Q1. What have the authors contributed in "Optimized optomechanical crystal cavity with acoustic radiation shield" ?
In this paper, surface label-free sensing by means of a fluorescent multilayered photonic structure is presented.
Optimized optomechanical crystal cavity with acoustic radiation shield
TL;DR: In this article, the design of an optomechanical crystal nanobeam cavity that combines finite-element simulation with numerical optimization is presented, and considers the optomchanical coupling arising from both moving dielectric boundaries and the photo-elastic effect.
Abstract: We present the design of an optomechanical crystal nanobeam cavity that combines finite-element simulation with numerical optimization, and considers the optomechanical coupling arising from both moving dielectric boundaries and the photo-elastic effect. Applying this methodology results in a nanobeam with an experimentally realized intrinsic optical Q-factor of 1.2×10^6, a mechanical frequency of 5.1 GHz, a mechanical Q-factor of 6.8×10^5 (at T = 10 K), and a zero-point-motion optomechanical coupling rate of g = 1.1 MHz.
Figures (4)
FIG. 2. (a) Plot of the unit cell parameters, a (blue ), hx (green dashed (), and hy (red (), along the length of the nanobeam, in units of anominal. (b) The normalized optical Ey field and (c) the normalized mechanical displacement field jQj of the localized optical and mechanical modes, respectively. (d) The normalized surface density of the integrand in Eq. (1), showing the contributions to gOM;MB. (e) The normalized volumetric density of the integrand in Eq. (3), showing the contributions to gOM;PE. (f) Scanning electron microscope (SEM) image of the experimentally realized cavity. 
FIG. 1. The (a) nominal unit cell with ða; t;w; hx; hyÞ ¼ ð436; 220; 529; 165; 366Þ nm and (b) defect unit cell with ða; t;w; hx; hyÞ ¼ ð327; 220; 529; 199; 170Þ nm of the OMC nanobeam cavity. The (c) optical and (e) mechanical band structure for propagation along the x-axis in the nominal unit cell, with quasi-bandgaps (red regions) and cavity mode frequencies (black dashed) indicated. In (c), the light line (green curve) divides the diagram into two regions: the gray shaded region above representing a continuum of radiation and leaky modes, and the white region below containing guided modes with y-symmetric (red bands) and y-antisymmetric (blue bands) vector symmetries. In (e), modes that are y- and z-symmetric (red bands), and modes of other vector symmetries (blue bands) are indicated. These mechanical simulations use the full anisotropic elasticity matrix, where ðC11;C12;C44Þ ¼ ð166; 64; 80ÞGPa, and assume a ½100 crystallographic orientation for the x-axis (½110 orientation simulations exhibit a small, <10% frequency shift in the bands below 8 GHz). The bands from which the localized cavity modes are formed are shown as thicker curves. Tuning of the (d) X-point optical and (f) C-point mechanical modes of interest as the unit cell is smoothly transformed from the nominal to the defect unit cell. 
FIG. 4. (a) Normalized optical transmission spectrum, centered at 1544.8 nm, showing the fundamental optical cavity mode of the nanobeam, with a measured intrinsic Qo;i ¼ 1:22 106. (b) Optically transduced thermal noise power spectral density centered at the mechanical frequency, xm=2p ¼ 5:1 GHz, of the breathing mode, taken at Tb ¼ 10 K with the input laser red-detuned (D ¼ xm; red curve) and blue-detuned (D ¼ xm; blue curve) from the cavity. (c) Measured cooperativity, C, as function of intracavity photon number, ncav, for red detuning D ¼ xm. 
FIG. 3. (a) The unit cell of the phononic shield with parameters ðca; ch; ct; tÞ ¼ ð534; 454; 134; 220Þ nm. (b) Full in-plane mechanical band diagram with complete phononic bandgap (red region) and frequency of the acoustic mode of the cavity indicated (black dashed line). (c) SEM image showing the phononic shield (green) around the nanobeam.
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TL;DR: In this article, three major approaches to generate optical nonlinearities based on cavity quantum electrodynamics, atomic ensembles with large Kerr non-linearities and strong atomic interactions are reviewed.
Abstract: This review article summarizes the emerging field of quantum nonlinear optics. Three major approaches to generate optical nonlinearities based on cavity quantum electrodynamics, atomic ensembles with large Kerr nonlinearities and strong atomic interactions are reviewed. Applications of quantum nonlinear optics and many-body physics with strongly interacting photons are also discussed.
565 citations
TL;DR: Here, coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system is theoretically proposed and experimentally demonstrated.
Abstract: We theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed, and in terms of an equivalent photon number signal level are found to correspond to an internal noise level of only 6 and 4x10^(-3) quanta, respectively.
425 citations
TL;DR: In this article, a silicon optomechanical circuit with both optical and mechanical connectivity between two optical cavities was designed and fabricated to enable non-reciprocal transport of photons with 35 dB isolation.
Abstract: Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which, in combination with dissipative coupling to the mechanical bath, leads to non-reciprocal transport of photons with 35 dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12 dB in the isolator through-direction. These results suggest the possibility of using optomechanical circuits to create a more general class of non-reciprocal optical devices, and further, to enable new topological phases for both light and sound on a microchip.
425 citations
TL;DR: An acoustic wave interference effect, similar to atomic coherent population trapping, is demonstrated, in which RF-driven coherent mechanical motion is cancelled by optically-driven motion.
Abstract: Optomechanical cavities have been studied for applications ranging from sensing to quantum information science. Here, we develop a platform for nanoscale cavity optomechanical circuits in which optomechanical cavities supporting co-localized 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency (RF) field through the piezo-electric effect, which produces acoustic waves that are routed and coupled to the optomechanical cavity by phononic crystal waveguides, or optically through the strong photoelastic effect. Along with mechanical state preparation and sensitive readout, we use this to demonstrate an acoustic wave interference effect, similar to atomic coherent population trapping, in which RF-driven coherent mechanical motion is cancelled by optically-driven motion. Manipulating cavity optomechanical systems with equal facility through both photonic and phononic channels enables new architectures for signal transduction between the optical, electrical, and mechanical domains.
357 citations
TL;DR: In this article, the authors reported non-classical correlations between single photons and phonons from a nanomechanical resonator, and implemented a quantum protocol involving initialization of the resonator in its quantum ground state of motion and subsequent generation and read-out of correlated photon-phonon pairs.
Abstract: Interfacing a single photon with another quantum system is a key capability in modern quantum information science. It allows quantum states of matter, such as spin states of atoms, atomic ensembles or solids, to be prepared and manipulated by photon counting and, in particular, to be distributed over long distances. Such light-matter interfaces have become crucial to fundamental tests of quantum physics and realizations of quantum networks. Here we report non-classical correlations between single photons and phonons--the quanta of mechanical motion--from a nanomechanical resonator. We implement a full quantum protocol involving initialization of the resonator in its quantum ground state of motion and subsequent generation and read-out of correlated photon-phonon pairs. The observed violation of a Cauchy-Schwarz inequality is clear evidence for the non-classical nature of the mechanical state generated. Our results demonstrate the availability of on-chip solid-state mechanical resonators as light-matter quantum interfaces. The performance we achieved will enable studies of macroscopic quantum phenomena as well as applications in quantum communication, as quantum memories and as quantum transducers.
355 citations
References
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TL;DR: This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2, and proves convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2.
Abstract: The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder--Mead algorithm. This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.
7,141 citations
2,467 citations
TL;DR: In this article, a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85±0.08).
Abstract: The simple mechanical oscillator, canonically consisting of a coupled mass–spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces and small masses. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology or as a means of coupling hybrid quantum systems. Here we report the development of a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85±0.08). This cooling is realized at an environmental temperature of 20 K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.
2,073 citations
TL;DR: Sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state is demonstrated and the device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons.
Abstract: It has been a long-standing goal in the field of cavity optomechanics to cool down a mechanical resonator to its motional quantum ground state by using light. Teufel et al. have now achieved just that with a recently developed system in which a drum-like flexible aluminium membrane is incorporated in a superconducting circuit. Ground-state cooling of a mechanical resonator was demonstrated for the first time last year in a different type of device, but the quantum states in this new device should be much longer lived, allowing direct tests of fundamental principles of quantum mechanics. As a first step, the authors perform a quantum-limited position measurement that is only a factor of about five away from the Heisenberg limit. The advent of laser cooling techniques revolutionized the study of many atomic-scale systems, fuelling progress towards quantum computing with trapped ions1 and generating new states of matter with Bose–Einstein condensates2. Analogous cooling techniques3,4 can provide a general and flexible method of preparing macroscopic objects in their motional ground state. Cavity optomechanical or electromechanical systems achieve sideband cooling through the strong interaction between light and motion5,6,7,8,9,10,11,12,13,14,15. However, entering the quantum regime—in which a system has less than a single quantum of motion—has been difficult because sideband cooling has not sufficiently overwhelmed the coupling of low-frequency mechanical systems to their hot environments. Here we demonstrate sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state. This achievement required a large electromechanical interaction, which was obtained by embedding a micromechanical membrane into a superconducting microwave resonant circuit. To verify the cooling of the membrane motion to a phonon occupation of 0.34 ± 0.05 phonons, we perform a near-Heisenberg-limited position measurement3 within (5.1 ± 0.4)h/2π, where h is Planck’s constant. Furthermore, our device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons16. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion17,18, possibly even testing quantum theory itself in the unexplored region of larger size and mass19. Because mechanical oscillators can couple to light of any frequency, they could also serve as a unique intermediary for transferring quantum information between microwave and optical domains20.
1,702 citations
TL;DR: Measurements at room temperature in the analogous regime of electromagnetically induced absorption show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.
Abstract: Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nanofabrication techniques. So far, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to effects such as electromagnetically induced transparency (EIT) and parametric normal-mode splitting. In atomic systems, studies of slow and stopped light (applicable to modern optical networks and future quantum networks) have thrust EIT to the forefront of experimental study during the past two decades. Here we demonstrate EIT and tunable optical delays in a nanoscale optomechanical crystal, using the optomechanical nonlinearity to control the velocity of light by way of engineered photon-phonon interactions. Our device is fabricated by simply etching holes into a thin film of silicon. At low temperature (8.7 kelvin), we report an optically tunable delay of 50 nanoseconds with near-unity optical transparency, and superluminal light with a 1.4 microsecond signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications. Measurements at room temperature in the analogous regime of electromagnetically induced absorption show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.
1,208 citations