Phonoritonic Crystals with a Synthetic Magnetic Field for an Acoustic Diode

We develop a rigorous theoretical framework to describe light-sound interaction in the laser-pumped periodic multiple-quantum-well structure accounting for hybrid phonon-polariton excitations, termed phonoritons. We show that phonoritons exhibit the pumping-induced synthetic magnetic field in the artificial “coordinate-energy” space that makes transmission of left- and right- going waves different. The sound transmission nonreciprocity allows one to use such phonoritonic crystals with realistic parameters as optically controlled nanoscale acoustic diodes.

Figure 1

(a) The regimes realized in laser-pumped MQWs, depending on the strength of the exciton-photon interaction and pumping-enhanced exciton-phonon interactions. $Q_m$ is the mechanical quality factor. (b) Sound propagation in MQWs pumped by the laser from the left involves conversion to anti-Stokes and Stokes light and is equivalent to quantum walks on an $N\times 3$ lattice in a synthetic magnetic field.

Figure 2

(a)–(c) Dependence of the phonon transmission coefficient on the phonon wave number and pump laser frequency for different numbers of QWs $N$ in the structure. A positive (negative) $k$ corresponds to left-to-right (right-to-left) transmission. (d),(e) The ratio of the left-to-right and right-to-left transmittances. (f),(g) Field distributions in the processes of left-to-right and right-to-left sound transmission, respectively, for the parameters indicated by the stars in panel (c). The dots are laser-generated excitons $|b_{L,j}|$, the black line is the acoustic deformation field $|a^{\prime }(z)|$, and the blue and red lines are the anti-Stokes and Stokes wave amplitudes $|c_{\text{aS}}(z)|$ and $|c_{\mathrm{S}}(z)|$. The vertical lines show the QW positions. The pump density is 0.1 mW per $1\mu {\mathrm{m}}^2$.

Figure 3

(a),(b) Dispersion of polaritons (black curves), emitted and absorbed phonons (red and blue lines), and phonoritons (avoided crossings at the intersections 1–6 of the polariton and phonon dispersions). Panels (c) and (d) illustrate the two types of avoided crossings, marked by the blue and red color in panels (a) and (b), yielding the attenuation and amplification of phonons, respectively. The areas 1–6 in panels (a) and (b) explain the corresponding patterns in the phonon transmission map of Fig. 2. The calculation is made for laser detunings $\mathrm{\Delta }=1\mathrm{meV}$ (a) and $\mathrm{\Delta }=-0.2\mathrm{meV}$ (b); the other parameters are the same as for Fig. 2 except for $\mathrm{\Gamma }=0$ and $\gamma =20\mu \mathrm{eV}$ at $\mathrm{\Omega }=1\mathrm{meV}$.