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arXiv:1011.2001 · Physics Letters A

Controlling phonon squeezing and correlation via one- and two-phonon interference

O. V. Misochko, Jianbo Hu, Kazutaka G. Nakamura

Published Oct 4, 2011• 21 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2011.09.054

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Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron—phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization ( i ) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter i is larger than the ordinary parameter α i (0) . In comparison with the electron-one-phonon interaction ( g ) corrected as i g , we have found the electron-two-phonon interaction ( g 1 ) corrected as i 2 g 1 is enhanced significantly. For this reason, the ground state energy ( E 0 (2) ) contributed by the electron-two-phonon interaction is more negative than the single-phonon case ( E 0 (1) ) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation ( f -correlation). Since this correlation parameter f > 1, this effect will strengthen the electron-one and two-phonon interactions by f i g and f 2 i 2 g 1 , respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.
Abstract We study the cross-correlation between two bosonic modes of a two-mode displaced squeezed thermal state. By calculating the equal-time second-order cross-correlation function, we find that strong anticorrelation between the two bosonic modes can be observed. The mechanism of anticorrelation between the two bosonic modes is the interference between two coherent displacements and a squeeze operation. The optimal values of the two displacements and the squeezing parameter for achieving the minimum value of g ab ( 2 ) ( 0 ) is derived. As an example, we explore the anticorrelation between phonons in a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. The two-mode displaced squeezed thermal state of the two mechanical oscillators can be achieved if the squeezing amplitude and the mean phonon occupation number of the two mechanical environments are not very large. Furthermore, we find that the two-time second-order correlation function has multiple minima if the frequency difference of the two mechanical oscillators is large. Our results provide us with a tool to generate anticorrelated photons and phonons which may have potential applications in quantum information networks.
We theoretically study a multimode nonequilibrium optomechanical system coupled to squeezed-vacuum and thermal reservoirs, focusing on the interplay between quantum coherence, dissipation, and heat transport. Using covariance-matrix methods, we analyze bipartite entanglement, EPR steering, and energy currents in the steady state. We show that weak optomechanical coupling preserves squeezing-induced entanglement, whereas strong coupling enhances phonon-mediated decoherence and suppresses quantum correlations. The system exhibits one-way quantum steering, indicating directional quantum information transfer. We further demonstrate that reservoir squeezing acts as a nonclassical energy source that sustains nonequilibrium heat flow, while substrate-mediated phonon correlations generate geometry-dependent thermal rectification controlled by the separation between mechanical resonators. Interference between transport pathways can strongly suppress heat currents, analogous to dark-state effects in quantum optics. These findings provide a unified framework linking squeezing, entanglement, steering, and heat transport, with potential applications in quantum thermal devices, phononic routing, and heat-resilient quantum technologies.