Dispersion and the transport of exciton-polaritons in an optical conveyor belt

TL;DR

The paper addresses how to engineer and control exciton-polariton transport via an optical conveyor belt implemented as a time-varying lattice potential. It combines Bloch-band analysis for static lattices with a Lagrangian variational treatment of dynamics under $V(t)=V_p\left(1-\cos\left[\omega t- G x\right]\right)$, using coupled cavity–exciton equations and a Gaussian variational ansatz to derive equations of motion. Key findings show that polaritons exhibit linear dispersion and linear transport with small oscillations, with transport direction and speed governed by the belt frequency $\omega$ and potential depth, while stability depends on $V_p$, $G$, $\Delta f$, and $g$, and boundary effects set finite lifetimes in open systems. This work highlights the optical conveyor belt as a versatile platform for high-speed, coherent polariton transport and band-structure engineering, with potential applications in photonic devices and quantum information processing.

Abstract

The growing interest in exciton-polaritons has driven the need to manipulate their motion and engineer their band structures to the forefront of contemporary research. This study explores the band structures that emerge from a spatially modulated potential, ingeniously realized through the use of an optical conveyor belt. By leveraging Bloch theory and conducting a meticulous analysis of the time evolution of polariton intensity in Fourier space, we have derived the energy dispersion relations both analytically and numerically within the context of a static lattice model. For time-dependent potentials, we employ the Lagrange variational method to elucidate the dynamics of polariton motion. Our results reveal that polaritons exhibit linear dispersion and follow linear trajectories with minor oscillations superimposed. This investigation not only deepens our fundamental understanding of exciton-polaritons but also provides a robust tool for advancing photonic devices and exerting precise control over current transport in quantum computing. Our findings pave the way for future innovations in high-speed and high-performance technologies.

Figures (7)

• Figure 1: (a) Sketch of the excitation scheme. The quantum well (QW) is embedded within a planar micro-cavity formed by two distributed Bragg reflectors (DBRs). Two laser beams are injected: one drives the condensate formation; the second imprints an optical lattice (belt). (b) The dashed red and blue lines represent the kinetic energy of the cavity photons and excitons, respectively, with the expression $E_{c,\text{X}}(k)=\hbar^2k^2/2m_{c,\text{X}}$. The light red and blue lines indicate the analytical dispersion obtained from Eq. (\ref{['LUbranch']}), while the colorful figures are derived from the numerical simulation of Eqs. (\ref{['Eqc']})-(\ref{['Eqex']}).
• Figure 2: The bandstructures for different lattice constants without interaction, determined through both analytical methods (white dashed lines) and numerical simulations (colorful figures), are presented in panels (a) and (d). The time evolution of the wavefunctions corresponding to the narrow potential is illustrated in panels (b) and (c), whereas the wavefunctions for the wide potential are displayed in panels (e) and (f). Parameters are: $V_p$= 10 (meV), $G$=2 ($\mu$m$^{-1}$) for (a)-(c) and $G$=1 ($\mu$m$^{-1}$) for (e)-(f)
• Figure 3: Intensity distribution (the first row) of polaritons in the energy-momentum space and the time evolution of the cavity mode (the second row) and the exciton mode (the third row). Parameters are: $V_p$= 10 (meV), $G$=0.2 ($\mu m^{-1}$), $g$=0, and $\Delta f$=-20, -10,10 and 20 (Ghz) for different columns.
• Figure 4: Time evolution of wavepackets for cavity modes ((a1)-(a4)) across different system sizes, along with the mean position of the wavepackets for various sizes (b). Parameters are: $V_p$= 10 (meV), $g$= 2$\times10^{-5}$ (meV/$\mu$m$^{-2}$), $G$=0.2 ($\mu$m$^{-1}$), $\Delta f$=20 (GHz), and the the system size $L=2x_{max}$= $16$, $40$, $80$, and $140$ ($\mu$m) for (a1)-(a4).
• Figure 5: The central position of the wavepackets at 20 ps with different potential depths and the lattice constant. Parameters are: $g$= 2$\times10^{-5}$ (meV/$\mu$m$^{-2}$), and $\Delta f$=20 (GHz) for different columns.