Synthetic frequency dimensions in dynamically modulated ring resonators

Three-frequency parametric amplification in magneto-inductive ring resonators

Parametric amplification of magneto-inductive (MI) waves propagating in magnetically coupled chains of nonlinear L–C resonators is studied. Analysis is first presented for a three-frequency travelling wave scheme in which the signal, idler and pump all propagate as MI waves. The effect of de-coupling the idlers is then considered and it is shown that this configuration relaxes the standard phas...

Frequency dependence of the magnetic response of split-ring resonators

Haldane quantum Hall effect for light in a dynamically modulated array of resonators: supplementary material

The spectrum εn has a Brillouin-zone like structure with Ω the width of the first zone, i.e. for any solution |un(t)〉 of quasienergy εn, and any integer m, exp(imΩt)|un(t)〉 is also a solution, with eigenvalue εn + mΩ. The states |un(t)〉 form a Hilbert space of T-periodic functions. The inner product in this space can be defined starting from the standard bra-ket inner product 〈•|•〉 for time-ind...

Haldane quantum Hall effect for light in a dynamically modulated array of resonators

Topological insulators have attracted abundant attention for a variety of reasons—notably, the possibility for lossless energy transport through edge states “protected” against disorder. Topological effects such as the quantum Hall state can be induced through a gauge field, which is, however, hard to create in practice, especially for charge-neutral particles. One way to induce an effective ga...

Gravity in Dynamically Generated Dimensions

A theory of gravity in d+1 dimensions is dynamically generated from a theory in d dimensions. As an application we show how N dynamically coupled gravity theories can reduce the effective Planck mass. PACS numbers: 11.10Kk, 04.50+h Typeset using REVTEX ∗Electronic address: [email protected] 1