Multi-cavity photonic systems, known as photonic molecules (PMs), are ideal multi-well potential building blocks for advanced quantum and nonlinear optics [1][2][3][4]. A key phenomenon arising in double well potentials is the spontaneous breaking of the inversion symmetry, i.e. a transition from a delocalized to two localized states in the wells, which are mirror images of each other. Although few theoretical studies have addressed mirror-symmetry breaking in micro and nanophotonic systems [5][6][7][8][9], no experimental evidence has been reported to date. Thanks to the potential barrier engineering implemented here, we demonstrate spontaneous mirror-symmetry breaking through a pitchfork bifurcation in a PM composed of two coupled photonic crystal nanolasers. Coexistence of localized states is shown by switching them with short pulses. This offers exciting prospects for the realization of ultra-compact, integrated, scalable optical flip-flops based on spontaneous symmetry breaking. Furthermore, we predict such transitions with few intracavity photons for future devices with strong quantum correlations.Spontaneous symmetry breaking (SSB) unifies diverse physical mechanisms through which a given symmetric system ends up in an asymmetric state [10]. It explains many central questions from particle and atomic physics to nonlinear optics (the Goldstone boson and the Higgs mechanism [11,12], phase transitions in BoseEinstein condensates -BECs- [13,14], metamaterials [15], bifurcations in lasers [16,17], photorrefractive media [18], to mention just a few). A paradigmatic symmetry in this context is given by reflection in a double-well potential (DWP), as it is the case of pyramidal molecules (e.g. ammonia) [19]: SSB dictates whether the state of a system will be delocalized or, in turn, confined within either well. In photonics, such a mechanism is possible provided the third order nonlinearities overcome photon tunneling [20]. In this work we experimentally show SSB in a photonic molecule (PM) given by two evanescently coupled photonic crystal (PhC) nanolasers. Switchable localized modes with broken mirror-symmetry will be demonstrated herein. This can be prospected as a nanoscale version of a laser flip-flop [21]; the memory is pumped incoherently, set and reset can be induced with positive pulses and there is no coherent driving beam to bias the device, as in conventional bistable cavities. This paves the way for the realization of ultra-small flip-flop optical memories based on SSB.We represent the PM as a DWP, symmetric with respect to the inversion plane. We describe the dynamics in terms of the complex amplitudes of the photonic field at the left (ψ L ) and right (ψ R ) sites, |ψ| 2 being photon number. A finite potential barrier leads to a tunneling rate K. We further consider a local (nonlinear) interaction U |ψ L,R | 2 , and a lifetime τ due to losses. SSB instabilities occur as long as K is lower than a critical value K c (|K| < |K c |), with |K c τ | ∼ |U | · |ψ| 2 [22]. In the case of our PM laser, |ψ| 2...

The present B → πK data is studied in the context of the standard model (SM) and with new physics (NP). We confirm that the SM has difficulties explaining the B → πK measurements. By adopting an effective-lagrangian parametrization of NP effects, we are able to rule out several classes of NP. Our model-independent analysis shows that the B → πK data can be accommodated by NP in the electroweak penguin sector.PACS numbers: 13.25. Hw, 11.30.Er, 12.15Ff, 14.40.Nd The B-factories BaBar and Belle have measured (most of) the branching ratios and CP asymmetries for the various B → ππ and B → πK decays, and these can be used to search for physics beyond the Standard Model (SM). By using flavor SU(3) symmetry to relate these processes [1,2,3,4,5,6,7], several analyses were able to constrain the SM parameters, and to look for signs of New Physics (NP). The advantage of this approach is that one takes into account a large number of processes. The disadvantage is that one has to deal with unknown effects related to the breaking of SU(3) symmetry. Also, B → ππ decays involve the quark-level processesb →dqq (q = u, d), while B → πK receives contributions fromb →sqq. If there is NP, it could affectb →d andb →s processes differently.For this reason, there are advantages to considering B → πK decays alone. As we will see, these processes contain enough information to constrain the SM parameters. Within the diagrammatic approach [8], the amplitudes for the four B → πK decays can be written in terms of seven diagrams: the color-favored and color-suppressed tree amplitudes T ′ and C ′ , the gluonic penguin amplitudes P ′ and P ′ uc , the color-favored and color-suppressed electroweak penguin amplitudes P In Ref.[8], the relative sizes of the amplitudes were roughly estimated aswhereλ ∼ 0.2. These estimates are expected to hold approximately in the SM. Thus, to O(λ), we can ignore all diagrams but P ′ , T ′ and P ′ EW in our B → πK amplitudes. We will perform a fit of the present B → πK data -the goodness or badness of the fit should not be much affected by the inclusion of the smaller amplitudes.The four amplitudes can then be written aswhere we have explicitly written the dependence on the weak phase (including the minus sign from V * tb V ts [P ′ ]), while the amplitudes contain strong phases. (The phase information in the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix is conventionally parametrized in terms of the unitarity triangle, in which the interior (CPviolating) angles are known as α, β and γ [9].)We have one additional piece of information: within the SM, to a good approximation, the diagram P ′ EW can be related to T ′ using flavor SU(3) [10]:Here, the c i are Wilson coefficients [11] andWith the above relation, the B → πK observables contain five theoretical parameters: |P ′ |, |T ′ |, β, γ, and one relative strong phase, δ. The phase β can be taken from the measurement of sin 2β in B 0 d (t) → J/ψK S : sin 2β = 0.726 ± 0.037 [12], leaving four theoretical unknowns. However, there are a total of nine B → πK mea...

We demonstrate a large tuning of the coupling strength in Photonic Crystal molecules without changing the inter-cavity distance. The key element for the design is the "photonic barrier engineering", where the "potential barrier" is formed by the air-holes in between the two cavities. This consists in changing the hole radius of the central row in the barrier. As a result we show, both numerically and experimentally, that the wavelength splitting in two evanescently-coupled Photonic Crystal L3 cavities (three holes missing in the ΓK direction of the underlying triangular lattice) can be continuously controlled up to 5× the initial value upon ∼ 30% of hole-size modification in the barrier. Moreover, the sign of the splitting can be reversed in such a way that the fundamental mode can be either the symmetric or the anti-symmetric one without altering neither the cavity geometry nor the inter-cavity distance. Coupling sign inversion is explained in the framework of a Fabry-Perot model with underlying propagating Bloch modes in coupled W1 waveguides.

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In this paper we present a system, AutoMashUpper, for making multi-song music mashups. Central to our system is a measure of "mashability" calculated between phrase sections of an input song and songs in a music collection. We define mashability in terms of harmonic and rhythmic similarity and a measure of spectral balance. The principal novelty in our approach centres on the determination of how elements of songs can be made fit together using key transposition and tempo modification, rather than based on their unaltered properties. In this way, the properties of two songs used to model their mashability can be altered with respect to transformations performed to maximize their perceptual compatibility. AutoMashUpper has a user interface to allow users to control the parameterization of the mashability estimation. It allows users to define ranges for key shifts and tempo as well as adding, changing or removing elements from the created mashups. We evaluate AutoMashUpper by its ability to reliably segment music signals into phrase sections, and also via a listening test to examine the relationship between estimated mashability and user enjoyment.