Collective enhancements in many-emitter phonon lasing

Abstract

We investigate theoretically the many-emitter phonon laser based on optically driven semiconductor quantum dots within an acoustic nanocavity. We map the phonon laser Hamiltonian to a Tavis-Cummings type interaction with an unexpected additional many-emitter energy shift. This many-emitter interaction with the cavity mode results in a variety of resonances dependent on the number of participating emitters. We show that the many-emitter phonon laser also includes the single emitter resonance besides these collective phenomena. However, we obtain a high quantum yield addressing these collective resonances. We clearly demonstrate the best setup for maximal enhancement and show that the output can be increased even more via lasing at the two phonon resonance.The optical laser is indispensable for fundamental physics and many applications and is well understood by now 1,2 . Adapting the concept of coherent amplification by stimulated emission to sound waves, the phonon laser is a promising candidate for a new type of non demolishing measurement 3 . In the past few years there have been different theoretical and experimental proposals for phonon lasing such as trapped ions 4,5 , compound microcavities 6 , NV-centers 7 , electromagnetic resonators 8 and semiconductor devices 9-14 . For most applications, especially for the latter, the embedding of the active medium within an acoustic cavity forms the basis for stimulated phonon emission. The design and technological control of such cavities have been progressing in the past years [15][16][17][18][19][20] . In a semiconductor device, two superlattices confine one single phonon mode within a spacer in between [15][16][17] . A careful design allows long phonon lifetimes due to a high quality factor up to Q = 10 5 of the acoustic nanocavity [18][19][20] . Based on such a phonon cavity, we investigate theoretically phonon lasing in a semiconductor nanodevice with quantum dots 21 as active medium and external coherent optical excitation 22 for coherent phonon generation via the induced raman process 12,13 . We want to extend the single emitter case 12 to many emitters 23,24 and focus on collective effects of the phonon lasing regime.In analogy to the Tavis-cummings model 25,26 we focus on identical emitters coupled via the cavity phonon field. First discovered by Dicke 27 , superradiance is one example for collective effects with applications to optical lasers 28-30 and has been investigated recently for phonons in general 31,32 . The coherent pump of identical emitters supports the buildup of collective quantum coherences 31,33,34 . We clarify that collective phenomena also appear in the phonon lasing regime and show an enhancement of the coherent cavity phonon field addressing collective processes. Even if there are similarities to the optical laser, the phonon laser differs fundamentally in the interaction as the electron-phonon coupling is diagonal. This results in a Tavis-Cummings type interaction with an additional new type of interaction between the emitters via the c...

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