Hidden and explicit quantum scale invariance

There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In this work, we study the effects of such scale invariant renormalisation procedures. On the one hand, an explicitly quantum scale invariant theory can emerge from the scale invariant renormalisation of a scale invariant Lagrangian. On the other hand, we show how a quantum scale invariant theory can equally emerge from a Lagrangian visibly breaking scale invariance renormalised with scale dependent renormalisation (such as the traditional MS-bar scheme). In this last case, scale invariance is hidden in the theory, in the sense that it only appears explicitly after renormalisation.Comment: Minor changes, updated references, matches published versio

Sideband Injection Locking in Microresonator Frequency Combs

Frequency combs from continuous-wave-driven Kerr-nonlinear microresonators have evolved into a key photonic technology with applications from optical communication to precision spectroscopy. Essential to many of these applications is the control of the comb's defining parameters, i.e., carrier-envelope offset frequency and repetition rate. An elegant and all-optical approach to controlling both degrees of freedom is the suitable injection of a secondary continuous-wave laser into the resonator onto which one of the comb lines locks. Here, we study experimentally such sideband injection locking in microresonator soliton combs across a wide optical bandwidth and derive analytic scaling laws for the locking range and repetition rate control. As an application example, we demonstrate optical frequency division and repetition rate phase-noise reduction to three orders of magnitude below the noise of a free-running system. The presented results can guide the design of sideband injection-locked, parametrically generated frequency combs with opportunities for low-noise microwave generation, compact optical clocks with simplified locking schemes and more generally, all-optically stabilized frequency combs from Kerr-nonlinear resonators.Comment: 13 pages, 6 figure

Ultraviolet astronomical spectrograph calibration with laser frequency combs from nanophotonic waveguides

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants across cosmological scales. Laser frequency combs can provide the critically required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is highly desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this exceedingly challenging. Here, we demonstrate for the first time astronomical spectrograph calibrations with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and may contribute to unlocking the full potential of next generation ground- and future space-based astronomical instruments

Sideband Injection Locking in Microresonator Frequency Combs

Frequency combs from continuous-wave-driven Kerr-nonlinear microresonators have evolved into a key photonic technology with applications from optical communication to precision spectroscopy. Essential to many of these applications is the control of the comb’s defining parameters, i.e., carrier-envelope offset frequency and repetition rate. An elegant and all-optical approach to controlling both degrees of freedom is the suitable injection of a secondary continuous-wave laser into the resonator onto which one of the comb lines locks. Here, we study experimentally such sideband injection locking in microresonator soliton combs across a wide optical bandwidth and derive analytic scaling laws for the locking range and repetition rate control. As an application example, we demonstrate optical frequency division and repetition rate phase-noise reduction to three orders of magnitude below the noise of a free-running system. The presented results can guide the design of sideband injection-locked, parametrically generated frequency combs with opportunities for low-noise microwave generation, compact optical clocks with simplified locking schemes and more generally, all-optically stabilized frequency combs from Kerr-nonlinear resonators

Photo-acoustic dual-frequency comb spectroscopy

Here, the authors show that the resolution and speed limitations in broadband photo-acoustic spectroscopy can be overcome by combining dual-comb spectroscopy with photo-acoustic detection. This enables broadband detection and allows for rapid and sensitive multi-species molecular analysis across all wavelengths of light

Photo-acoustic dual-frequency comb spectroscopy

Photo-acoustic spectroscopy (PAS) is one of the most sensitive non-destructive analysis techniques for gases, fluids and solids. It can operate background-free at any wavelength and is applicable to microscopic and even non-transparent samples. Extension of PAS to broadband wavelength coverage is a powerful tool, though challenging to implement without sacrifice of wavelength resolution and acquisition speed. Here we show that dual-frequency comb spectroscopy (DCS) and its potential for unmatched precision, speed and wavelength coverage can be combined with the advantages of photo-acoustic detection. Acoustic wave interferograms are generated in the sample by dual-comb absorption and detected by a microphone. As an example, weak gas absorption features are precisely and rapidly sampled; long-term coherent averaging further increases the sensitivity. This novel approach of dual-frequency comb photo-acoustic spectroscopy (DCPAS) generates unprecedented opportunities for rapid and sensitive multi-species molecular analysis across all wavelengths of light

Sideband injection locking in microresonator frequency combs

Frequency combs from continuous-wave-driven Kerr-nonlinear microresonators have evolved into a key photonic technology with applications from optical communication to precision spectroscopy. Essential to many of these applications is the control of the comb’s defining parameters, i.e., carrier-envelope offset frequency and repetition rate. An elegant and all-optical approach to controlling both degrees of freedom is the suitable injection of a secondary continuous-wave laser into the resonator onto which one of the comb lines locks. Here, we experimentally study such sideband injection locking in microresonator soliton combs across a wide optical bandwidth and derive analytic scaling laws for the locking range and repetition rate control. As an application example, we demonstrate optical frequency division and repetition rate phase-noise reduction to three orders of magnitude below the noise of a free-running system. The presented results can guide the design of sideband injection-locked, parametrically generated frequency combs with opportunities for low-noise microwave generation, compact optical clocks with simplified locking schemes, and, more generally, all-optically stabilized frequency combs from Kerr-nonlinear resonators