Detuned Mechanical Parametric Amplification as a Quantum Non-Demolition Measurement

Recently it has been demonstrated that the combination of weak-continuous position detection with detuned parametric driving can lead to significant steady-state mechanical squeezing, far beyond the 3 dB limit normally associated with parametric driving. In this work, we show the close connection between this detuned scheme and quantum non-demolition (QND) measurement of a single mechanical quadrature. In particular, we show that applying an experimentally realistic detuned parametric drive to a cavity optomechanical system allows one to effectively realize a QND measurement despite being in the bad-cavity limit. In the limit of strong squeezing, we show that this scheme offers significant advantages over standard backaction evasion, not only by allowing operation in the weak measurement and low efficiency regimes, but also in terms of the purity of the mechanical state.Comment: 17 pages, 2 figure

Optimisation of Quantum Trajectories Driven by Strong-field Waveforms

Quasi-free field-driven electron trajectories are a key element of strong-field dynamics. Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecond duration XUV emission in the process of high harmonic generation (HHG). The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer, and it has been predicted that this limit can be significantly exceeded by an appropriately ramped-up cycleshape. Here, we present an experimental realization of such cycle-shaped waveforms and demonstrate control of the HHG process on the single-atom quantum level via attosecond steering of the electron trajectories. With our optimized optical cycles, we boost the field-ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration. We demonstrate, in realistic experimental conditions, two orders of magnitude enhancement of the generated XUV flux together with an increased spectral cutoff. This application, which is only one example of what can be achieved with cycle-shaped high-field light-waves, has farreaching implications for attosecond spectroscopy and molecular self-probing

Nonlinear and Quantum Optics with Whispering Gallery Resonators

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.Comment: This is a review paper with 615 references, submitted to J. Op

BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature $T_c$, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of $T_c$. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify $T_c$. Our results hold universally for the large class of normal BCS superconductors

Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities

We present a comprehensive study of second-order nonlinear difference frequency generation in triply resonant cavities using a theoretical framework based on coupled-mode theory. We show that optimal quantum-limited conversion efficiency can be achieved at any pump power when the powers at the pump and idler frequencies satisfy a critical relationship. We demonstrate the existence of a broad parameter range in which all triply-resonant DFG processes exhibit monostable conversion. We also demonstrate the existence of a geometry-dependent bistable region.Comment: 10 pages, 3 figure

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed