Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra.

Coherent extreme ultraviolet (XUV) radiation produced by table-top high-harmonic generation (HHG) sources provides a wealth of possibilities in research areas ranging from attosecond physics to high resolution coherent diffractive imaging. However, it remains challenging to fully exploit the coherence of such sources for interferometry and Fourier transform spectroscopy (FTS). This is due to the need for a measurement system that is stable at the level of a wavelength fraction, yet allowing a controlled scanning of time delays. Here we demonstrate XUV interferometry and FTS in the 17-55 nm wavelength range using an ultrastable common-path interferometer suitable for high-intensity laser pulses that drive the HHG process. This approach enables the generation of fully coherent XUV pulse pairs with sub-attosecond timing variation, tunable time delay and a clean Gaussian spatial mode profile. We demonstrate the capabilities of our XUV interferometer by performing spatially resolved FTS on a thin film composed of titanium and silicon nitride.A well-known feature of high-harmonic generation (HHG) is broadband spectra in the XUV and soft X-ray regions [1][2][3]. This radiation is typically emitted in a train of attosecond pulses with excellent spatial and temporal coherence, as shown in various interferometric and spectroscopic measurements [4][5][6][7][8][9][10][11][12]. As a result, interferometry with high harmonics found important applications in e.g. Molecular Orbital Tomography [13], in wavefront reconstruction [14] and electric field characterization [15] of high harmonics. Recently, interferometry with high harmonics provided added value to coherent diffractive imaging (CDI) [16,17] using the full high harmonics bandwidth and photon flux. However, in the extreme ultraviolet (XUV) spectral range, interferometry and Fourier transform spectroscopy (FTS) are challenging due to the high stability requirements of the interferometer itself. Two main types of HHG interferometers have been devised. In one scheme, the near-infrared fundamental driving pulse is split into two phase-locked pulses with an adjustable time delay, and this pulse pair is subsequently used for HHG [5,[7][8][9]. Although this method has been successfully used it is typically limited by the stability of the optical interferometer. The other scheme is based on wavefront division, whereby one HHG beam is divided into two phase-locked sources by a piezo-mounted split mirror. This configuration allows more stable interferometry [10,[18][19][20][21], but results in two beams with different spatial profiles and strong diffraction effects due to the hard edge of the split mirror. Wavefront division interferometry is also less flexible when one would like to change the intensity ratio between the two beams.In this letter we present XUV interferometry using a novel ultrastable common-path interferome-1 arXiv:1607.02386v2 [physics.optics]

Adding or subtracting a single quantum of excitation to a thermal state of a bosonic system has the counter-intuitive effect of approximately doubling its mean occupation. We perform the first experimental demonstration of this effect outside optics by implementing single-phonon addition and subtraction to a thermal state of a mechanical oscillator via Brillouin optomechanics in an optical whispering-gallery microresonator. Using a detection scheme that combines single-photon counting and optical heterodyne detection, we observe this doubling of the mechanical thermal fluctuations to a high precision. The capabilities of this joint click-dyne detection scheme adds a significant new dimension for optomechanical quantum science and applications.

Wavefront sensors are an important tool to characterize coherent beams of extreme ultraviolet radiation. However, conventional Hartmann-type sensors do not allow for independent wavefront characterization of different spectral components that may be present in a beam, which limits their applicability for intrinsically broadband high-harmonic generation (HHG) sources. Here we introduce a wavefront sensor that measures the wavefronts of all the harmonics in a HHG beam in a single camera exposure. By replacing the mask apertures with transmission gratings at different orientations, we simultaneously detect harmonic wavefronts and spectra, and obtain sensitivity to spatiotemporal structure such as pulse front tilt as well. We demonstrate the capabilities of the sensor through a parallel measurement of the wavefronts of 9 harmonics in a wavelength range between 25 and 49 nm, with up to λ/32 precision.