Topical review on acousto-optical Floquet engineering of single-photon emitters

Abstract

The combination of solid state single-photon emitters and mechanical excitations on a common platform is a promising approach for the development of hybrid quantum technologies. In this topical review we discuss state-of-the-art platforms for emitter-based acousto-optics and their feasibility for acousto-optical Floquet engineering. To this aim we investigate theoretically the resonance fluorescence (RF) spectrum of an acoustically modulated single-photon emitter under arbitrarily strong optical driving. In the spectrum, the combination of Mollow triplet physics and phonon sidebands results in a complex structure of crossings, anti-crossings, and line suppressions. We apply Floquet theory to develop an analytical expression for the RF spectrum. Complemented with perturbative and non-perturbative techniques, this allows us to fully understand the underlying acousto-optical double dressing physics of the hybrid quantum system, explaining the observed spectral features. We use these insights to perform an experimental feasibility study of existing emitter-based acousto-optical platforms and come to the conclusion that surface and bulk acoustic waves interfaced with quantum dots as an established Mollow triplet platform represent particularly promising infrastructures for acousto-optical Floquet engineering.

Figures (6)

• Figure 1: Schematic of the considered hybridization interfaces. (a) The light-emitter interface: A continuous wave laser (green) drives transitions in a two-level system generating light emission. (b) The acoustics-emitter interface modulates the transition energy of the two-level system which leads to the generation of phonon replica. (c) Combined acousto-optical driving of a quantum emitter.
• Figure 2: Numerical simulations of RF spectra using Eq. \ref{['eq:I_RF_full']}. We consider sinusoidal acoustic modulation and resonant optical excitation of the TLS, i.e., the detuning given in Eq. \ref{['eq:detuning_sinus']}, implying $\Omega=\Omega_{\rm ac}$ in Eq. \ref{['eq:I_RF_full']}. (a) and (c): RF spectra as a function of the emission frequency shift $\omega$ and the Rabi frequency $\Omega_{\rm R}$ in units of the acoustic modulation frequency $\Omega_{\rm ac}$. We consider a fixed ratio between acoustic modulation amplitude $A_{\rm ac}$ and Rabi frequency $\Omega_{\rm R}$ for better visibility of the resonance structure in the spectrum, where in (a) we have $A_{\rm ac}/\Omega_{\rm R}=0.5$ and in (c) we have $A_{\rm ac}/\Omega_{\rm R}=1$. In addition (b) shows cuts in (a) and (c) at fixed values of the Rabi frequency $\Omega_{\rm R}$. Solid red lines correspond to solid horizontal cuts in (a), while dashed blue lines correspond to dashed horizontal cuts in (c), as indicated by the labels (i)-(iv), respectively. The finite line broadening is due to the spectrometer resolution $\Gamma/\Omega_{\rm ac}=10^{-2}$ and the dissipation rates $\gamma_{\rm xd}/\Omega_{\rm ac}=4\times10^{-2}$, $\gamma_{\rm pd}/\Omega_{\rm ac}=2\times10^{-2}$.
• Figure 3: Numerical simulations of RF spectra using Eq. \ref{['eq:I_RF_full']} for fixed emission frequency shift $\omega$ as a function of the Rabi frequency $\Omega_{\rm R}$. ZPL ($\omega=0$) in blue, first PSBs $(\omega=\pm\Omega_{\rm ac})$ in red. The acoustic modulation amplitude is fixed at $A_{\rm ac}/\Omega_{\rm ac}=\frac{1}{2}$ (solid lines) and $A_{\rm ac}/\Omega_{\rm ac}=1$ (dashed lines). The parameters $\Gamma$, $\gamma_{\rm xd}$ and $\gamma_{\rm pd}$ constituting the line broadening are kept as in Fig. \ref{['fig:2']}. The gray shaded areas denote the regions of possible high harmonic resonances with $\Omega_{\rm R}\approx n\Omega_{\rm ac}$ and $n=1,2,3,...$.
• Figure 4: Floquet spectrum. (a) Colored lines: Unperturbed eigenvalues of $\mathbb{H}_0$ i.e., $\epsilon_\alpha=\pm\Omega_{\rm R}/2+m\Omega_{\rm ac}$ belonging to the unperturbed states $\left.\ket{\pm,m}\right>$ as a function of the Rabi frequency $\Omega_{\rm R}$. The first BZ is given by the shaded gray region and coloring of the lines denotes the two possible parity values $\pm 1$ (blue/red). Crossing of unperturbed lines is marked by circles for two different cases: same parity (green circles), opposite parity (gray circles). Black lines: The Floquet eigenvalues $\epsilon_\alpha$ for finite acoustic modulation with $A_{\rm ac}=0.5\Omega_{\rm R}$ (solid black lines) and $A_{\rm ac}=\Omega_{\rm R}$ (dotted black lines). (b) Unperturbed level structure for high harmonic resonances $\Omega_{\rm R}=n\Omega_{\rm ac}$. Colors encode parity and degenerate states are connected by horizontal arrows with arrow colors corresponding to the circles in (a).
• Figure 5: Parameter study of different acoustic platforms coupled to single-photon emitters. The underlying parameters for the data points (dots) are given in Tabs. \ref{['tab:lifetimes']} and \ref{['tab:platforms']}, except for the quantum well (QW) exciton lifetime, which is here taken to be $T_1=0.5$ ns martinez1993temperature. Also for Ref. zhan2025dynamical (blue circle with white border), which is the first successful experimental demonstration of acousto-optical Floquet engineering of a solid state single photon emitter, we used the lifetime $T_1=1.19$ ns, given therein. The open symbols correspond to emitter platforms that cannot be described by TLSs, i.e., by the theory presented in this work. The green shaded area marks the parameter range that has the potential for acousto-optical Floquet engineering, i.e., $\Omega_{\rm ac}/\gamma_{\rm xd}\gtrsim 1$, $A_{\rm ac}/\gamma_{\rm xd}\gtrsim 1$. The detrimental effect of additional pure dephasing discussed in the context of Tab. \ref{['tab:dephasing']} is obtained by replacing the lifetimes with the dephasing times $T_1\rightarrow T_2$, i.e., by replacing $\gamma_{\rm xd}$ with $\gamma$ in the calculation of the parameter ratios, as denoted by the arrows attached to the data points.