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We develop methods to find the limits to finite-time single photon extraction from emitter-cavity systems. We first establish analytic upper and lower bounds on the maximum extraction probability from a canonical $\Lambda$-system before developing a numeric method to optimise generic output probabilities from $\Lambda$-systems generalised to multiple ground states. We use these methods to study the limits to finite-time photon extraction and the wavepackets that satisfy them, finding that using an optimised wavepacket ranging between a sinusoidal and exponentially decaying profile can considerably reduce photon duration for a given extraction efficiency. We further optimise the rates of quantum protocols requiring emitter-photon correlation to obtain driving-independent conclusions about the effect of system parameters on success probability. We believe that these results and methods will provide valuable tools and insights for the development of cavity-based single photon sources combining high efficiency and high rate., Comment: 26 pages, 7 figures

The transverse field structure and diffraction loss of the resonant modes of Fabry-P\'erot optical cavities are acutely sensitive to the alignment and shape of the mirror substrates. We develop extensions to the `mode mixing' method applicable to arbitrary mirror shapes, which both facilitate fast calculation of the modes of cavities with transversely misaligned mirrors and enable the determination and transformation of the geometric properties of these modes. We show how these methods extend previous capabilities by including the practically-motivated case of transverse mirror misalignment, unveiling rich and complex structure of the resonant modes., Comment: 17 pages, 7 figures

We present a study on the optical losses of Fabry-P\'erot cavities subject to realistic transverse mirror misalignment. We consider mirrors of the two most prevalent surface forms: idealised spherical depressions, and Gaussian profiles generated by laser ablation. We first describe the mode mixing phenomena seen in the spherical mirror case and compare to the frequently-used clipping model, observing close agreement in the predicted diffraction loss, but with the addition of protective mode mixing at transverse degeneracies. We then discuss the Gaussian mirror case, detailing how the varying surface curvature across the mirror leads to complex variations in round trip loss and mode profile. In light of the severe mode distortion and strongly elevated loss predicted for many cavity lengths and transverse alignments when using Gaussian mirrors, we suggest that the consequences of mirror surface profile are carefully considered when designing cavity experiments., Comment: 20 pages, 12 figures

In the design optimisation of ion-cavity interfaces for quantum networking applications, difficulties occur due to the many competing figures of merit and highly interdependent design constraints, many of which present `soft-limits', amenable to improvement at the cost of engineering time. In this work we present a systematic approach to this problem which offers a means to identify efficient and robust operating regimes, and to elucidate the trade-offs involved in the design process, allowing engineering efforts to be focused on the most sensitive and critical parameters. We show that in many relevant cases it is possible to approximately separate the geometric aspects of the cooperativity from those associated with the atomic system and the mirror surfaces themselves, greatly simplifying the optimisation procedure. Although our approach to optimisation can be applied to most operating regimes, here we consider cavities suitable for typical ion trapping experiments, and with substantial transverse misalignment of the mirrors. We find that cavities with mirror misalignments of many micrometres can still offer very high photon extraction efficiencies, offering an appealing route to the scalable production of ion-cavity interfaces for large scale quantum networks.

Supergenes are genomic regions containing sets of tightly linked loci that control multi-trait phenotypic polymorphisms under balancing selection. Recent advances in genomics have uncovered significant variation in both the genomic architecture as well as the mode of origin of supergenes across diverse organismal systems. Although the role of genomic architecture for the origin of supergenes has been much discussed, differences in the genomic architecture also subsequently affect the evolutionary trajectory of supergenes and the rate of degeneration of supergene haplotypes. In this review, we synthesize recent genomic work and historical models of supergene evolution, highlighting how the genomic architecture of supergenes affects their evolutionary fate. We discuss how recent findings on classic supergenes involved in governing ant colony social form, mimicry in butterflies, and heterostyly in flowering plants relate to theoretical expectations. Furthermore, we use forward simulations to demonstrate that differences in genomic architecture affect the degeneration of supergenes. Finally, we discuss implications of the evolution of supergene haplotypes for the long-term fate of balanced polymorphisms governed by supergenes.

We present a design for an atomic oven suitable for loading ion traps, which is operated via optical heating with a continuous-wave multimode diode laser. The absence of the low-resistance electrical connections necessary for Joule heating allows the oven to be extremely well thermally isolated from the rest of the vacuum system, and for an oven filled with calcium we achieve a number density suitable for rapid ion loading in the target region with ~200 mW of laser power, limited by radiative losses. With simple feedforward to the laser power, the turn-on time for the oven is less than 20 s, while the oven contains enough calcium to operate continuously for many thousands of years without replenishment., Comment: 7 pages, 5 figures

The generation of entanglement between distant atoms via single photons is the basis for networked quantum computing, a promising route to large-scale trapped-ion and trapped-atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the polarisation of the photons produced. We show that such `polarisation oscillation' effects can lead to severe loss of fidelity in the context of two-photon, polarisation encoded measurement-based remote entanglement schemes. It is always preferable to suppress these errors at source by minimising mirror ellipticity, but we propose two remedies for systems where this cannot be achieved. We conclude that even modest cavity birefringence can be detrimental to remote entanglement performance, to an extent that may limit the suitability of polarisation-encoded schemes for large-scale quantum networks., Comment: 18 pages, 8 figures

As integrated circuits have become progressively more complex, constrained random stimulus has become ubiquitous as a means of stimulating a designs functionality and ensuring it fully meets expectations. In theory, random stimulus allows all possible combinations to be exercised given enough time, but in practice with highly complex designs a purely random approach will have difficulty in exercising all possible combinations in a timely fashion. As a result it is often necessary to steer the Design Verification (DV) environment to generate hard to hit combinations. The resulting constrained-random approach is powerful but often relies on extensive human expertise to guide the DV environment in order to fully exercise the design. As designs become more complex, the guidance aspect becomes progressively more challenging and time consuming often resulting in design schedules in which the verification time to hit all possible design coverage points is the dominant schedule limitation. This paper describes an approach which leverages existing constrained-random DV environment tools but which further enhances them using supervised learning and reinforcement learning techniques. This approach provides better than random results in a highly automated fashion thereby ensuring DV objectives of full design coverage can be achieved on an accelerated timescale and with fewer resources. Two hardware verification examples are presented, one of a Cache Controller design and one using the open-source RISCV-Ariane design and Google's RISCV Random Instruction Generator. We demonstrate that a machine-learning based approach can perform significantly better on functional coverage and reaching complex hard-to-hit states than a random or constrained-random approach., Comment: 9 pages, 16 figures