Towards minimum achievable phase noise of relaxation oscillators

A relaxation oscillator design is described, which has a phase noise rivaling ring oscillators, while also featuring linear frequency tuning. We show that the comparator in a relaxation-oscillator loop can be prevented from contributing to 1/f2 colored phase noise and degrading control linearity. The resulting oscillator is implemented in a power efficient way with a switched-capacitor circuit. The design results from a thorough analysis of the fundamental phase noise contributions. Simple expressions modeling the theoretical phase noise performance limit are presented, as well as a design strategy to approach this limit. To verify theoretical predictions, a relaxation oscillator is implemented in a baseline 65 nm CMOS process, occupying 200 µm × 150 µm. Its frequency tuning range is 1–12 MHz, and its phase noise is L(100kHz) = −109dBc/Hz at fosc = 12MHz, while consuming 90 μW. A figure of merit of −161dBc/Hz is achieved, which is only 4 dB from the theoretical limit

Multimode laser cooling and ultra-high sensitivity force sensing with nanowires

Photo-induced forces can be used to manipulate and cool the mechanical motion of oscillators. When the oscillator is used as a force sensor, such as in atomic force microscopy, active feedback is an enticing route to enhancing measurement performance. Here, we show broadband multimode cooling of $-23$ dB down to a temperature of $8 \pm 1$~K in the stationary regime. Through the use of periodic quiescence feedback cooling, we show improved signal-to-noise ratios for the measurement of transient signals. We compare the performance of real feedback to numerical post-processing of data and show that both methods produce similar improvements to the signal-to-noise ratio of force measurements. We achieved a room temperature force measurement sensitivity of $< 2\times10^{-16}$ N with integration time of less than $0.1$ ms. The high precision and fast force microscopy results presented will potentially benefit applications in biosensing, molecular metrology, subsurface imaging and accelerometry.Comment: 16 pages and 3 figures for the main text, 14 pages and 5 figures for the supplementary informatio

Optimal synchronization deep in the quantum regime: resource and fundamental limit

We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare quantitatively the synchronization behavior of different limit cycles and signals. We focus on the most elementary quantum system that is able to host a self-sustained oscillation, namely a single spin 1. Despite the spin having no classical analogue, we first show that it can realize the van der Pol limit cycle deep in the quantum regime, which allows us to provide an analytical understanding to recently reported numerical results. Moving on to the equatorial limit cycle, we then reveal the existence of an interference-based quantum synchronization blockade and extend the classical Arnold tongue to a snake-like split tongue. Finally, we derive the maximum synchronization that can be achieved in the spin-1 system, and construct a limit cycle that reaches this fundamental limit asymptotically.Comment: 15 pages, 9 figures, equivalent to published versio

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state

Frequency comb offset dynamics of SESAM modelocked thin disk lasers

We present a detailed study of the carrier-envelope offset (CEO) frequency dynamics of SESAM modelocked thin disk lasers (TDLs) pumped by kW-class highly transverse multimode pump diodes with a typical M2 value of 200-300, and give guidelines for future frequency stabilization of multi-100-W oscillators. We demonstrate CEO frequency detection with > 30 dB signal-to-noise ratio with a resolution bandwidth of 100 kHz from a SESAM modelocked Yb:YAG TDL delivering 140 W average output power with 748-fs pulses at 7-MHz pulse repetition rate. We compare with a low-power CEO frequency stabilized Yb:CALGO TDL delivering 2.1 W with 77-fs pulses at 65 MHz. For both lasers, we perform a complete noise characterization, measure the relevant transfer functions (TFs) and compare them to theoretical models. The measured TFs are used to determine the propagation of the pump noise step-by-step through the system components. From the noise propagation analysis, we identify the relative intensity noise (RIN) of the pump diode as the main contribution to the CEO frequency noise. The resulting noise levels are not excessive and do not prevent CEO frequency stabilization. More importantly, the laser cavity dynamics are shown to play an essential role in the CEO frequency dynamics. The cavity TFs of the two lasers are very different which explains why at this point a tight CEO frequency lock can be obtained with the Yb:CALGO TDL but not with the Yb:YAG TDL. For CEO stabilization laser cavities should exhibit high damping of the relaxation oscillations by nonlinear intra-cavity elements, for example by operating a SESAM in the roll-over regime. Therefore the optimum SESAM operation point is a tradeoff between enough damping and avoiding multiple pulsing instabilities. Additional cavity components could be considered for supplementary damping independent of the SESAM operation point

Theory on the Dynamics of Oscillatory Loops in the Transcription Factor Networks

We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes.Comment: 37 pages, 13 figures, 2 table