Stability and collisions of moving semi-gap solitons in Bragg cross-gratings

We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system's spectrum contains no true bandgap, but only semi-gaps (which are gaps only with respect to one branch of the dispersion relation), that nevertheless support soliton families. Solely zero-velocity solitons were previously studied in this system, while current experiments cannot generate solitons with the velocity smaller than half the maximum group velocity. We find the semi-gaps for the moving solitons in an analytical form, and demonstrated that they are completely filled with (numerically found) solitons. Stability of the moving solitons is identified in direct simulations. The stability region strongly depends on the frustration parameter, which controls the difference of the present system from the usual model for the single BG. A completely new situation is possible, when the velocity interval for stable solitons is limited not only from above, but also from below. Collisions between stable solitons may be both elastic and strongly inelastic. Close to their instability border, the solitons collide elastically only if their velocities c1 and c2 are small; however, collisions between more robust solitons are elastic in a strip around c1=-c2.Comment: 16 pages, 7 figures, Physics Letters A, in pres

Nonlinear multilevel dynamics of a coupled SQUID ring-resonator system in the hysteretic regime

We consider the dynamical behavior of a strongly hysteretic SQUID ring coupled to a radio frequency resonator. By experiment we show that this system can display novel multiple level structures in its rf voltage-current characteristics which are solutions of the nonlinear equations of motion describing the system

An Ultra High Quality Factor Radio Frequency SQUID Magnetometer Based on a Liquid Helium Cooled Quartz Resonator

We discuss a technique for coupling a single weak link SQUID ring to a very high quality factor (Q) external resonator. For this purpose, we make use of a radio frequency (20MHz) quartz crystal compatible with liquid helium operation Knowing the equivalent circuit of the resonator, we have been able to design the proper inductive coupling between it resonator and the SQUID ring. We provide an experimental example of this system utilizing a niobium point contract ring coupled to a 4.2K quartz crystal with a loaded Q of 10(5). We consider the application of these narrow band systems to magnetometer arrays where it is essential that cross talk between elements in the arrays be minimised

Opposed (hammerhead) Bifurcations in the Resonant Lineshape of a Strongly Driven SQUID Ring - Tank Circuit System

In this paper we describe very unusual paired bifurcations which can appear in the resonance curve of a coupled SQUID ring-radio frequency (rf) tank circuit system when the rf flux at the ring is comparable to Fo (= h/2e). We demonstrate that the position of these bistabilities is controlled by the static magnetic flux Fxstat applied to the ring, with simple bistable regions being observed on the lower or upper side of the resonance when (for n integer) Fxstat is close to nFo or (n + 1/2) Fo, respectively. More interestingly, we show that for values of Fx close to (n ± 1/4) Fo this resonance exhibits bistability on both its lower and upper sides. We discuss this very unusual phenomenon in terms of the non-linear equation of motion for the coupled system

Microwave Induced Quantum Transitions in a SQUID Ring

In this paper we consider the interaction of a quantum-mechanical superconducting quantum interference device (SQUID) with a classical monochromatic electromagnetic (EM) field. We solve the time-dependent Schrödinger equation for the SQUID ring in this EM field. We demonstrate that non-perturbative transitions between the low-lying states of the ring, due to coherent multiphoton absorption processes, dominate, even when the single-photon energy is small compared with the energy separation between these states. We present experimental data on small-capacitance SQUID rings, interacting with microwave fields, which point to the existence of such non-perturbative transitions

Adiabatic Modulation of a SQUID Ring by an Electromagnetic Field

Closed access. This article was published in the Journal of Physics: Condensed Matter [© Institute of Physics] and the definitive version is available at: http://dx.doi.org/10.1088/0953-8984/10/44/004In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory