16 research outputs found
A Generalized Hybrid Hoare Logic
Deductive verification of hybrid systems (HSs) increasingly attracts more
attention in recent years because of its power and scalability, where a
powerful specification logic for HSs is the cornerstone. Often, HSs are
naturally modelled by concurrent processes that communicate with each other.
However, existing specification logics cannot easily handle such models. In
this paper, we present a specification logic and proof system for Hybrid
Communicating Sequential Processes (HCSP), that extends CSP with ordinary
differential equations (ODE) and interrupts to model interactions between
continuous and discrete evolution. Because it includes a rich set of algebraic
operators, complicated hybrid systems can be easily modelled in an algebra-like
compositional way in HCSP. Our logic can be seen as a generalization and
simplification of existing hybrid Hoare logics (HHL) based on duration calculus
(DC), as well as a conservative extension of existing Hoare logics for
concurrent programs. Its assertion logic is the first-order theory of
differential equations (FOD), together with assertions about traces recording
communications, readiness, and continuous evolution. We prove continuous
relative completeness of the logic w.r.t. FOD, as well as discrete relative
completeness in the sense that continuous behaviour can be arbitrarily
approximated by discretization. Besides, we discuss how to simplify proofs
using the logic by providing a simplified assertion language and a set of sound
and complete rules for differential invariants for ODEs. Finally, we implement
a proof assistant for the logic in Isabelle/HOL, and apply it to verify two
case studies to illustrate the power and scalability of our logic
Chip-Based Laser with 1 Hertz Integrated Linewidth
Lasers with hertz-level linewidths on timescales up to seconds are critical
for precision metrology, timekeeping, and manipulation of quantum systems. Such
frequency stability typically relies on bulk-optic lasers and reference
cavities, where increased size is leveraged to improve noise performance, but
with the trade-off of cost, hand assembly, and limited application
environments. On the other hand, planar waveguide lasers and cavities exploit
the benefits of CMOS scalability but are fundamentally limited from achieving
hertz-level linewidths at longer times by stochastic noise and thermal
sensitivity inherent to the waveguide medium. These physical limits have
inhibited the development of compact laser systems with frequency noise
required for portable optical clocks that have performance well beyond
conventional microwave counterparts. In this work, we break this paradigm to
demonstrate a compact, high-coherence laser system at 1548 nm with a 1 s
integrated linewidth of 1.1 Hz and fractional frequency instability less than
10 from 1 ms to 1 s. The frequency noise at 1 Hz offset is suppressed
by 11 orders of magnitude from that of the free-running diode laser down to the
cavity thermal noise limit near 1 Hz/Hz, decreasing to 10 Hz/Hz
at 4 kHz offset. This low noise performance leverages wafer-scale integrated
lasers together with an 8 mL vacuum-gap cavity that employs micro-fabricated
mirrors with sub-angstrom roughness to yield an optical of 11.8 billion.
Significantly, all the critical components are lithographically defined on
planar substrates and hold the potential for parallel high-volume
manufacturing. Consequently, this work provides an important advance towards
compact lasers with hertz-level linewidths for applications such as portable
optical clocks, low-noise RF photonic oscillators, and related communication
and navigation systems
Micro-fabricated mirrors with finesse exceeding one million
The Fabry–Perot resonator is one of the most widely used optical devices, enabling scientific and technological breakthroughs in diverse fields including cavity quantum electrodynamics, optical clocks, precision length metrology, and spectroscopy. Though resonator designs vary widely, all high-end applications benefit from mirrors with the lowest loss and highest finesse possible. Fabrication of the highest-finesse mirrors relies on centuries-old mechanical polishing techniques, which offer losses at the parts-per-million (ppm) level. However, no existing fabrication techniques are able to produce high-finesse resonators with the large range of mirror geometries needed for scalable quantum devices and next-generation compact atomic clocks. In this paper, we introduce a scalable approach to fabricate mirrors with ultrahigh finesse (≥106</p
Photonic chip-based low noise microwave oscillator
Numerous modern technologies are reliant on the low-phase noise and exquisite
timing stability of microwave signals. Substantial progress has been made in
the field of microwave photonics, whereby low noise microwave signals are
generated by the down-conversion of ultra-stable optical references using a
frequency comb. Such systems, however, are constructed with bulk or fiber
optics and are difficult to further reduce in size and power consumption. Our
work addresses this challenge by leveraging advances in integrated photonics to
demonstrate low-noise microwave generation via two-point optical frequency
division. Narrow linewidth self-injection locked integrated lasers are
stabilized to a miniature Fabry-P\'{e}rot cavity, and the frequency gap between
the lasers is divided with an efficient dark-soliton frequency comb. The
stabilized output of the microcomb is photodetected to produce a microwave
signal at 20 GHz with phase noise of -96 dBc/Hz at 100 Hz offset frequency that
decreases to -135 dBc/Hz at 10 kHz offset--values which are unprecedented for
an integrated photonic system. All photonic components can be heterogeneously
integrated on a single chip, providing a significant advance for the
application of photonics to high-precision navigation, communication and timing
systems
Unified graphical co-modeling, analysis and verification of cyber-physical systems by combining AADL and Simulink/Stateflow
International audienc
A novel approach to interface high-Q FabryâPĂ©rot resonators with photonic circuits
The unique benefits of FabryâPĂ©rot resonators as frequency-stable reference cavities and as an efficient interface between atoms and photons make them an indispensable resource for emerging photonic technologies. To bring these performance benefits to next-generation communications, computation, and time-keeping systems, it will be necessary to develop strategies to integrate compact FabryâPĂ©rot resonators with photonic integrated circuits. In this paper, we demonstrate a novel reflection cancellation circuit that utilizes a numerically optimized multi-port polarization-splitting grating coupler to efficiently interface high-finesse FabryâPĂ©rot resonators with a silicon photonic circuit. This circuit interface produces a spatial separation of the incident and reflected waves, as required for on-chip PoundâDreverâHall frequency locking, while also suppressing unwanted back reflections from the FabryâPĂ©rot resonator. Using inverse design principles, we design and fabricate a polarization-splitting grating coupler that achieves 55% coupling efficiency. This design realizes an insertion loss of 5.8 dB for the circuit interface and more than 9 dB of back reflection suppression, and we demonstrate the versatility of this system by using it to interface several reflective off-chip devices