Lattices

Abstract

We demonstrate that Hilbert-space quantization in polariton lattices-manifested as multiple quantized energy levels in strongly confined sites-provides an unconventional route to realizing and manipulating different quantum phases. We show that nonlinear interactions transfer population into excited on-site quantum levels, which acts as an intrinsic dynamical channel controlling quantum coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuations suppress global phase coherence and drives the system into a dynamical Bose-insulating phase. The changes between these phases occurs either as a nonequilibrium phase transition or a sharp crossover.

Figures (4)

• Figure 1: A lattice with internal quantized energy levels due local potential minima. (a) A lattice with $L$ sites and $Q$ quantum levels per site. (b) A local potential minimum holding multiple quantized energy levels allowing mode mixing through the interaction coefficients $\tilde{U}^{ab}_{cd}(t)$ between the levels $a,b,c,$ and $d$.
• Figure 2: Dynamical superfluid to Bose-insulator transition. (a) Long-time condensate fraction $f_c^\infty$ as a function of the interaction strength $g/K$. The condensate fraction suddenly drops at around $g/K\sim 1$. (b) The condensate fraction $f_c(t)$ as a function of time $t$ for a single-mode (blue, $Q=1$) and multi-mode (red, $Q=4$) configurations per site in the strong interaction regime $g/K = 4.5$. (c) Log-log plot of the long time condensate fraction $f_c^\infty$ as a function of the size $L$.
• Figure 3: Phase fluctuations induced by quantized levels. (a) Time dependence of the relative phase ($\Delta\theta_i$; light blue) time averaged phase ($\langle\Delta\theta_i\rangle_t$; green), and the second moment ($\langle\Delta\theta_i^2\rangle_t$; red) in the strong interaction regime $g/K=3$ and $Q=4$. The solid black line is the theoretical prediction for the second moment from Eq. \ref{['eq:second_moment']}. (b) Time dependence of $\Delta\theta_i$ (light blue), $\langle\Delta\theta_i\rangle_t$ (green), and $\langle\Delta\theta_i^2\rangle_t$ (red) for weak interaction $g/K=0.5$ and $Q=4$. (c) For a single mode per site configuration $(Q=1)$, all $\Delta\theta_i$ (blue) remain zero for any interaction $g/K = 3$ or $0.5$.
• Figure 4: Continuous-model energy-resolved intensity.(a) The energy-resolved intensity exhibits a strong signal only at the lowest-energy state for weak nonlinearity ($P=0.3\, meV$). (b) The energy-resolved intensity shows significant contributions at multiple energy levels within each lattice site when the nonlinearity is large ($P=2.3\, meV$). We consider $\gamma = 0.2\, meV$, $g= (0.02 - i 0.01)\, meV/\mu m$, $V(x)= -V_0\sum_n \exp(-(x-nd_0)^2/\sigma^2)$, $V_0=25\, meV$, $d_0=5.76\,\mu m$, and $\sigma = 2\, \mu m$.