Nonadiabatic switching of a photonic band structure: Ultrastrong light-matter coupling and slow-down of light

We map out the band structure of a one-dimensional photonic crystal while a 12-fs control pulse activates ultrastrong interaction with quantized electronic transitions in semiconductor quantum wells. Phase-locked multi-terahertz transients trace the buildup of a large vacuum Rabi splitting and an unexpected asymmetric formation of the upper and lower polariton bands. The pronounced flattening of the photonic bands causes a slow-down of the group velocity by one order of magnitude on the time scale of the oscillation period of light.

Figure 1

(a) Sample design: heterostructure consisting of 50 repetitions of 8.3-nm-thick GaAs QWs separated by 30-nm-thick Al${}_{0.33}$Ga${}_{0.67}$As barriers grown on top of a 2-$\mu$m-thick Al${}_{0.95}$Ga${}_{0.05}$As cladding layer and an undoped GaAs substrate. The planar waveguide defined by the refractive index contrast ($n_{\mathrm{air}}=1$, $n_{\mathrm{MQW}}=3.2$, $n_{\mathrm{cladd}}=2.8$) is structured as a PC via a lateral gold grating. (b) Transmission of multi-terahertz pulses maps out the band structure of the system. A co-propagating NIR pump pulse injects electrons in the MQWs (delay time: $\tau$), activating ultrastrong light-matter coupling. (c) Electro-optically sampled multi-terahertz field transient and (d) corresponding amplitude spectrum. (e) Measured (dots) and calculated (line) field transmission of the equilibrium PC structure ($a=4.1\mu \mathrm{m}$) at $\theta ={20}^{\circ }$.

Figure 2

Transmission spectra of the PC structure ($a=4.1\mu \mathrm{m}$) as a function of $k_{\left|\right|}$. Experimental results in (a) equilibrium and (b) $1000\mathrm{ps}$ after photo-activation of the ISB transition ($\Phi =1.6\mathrm{mJ}/{\mathrm{cm}}^2$) for $0⩽\theta ⩽{40}^{\circ }$. Black spheres: experimental position of local transmission peaks indicate the eigenmodes. Dashed black lines: numerically adapted polariton dispersion. (c) and (d) FDFD simulations of the unpumped and pumped sample, respectively, for $0⩽\theta ⩽89.9^{\circ }$. Black dotted curves indicate the eigenmodes in all panels. Dashed grey lines in (a) and (c): cross sections displayed in Fig. 1e. White tetragons in (c) and (d): area covered by the experiments in (a) and (b).

Figure 3

Transmission spectra of the PC structure ($a=3.6\mu \mathrm{m}$, no substrate) showing the polariton formation at the anticrossing point ($\theta ={13}^{\circ }$). To ensure that additional membrane guided modes are far above our measurement window, we now couple the ISB transition to the lower photon band by setting $a$ to $3.6\mu \mathrm{m}$. (a) Spectra measured at $\tau =1000\mathrm{ps}$ for various pump fluences $\Phi$ (stated in $\mu \mathrm{J}/{\mathrm{cm}}^2$). Inset: $2{\Omega }_R/2\pi$ as a function of ${\Phi }^{1/2}$. (b) Transmission for selected $\tau$ with $\Phi$ $=$ $1600\mu \mathrm{J}/{\mathrm{cm}}^2$. A maximum splitting of $3.4\mathrm{THz}$ is reached at $\tau =340\mathrm{fs}$. All spectra are separated by a linearly increasing offset.

Figure 4

$n_{\mathrm{eff}}$ at the spectral peak position of the upper photonic modes in the pumped and unpumped sample, as represented by the black curves in Figs. 2a and 2b. The solid curve is the theoretical $n_{\mathrm{eff}}=3.15$ of the light mode propagating inside the unpumped QW region.