Optically Driven Quantum Dots as Source of Coherent Cavity Phonons: A Proposal for a Phonon Laser Scheme

We present a microscopically based scheme for the generation of coherent cavity phonons (phonon laser) by an optically driven semiconductor quantum dot coupled to a THz acoustic nanocavity. External laser pump light on an anti-Stokes resonance creates an effective Lambda system within a two-level dot that leads to coherent phonon statistics. We use an inductive equation of motion method to estimate a realistic parameter range for an experimental realization of such phonon lasers. This scheme for the creation of nonequilibrium phonons is robust with respect to radiative and phononic damping and only requires optical Rabi frequencies of the order of the electron-phonon coupling strength.

Figure 1

Scheme of the QD interacting with an external laser field (Rabi frequency $\Omega$). The QD is assumed as a two-level system with a valence band state $|v⟩$ and a conduction band state $|c⟩$. The QD is coupled to a single THz acoustic phonon mode, which is indicated by the multilayered structures.

Figure 2

(a) Temporal evolution $\overline{n}$ (solid line) and $g_{\mathrm{ph}}^{(2)}(0)$ (dashed line). (b) Temporal evolution of $P_n$ for stationary excitation. Parameters: Rabi frequency $\Omega =1.5\mathrm{meV}$, QD-phonon coupling $|g|=0.3\mathrm{meV}$ [33, 34], QD level splitting ${\omega }_{\mathrm{cv}}=1.5\mathrm{eV}$, phonon lifetime ${\kappa }^{-1}\equiv 2\mathrm{ns}$ [35], QD relaxation rate ${\Gamma }_r^{-1}\equiv 200\mathrm{ps}$ [36], QD pure dephasing rate ${\Gamma }_{\mathrm{pd}}^{-1}\equiv 10\mathrm{ps}$ [36], and initial temperature $T=4\mathrm{K}$.

Figure 3

Snapshots of the phonon number probabilities $P_n$ (a) before the optical excitation and (b) in the stationary limit of 1.5 meV.

Figure 4

(a) Top: $\overline{n}$ (black solid curve) and $g_{\mathrm{ph}}^{(2)}(0)$ (dashed curve) over varying laser strength. Excitation dependence of the polarization $P^{(0|0)}$ (inset: dash-dotted curve). Bottom: evolution of $Q$ (gray solid curve) and the first threshold pump power $\Omega (Q_{\max })$ (inset: dotted curve) in area A (dark shaded area) over varying phonon damping $\kappa$. (b) $P_n$ over varying laser strength in the stationary regime.

Figure 5

$P_n$ at three different excitation strengths: $\Omega =$ (a) 0.006 meV, (b) 1.5 meV, and (c) 6 meV.