Proposal for a Phonon Laser Utilizing Quantum-Dot Spin States

We propose a nanoscale realization of a phonon laser utilizing phonon-assisted spin flips in quantum dots to amplify sound. Owing to a long spin relaxation time, the device can be operated in a strong pumping regime, in which the population inversion is close to its maximal value allowed under Fermi statistics. In this regime, the threshold for stimulated emission is unaffected by spontaneous spin flips. Considering a nanowire with quantum dots defined along its length, we show that a further improvement arises from confining the phonons to one dimension, and thus reducing the number of phonon modes available for spontaneous emission. Our work calls for the development of nanowire-based, high-finesse phonon resonators.

Figure 1

(a) Phonon emitter: A QD in the sequential-tunneling regime with ferromagnetic leads of opposite polarizations. (b) The threshold value of the phonon lifetime ${\tau }_Q$ as a function of the tunnel rate $W^L$, showing the crossover between the weak ($W^L\ll 1/T_1$) and the strong ($W^L\gg 1/T_1$) pumping regimes. For ${\tau }_Q<{\gamma }_D^{-1}$ (below dashed line), no lasing is possible regardless of the pumping regime.

Figure 2

Phonon population $N_Q$ as a function of $W^L$, obtained from Eq. (9) for a single dot (solid line). The squares represent $N_Q$ obtained from a quantum treatment (see Supplemental Material [38]). The parameters used are $W^L{T}_1=100$, $\gamma T_1=0.8$, ${\tau }_Q/T_1=10$. Inset: shaded area shown in a larger scale.

Figure 3

(a) Phonon nanolaser: QDs defined along a nanowire and contacted by ferromagnetic fingers. Phonons are emitted along the nanowire and are reflected at its ends. (b) Coupling constant $|M_{\Downarrow \Uparrow }{|}^2$ versus the Zeeman splitting ${\Delta }_Z$; maximal coupling is achieved at ${\Delta }_Z\simeq \hslash s/a$.