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Coherent quantum noise cancellation (CQNC) can be used in optomechanical sensors to surpass the standard quantum limit (SQL). In this paper, we investigate an optomechanical force sensor that uses the CQNC strategy by cascading the optomechanical system with an all-optical effective negative mass oscillator. Specifically, we analyze matching conditions, losses and compare the two possible arrangements in which either the optomechanical or the negative mass system couples first to light. While both of these orderings yield a sub-SQL performance, we find that placing the effective negative mass oscillator before the optomechanical sensor will always be advantageous for realistic parameters. The modular design of the cascaded scheme allows for better control of the sub-systems by avoiding undesirable coupling between system components, while maintaining similar performance to the integrated configuration proposed earlier. We conclude our work with a case study of a micro-optomechanical implementation., Comment: 9 pages, 6 figures, Appendix A and B

Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems. Recently, some of these concepts have been successfully applied to acoustic phonons in nanoscale multilayered systems. The reported demonstration of confined topological phononic modes was based on Raman scattering spectroscopy [M. Esmann et al., Phys. Rev. B 97, 155422 (2018)], yet the resolution did not suffice to determine lifetimes and to identify other acoustic modes in the system. Here, we use time-resolved pump-probe measurements using an asynchronous optical sampling (ASOPS) technique to overcome these resolution limitations. By means of one-dimensional GaAs/AlAs distributed Bragg reflectors (DBRs) used as building blocks, we engineer high frequency (∼200 GHz) topological acoustic interface states. We are able to clearly distinguish confined topological states from stationary band edge modes. The generation/detection scheme reflects the symmetry of the modes directly through the selection rules, evidencing the topological nature of the measured confined state. These experiments enable a new tool in the study of the more complex topology-driven phonon dynamics such as phonon nonlinearities and optomechanical systems with simultaneous confinement of light and sound., This work was supported by the European Commission in the form of the H2020 FET Proactive project TOCHA (No. 824140). The authors acknowledge funding by the European Research Council Starting Grant No. 715939, Nanophennec; by the French RENATECH network, and through a public grant overseen by the ANR as part of the “Investissements d’Avenir” program (Labex NanoSaclay Grant No. ANR-10-LABX-0035). ICN2 was supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706) and the project PHENTOM (Fis 2015-70862-P), as well as by the CERCA Programme/Generalitat de Catalunya, and by the European Commission in the form of the H2020 FET Open project PHENOMEN (No. 713450 to G.A.). G.A. was supported by a BIST Ph.D. fellowship and P.D.G. by a Ramon y Cajal Fellowship No. RyC-2015-18124. M.E. acknowledges funding from the German Research Foundation DFG (Forschungsstipendium ES 560/1-1).

Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Physical Review Letters, 109, 253601 (2012)]. Here we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime which correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation, and is based on techniques borrowed from the laser theory due to Haake's and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte-Carlo simulations, and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e. outside the single-photon strong coupling regime, for strong cavity drive, and rather large limit cycle amplitudes. The general approach taken here provides a natural starting point for further studies of quantum effects in optomechanics., 17 pages, 7 figures

The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system., 8 pages; 6 figures

Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this new modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects., 10 pages, 4 figures

A freeform optical surface is typically defined as any surface that does not have an axis of rotational symmetry. These surfaces provide additional degrees of freedom that can lead to improved performance compared to systems that make use solely of conventional optics. The benefits of using freeforms are: • Less optics can be used in the opto-mechanical system and therefore a decrease in the amount of optical surfaces occurs. Since every surface is a reduction of light intensity (e.g. by scattering), a higher throughput of the optical system is the result. • Less optics also means a reduction in mass and size • An improvement in optical quality (e.g. spherical aberration, coma, distortion) • A more favourable position of the optical components is possible. Generally, these freeform surfaces are more difficult to manufacture, and therefore more expensive both in cost and in development time. Furthermore, there is a danger with the application of exotic freeforms that have a large number of parameters, and consequently, degrees of freedom. For the latter reason they may naively seem attractive from the point of view of an optical designer, providing many knobs to optimize the performance; however, the overwhelming number of parameters may also cause a hotchpotch of local optima in merit function landscape. Many of those will not lead to an improved design because e.g. the particular freeform representation does not provide the correct handles, or the location in the optical train is unsuitably chosen. Another difficulty in the application of freeforms is the complexity of describing and evaluating the surface form tolerances of non-symmetric surfaces. Yet another difficulty is the following. An appropriate conventional design can often be obtained as an optimization from a paraxial system that can be defined analytically. For instance, both the telecentric beam expander and the push broom telescope that will be described in more detail below, can be derived from standard optical rules. Then, the paraxial design is a good starting point for an optimization algorithm as is used in optical design software in the hunt for an optimum design. In contrast, for a design that includes nonsymmetric optics, the parameters that provide the departure from symmetry are not so easily obtained with an analytically determined first guess. This makes it difficult to coax the optimizer into the right direction. Thus, with the benefits of using freeforms come disadvantages: • Difficult to determine the optimal freeform representation and location in the optical train • Optical tolerance analyses are not yet common practice in optical design packages • Difficult to manufacture with classical production technologies • Difficult to validate the surface shape • More difficult to align, because of the increased degrees of freedom • For all of the reasons above: more expensive Consequently, optical designers sometimes are hesitant to apply free form surfaces in an optical design difficult as they are to handle both from design and manufacturability of point of view.

A freeform optical surface is typically defined as any surface that does not have an axis of rotational symmetry. These surfaces provide additional degrees of freedom that can lead to improved performance compared to systems that make use solely of conventional optics. The benefits of using freeforms are: • Less optics can be used in the opto-mechanical system and therefore a decrease in the amount of optical surfaces occurs. Since every surface is a reduction of light intensity (e.g. by scattering), a higher throughput of the optical system is the result. • Less optics also means a reduction in mass and size • An improvement in optical quality (e.g. spherical aberration, coma, distortion) • A more favourable position of the optical components is possible. Generally, these freeform surfaces are more difficult to manufacture, and therefore more expensive both in cost and in development time. Furthermore, there is a danger with the application of exotic freeforms that have a large number of parameters, and consequently, degrees of freedom. For the latter reason they may naively seem attractive from the point of view of an optical designer, providing many knobs to optimize the performance; however, the overwhelming number of parameters may also cause a hotchpotch of local optima in merit function landscape. Many of those will not lead to an improved design because e.g. the particular freeform representation does not provide the correct handles, or the location in the optical train is unsuitably chosen. Another difficulty in the application of freeforms is the complexity of describing and evaluating the surface form tolerances of non-symmetric surfaces. Yet another difficulty is the following. An appropriate conventional design can often be obtained as an optimization from a paraxial system that can be defined analytically. For instance, both the telecentric beam expander and the push broom telescope that will be described in more detail below, can be derived from standard optical rules. Then, the paraxial design is a good starting point for an optimization algorithm as is used in optical design software in the hunt for an optimum design. In contrast, for a design that includes nonsymmetric optics, the parameters that provide the departure from symmetry are not so easily obtained with an analytically determined first guess. This makes it difficult to coax the optimizer into the right direction. Thus, with the benefits of using freeforms come disadvantages: • Difficult to determine the optimal freeform representation and location in the optical train • Optical tolerance analyses are not yet common practice in optical design packages • Difficult to manufacture with classical production technologies • Difficult to validate the surface shape • More difficult to align, because of the increased degrees of freedom • For all of the reasons above: more expensive Consequently, optical designers sometimes are hesitant to apply free form surfaces in an optical design difficult as they are to handle both from design and manufacturability of point of view.