I. DESIGN OF MECHANICAL CAVITY AND WAVEGUIDE COUPLINGIn the optomechanical cavity-waveguide coupled devices, we can change the cavity-waveguide coupling (i.e. γ e ) on purpose. This is achieved by the design of a low-Q mechanical cavity mode and varying the number of mirror cells . As shown in Fig. S-1b, the blue curves are the mechanical band structure of the mirror unit cell (blue rectangle in Fig. S-1a). We design the cavity such that the mechanical cavity frequency (red dashed line in Fig. S-1b) overlaps with the band of mirror unit cell, such that the mechanical cavity mode can tunnel through the mirror cells into waveguide. Meanwhile, the optical cavity frequency (red dashed line in Fig. S-1c) lies within the optical band gap of mirror unit cell, such that the optical cavity mode keeps high-Q. By varying the number of unit cells, we find the simulated radiation mechanical coupling rate into waveguide (γ e /2π) oscillates between a few MHz to as high as 30 MHz, due to the interference within the mirror unit cells. II. SIMULATION OF PHONON PULSE PROPAGATIONIn this section, we show propagation and bouncing of phonon pulses in the cavity-waveguide system (Fig. 3a) can be well simulated by a group of coupled mode equations using input-output formalism. The dynamics captured by the coupled mode equations is a phonon pulse travelling in a waveguide terminated by two cavities with bare mechanical frequency ω mL,R and waveguide coupling rate γ eL,R . We approximate ω mL,R to be the frequency of cavity-dominated modes L 1 and R 1 in the simulation. Since the response time of the optical cavity is much shorter than that of the mechanical cavity, we can exclude the dynamics of optical modes from these equations. Thus, the coupled mode equations can be written as follows,where α 0L and α +L are the amplitudes of optical pump and its red sideband in the left cavity, τ is the duration of excitation pulse, ω s is the frequency of pulse, Θ(t) is the Heaviside step function, γ is the effective decay rate of the excited mechanical mode, α ≈ γ/v g is the waveguide loss rate, and t w = 1/(is the single trip time the pulse spent in the waveguide.From the mechanical spectrum we find γ = 2π × 2.1 MHz for L 1 mode (the main coherently-driven mode) during the pulse measurement; and by fitting the pulse tails detected in each cavity we find γ eL = 2π ×34.7 MHz and γ eR = 2π × 25.5 MHz. Using these parameters, |b L | and |b R | can be numerically calculated from the coupled mode equations and the proportional voltage signals are shown in Fig. 3a. The simulated result captures the main features of the measured pulse data. In particular, the pulse splitting observed from cavity R is due to the fact that the pulse frequency is not in resonant with cavity R and thus experiences destructive interference inside this cavity.The phonon transfer efficiency from cavity L to cavity R is about e −γ/(2fFSR) ≈ 67%. The phonon transfer efficiency from cavity to waveguide for cavity L and R is γ eL(R) /(γ eL(R) + γ) ≈ 94%(92%).We summarize the measu...

Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. In this Letter, in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring mesoscopic quantum physics.

Coherent light-matter interaction at the single photon and electronic qubit level promises the remarkable potential for nonclassical information processing. Against the efforts of improving the figure of merit of the cavities, here we demonstrate strong anharmonicity in the polariton dressed states via dark state resonances in a highly dissipative cavity. It is shown that vacuum Rabi oscillation occurs for a single quantum emitter inside a cavity even with bosonic decay-to-interaction rate ratio exceeding 10 2 , when the photon field is coupled to an auxiliary high-Q cavity. Moreover, photon blockade is observable in such a highly-dissipative cavity quantum electrodynamics system. This study provides a promising platform for overcoming decoherence and advancing the coherent manipulation of polariton qubits. PACS numbers: 42.50.Pq, 42.50.Ct Cavity quantum electrodynamics (QED) (for a review, see [1]) provides a critical resource for quantum information processing [2][3][4][5][6][7][8][9][10][11][12] . For coherent manipulation, a key prerequisite is to reach the strong coupling regime, where the emitter-field coupling strength exceeds the decay rates of the emitter and the cavity field. In the past two decades great efforts have been made to improve the quality (Q) factor and reduce the mode volume (V ) of the resonators for stronger interactions, using Fabry-Pérot cavities [13,14], Bragg cavities [15-17], whispering-gallery mode cavities [18-23] , photonic crystal cavities [24-30], hybrid plasmonic-photonic cavities [31] and transmission-line microwave cavities [32], along with theoretical studies of coupled-cavity QED through a waveguide [33][34][35][36]. However, it remains difficult to achieve high Q and small V simultaneously for the sametype resonator. Fundamentally, this is related to the diffraction limit. A smaller V corresponds to a larger radiative decay rate and more significant roughness scattering, leading to a lower Q. Different-type resonators possess their own unique properties, but the trade-off between high Q and small V still exists. For example, whispering-gallery mode cavities possess ultrahigh Q factors, while the mode volumes are relatively large; for photonic crystal cavities, sub-wavelength light confinement can be realized whereas the Q factors are relatively low.Unlike the efforts to improve the Q/ √ V figure of merit of the cavities, here we propose to reach the strong coupling regime via dark state resonances, which removes the requirement for high Q and small V for the same cavity. By coupling the originally weak-coupled cavity QED system with high cavity dissipation to an auxiliary cavity mode with high-Q but large V , a strong dark state interaction takes place. We demonstrate that vacuum Rabi oscillations and anharmonicity in the polariton dressed states occur even when the cavity decay rate is FIG. 1. (color online) (a) Schematic of the cavity QED system coupled to an auxiliary cavity. (b) Energy level diagram of the coupled system. The lowest four energy levels are plotted, i...