Higher-harmonic acoustic driving of quantum-dot optical transitions beyond Rabi-frequency resonance

Abstract

Acoustic control and coupling of quantum systems via phonons can enable miniaturized quantum technology devices for on-chip integration. Optically active quantum dots (QDs) are essential for such platforms, yet they have long lacked direct acoustic transitions between charge states. The recently proposed hybrid acousto-optical swing-up scheme introduces such high-fidelity transitions but has been proposed for sub-THz phonon frequencies, limiting practical implementations. Here, we overcome this limitation by exploiting higher-harmonic-assisted processes arising from strain-induced modulation of the optical transition energy. This parametric modulation of the optically dressed splitting produces multi-phonon-like resonances when a harmonic of the mechanical modulation matches the generalized Rabi frequency. We predict faithful state preparation with an acoustic frequency that is only a fraction of this splitting, specifically 42 GHz for a 0.341 THz splitting, thereby bridging control at accessible acoustic frequencies with the THz energy scales. In doing so, we establish control principles that separate optical energy delivery from coherent acoustic control. We complement numerical simulations with an effective model and a geometric interpretation. Evaluation of phonon-induced decoherence within a non-Markovian framework indicates high state-preparation fidelities, comparable to one-phonon and all-optical schemes. Potential applications extend beyond QD charge state preparation. Since the same interaction structure arises for a quantized acoustic field, our results provide a foundation for multi-phonon processes in QDs coupled to phononic resonators, including QD-phonon entanglement, state transfer, and the optical preparation of nonclassical multi-phonon states in quantized acoustic modes, all essential for future on-chip quantum technologies.

Figures (5)

• Figure 1: (a) Schematic energy structure of the three-level system with external fields. Laser (red arrows) couples charge states $\lvert\mathrm{g}\rangle$ and $\lvert\mathrm{x}\rangle$ corresponding to empty QD and exciton state with detuning $\Delta$, while it is detuned from the two-photon transition to the biexciton state $\lvert\mathrm{xx}\rangle$ by $\Delta_{\mathrm{xx}}$. Acoustic modulation of states $\lvert\mathrm{x}\rangle$ and $\lvert\mathrm{xx}\rangle$ is marked with the blue arrows. (b) States of the system dressed by light; exemplary case of strong $\lvert\mathrm{g}\rangle\leftrightarrow\lvert\mathrm{x}\rangle$ mixing into $\lvert+\rangle$ and $\lvert-\rangle$, while $\lvert\widetilde{\mathrm{xx}}\rangle$ is a weakly perturbed $\lvert\mathrm{xx}\rangle$ state. Acoustic field energy is marked with green arrows, and its multiple $n\omega_{\mathrm{ac}}$ corresponds to the $\lvert+\rangle$--$\lvert-\rangle$ splitting.
• Figure 2: Final occupation of the (a) exciton state, (b) biexciton state as a function of acoustic field amplitude and inverse of its frequency.
• Figure 3: (a)-(c) Evolution of exciton occupation for $\pi$-rotations from Fig. \ref{['fig:fractionalMapOccupation']} for (a) one- ($\hbar\omega_{\mathrm{ac}}\approx0.141$ meV, $\hbar A_{\mathrm{ac}}\approx0.0213$ meV), (b) two- ($\hbar\omega_{\mathrm{ac}}\approx0.0733$ meV, $\hbar A_{\mathrm{ac}}\approx0.0696$ meV), and (c) three-phonon processes ($\hbar\omega_{\mathrm{ac}}\approx0.0536$ meV, $\hbar A_{\mathrm{ac}}\approx0.125$ meV). Insets show the state evolution on the $\lvert\text{g}\rangle$-$\lvert\text{x}\rangle$ Bloch sphere. (d)-(f) Nonlinear spectral function $S(\omega)$ for evolution from panels (a)-(c). Filled curves show phonon spectral density $R(\omega)$ calculated for typical GaAs/AlGaAs QDs at $T=4$ K; vertical dashed lines show $\omega_{\mathrm{ac}}$.
• Figure 4: Error of the (a) exciton and (b) biexciton preparation as a function of the corresponding detuning for one- (solid lines), two- (dashed), and three-phonon (dotted) processes for GaAs QDs. The inset in (a) shows minimal differences between curves. In (b), we omit a narrow range of detunings around $0.65$ meV, where we encounter an unwanted resonance leading to exciton occupation.
• Figure 5: Evolution of exciton occupation in the sub-THz detuning regime. Using 10-phonon processes, QD is excited with an acoustic wave with feasible frequency $\omega_{\mathrm{ac}}/2\pi\approx42$ GHz and $\hbar A_{\mathrm{ac}}\approx2.49$ meV on top of a far-detuned cw laser with $\hbar\Delta = 1$ meV, and $A_{\mathrm{L}} = 1$ meV.