Phonon Propagator

Phillip F. Schewe

M. Gustafsson, Thomas Aref, Anton Frisk Kockum +3 more

Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics, with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics to be explored that cannot be reached in photonic systems.

Han Yong Choi, Tae-Ho Park, Gun Sang Jeon

We study the symmetric Anderson–Holstein (AH) model at zero temperature with Wilson's numerical renormalization group (NRG) technique to study the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented and applied to the AH model as the onsite Coulomb repulsion U and electron-phonon coupling constant g are varied. As g is increased, the phonon propagator is successively renormalized, and for g≳gco crosses over to the regime where the mode splits into two components, one of which approaches back to the bare frequency and the other develops into a soft mode. The initial renormalization of the phonon mode, as g is increased from 0, can be either positive or negative depending on U and the hybridization Δ.

Egor R. Verevkin, Ilya V. Doronin, Alexander A. Zyablovsky +1 more

We consider Brillouin scattering on short-lived phonon modes, such that the relative Brillouin shift between propagating and scattered waves is smaller than the relative width of phonon modes. In this case one phonon mode facilitates scattering between many pairs of optical modes. We show that in this limit two phonon modes are sufficient for cascade Brillouin scattering (one forward propagating wave and one counter propagating wave), and that the cascade behavior is qualitatively different from the cascade in conventional Brillouin systems with distinct phonon modes for each optical mode pair. In particular, our results show that there is a pump threshold above which many optical modes become excited simultaneously, as opposed to a cascade gradually building up. The resulting cascade scattering can be exploited for frequency comb generation with uniform amplitudes and without the need for anomalous dispersion in the medium.

K.J. Vahala, M. G. Herrmann, S. Knünz +4 more