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arXiv:1805.10155 · Physical Review A

Bistability of a slow mechanical oscillator coupled to a laser-driven two-level system

F. Pistolesi

Published Jun 15, 2018• 9 citations
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Abstract

It has been recently proposed that single molecule spectroscopy could be employed to detect the motion of nanomechanical resonators. Estimates of the coupling constant ($g$) between the molecular two-level system and the oscillator indicate that it can reach values much larger than the mechanical resonating pulsation (${\ensuremath{\omega}}_{m}$) and the two-level system linewidth ($\mathrm{\ensuremath{\Gamma}}$). Other experimental realizations of the same system are also approaching this strong-coupling regime. In this paper we investigate the behavior of the system in the limit for slow mechanical oscillator ${\ensuremath{\omega}}_{m}\ensuremath{\ll}\mathrm{\ensuremath{\Gamma}}$. We find that, for sufficiently large coupling, the system undergoes a bistability reminiscent of that observed in optical cavities coupled to mechanical resonators.

DOI
10.1103/physreva.97.063833

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It has been recently proposed that single molecule spectroscopy could be employed to detect the motion of nanomechanical resonators. Estimates of the coupling constant (ggg) between the molecular two-level system and the oscillator indicate that it can reach values much larger than the mechanical resonating pulsation (\ensuremathωm{\ensuremath{\omega}}_{m}\ensuremathωm​) and the two-level system linewidth (\ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ). Other experimental realizations of the same system are also approaching this strong-coupling regime. In this paper we investigate the behavior of the system in the limit for slow mechanical oscillator \ensuremathωm\ensuremath≪\ensuremathΓ{\ensuremath{\omega}}_{m}\ensuremath{\ll}\mathrm{\ensuremath{\Gamma}}\ensuremathωm​\ensuremath≪\ensuremathΓ. We find that, for sufficiently large coupling, the system undergoes a bistability reminiscent of that observed in optical cavities coupled to mechanical resonators.
Among the various nanoscale systems operating in the quantum limit, nanomechanical oscillators have emerged as particularly powerful platforms. They constitute highly sensitive sensors and can mediate interactions between light and localized quantum systems, playing a central role in various quantum information processing architectures. Due to their relatively large mass, they also serve as ideal platforms for investigating the transition between classical and quantum behavior. This thesis examines the dynamics of a nanomechanical oscillator coupled to a driven two-level system. The analysis focuses on the resolved sideband limit, where the twolevel system’s damping rate Γ is much smaller than the mechanical frequency ωm, and explores both the strong coupling (ωm ≫ g0 ≫ Γ) and ultra-strong coupling (g0 ∼ ωm ≫ Γ) regimes, where g0 denotes the coupling strength. These regimes enable coherent manipulation of the mechanical state while preserving its quantum coherence. Under blue-detuned driving of the two-level system and assuming low mechanical damping, the system exhibits a dynamical instability marked by the emergence of limit cycles in the mechanical oscillator. The onset of this regime is accompanied by pronounced fluctuations in the photon emission from the two-level system, indicated by a large deviation from Poissonian statistics. The phonon statistics display a similar behavior, offering an additional experimental signature. As the coupling strength approaches ωm, the mechanical oscillator reaches a steady state with non-classical feature. The phonon number distribution in this regime resembles that of Fock states, and the corresponding quasi-probability distribution in phase space displays negative regions, a signature of nonclassicality. A method is proposed to detect this non-classicality experimentally through measurements of the emitted light, from which the full quantum state of the coupled system can be reconstructed. The robustness of this approach is analyzed in the presence of realistic noise sources. The thesis further investigates the response of the system under two-tone driving. A tailored model is developed to describe this regime at strong coupling. When the driving frequencies are tuned to the first blue and red sidebands, the mechanical oscillator reaches a steady state exhibiting quadrature squeezing. In the case where both driving frequencies are red-detuned, the oscillator evolves into a superposition of coherent states, analogous to the behavior of a parametrically driven resonator. In both configurations, non-classical features become prominent when g0 approaches ωm. These results provide new insights into the generation and stabilization of non-classical and squeezed mechanical states. We outline feasible strategies for their detection, offering potential applications in hybrid quantum systems and foundational tests of quantum mechanics.
We study a mechanical oscillator coupled to a two-level system driven by a blue-detuned coherent source in the resolved sideband regime. For weak mechanical damping, we find dynamical instabilities leading to limit cycles. They are signaled by strong fluctuations in the number of emitted photons, with a large Fano factor. The phonon-number fluctuations exhibit strikingly similar behavior. When the coupling strength becomes comparable to the mechanical frequency, nonclassical mechanical states appear. We demonstrate that these properties can be detected by measuring the photon-emission spectrum, which enables the reconstruction of the Wigner function. We then discuss the relation with cavity optomechanical systems. Candidates for observing these effects include superconducting qubits, NV centers, and single molecules coupled to oscillators.
We investigate theoretically how single molecule spectroscopy techniques can be used to perform fast and high resolution displacement detection and manipulation of nanomechanical oscillators, such as singly clamped carbon nanotubes. We analyze the possibility of real time displacement detection by the luminescence signal and of displacement fluctuations by the degree of second order coherence. Estimates of the electromechanical coupling constant indicate that intriguing regimes of strong backaction between the two-level system of a molecule and the oscillator can be realized.
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We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the single driving laser as well as by varying different system parameters provided by the hybrid interaction. Significantly, even though the atomic cavity is not driven by any laser pump and there is no coupling with the mechanical oscillator directly, the intracavity optical field in the atomic cavity also exhibits bistability due to the optical coupling with the optomechanical cavity. In essence, our work emphasizes the possibility of realization of a better controllable optical switch depending on the hybrid interaction.
We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong-coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators, we show that the system can classically exhibit bistability and bifurcations, and we explore how these manifest themselves in interference, entanglement, and correlation in the quantum theory, while revealing the impact of decoherence of the mechanical system due to cavity fluctuations and coherent driving.