We define the “maximally integrable” isotropic oscillator on I CP and discuss its various properties, in particular, the behaviour of the system with respect to constant magnetic field. We show that the properties of the oscillator on I CP qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the “axially symmetric” system which is locally equivalent to the oscillat...

We theoretically describe the weak measurement of a two-level system qubit and quantify the degree to which such a qubit measurement has a quantum nondemolition QND character. The qubit is coupled to a harmonic oscillator, which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is in...

We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number...

We derive the conditions for establishment of a transverse supermode in a free-electron laser ~FEL! oscillator, and demonstrate the evolution of a supermode by means of a three-dimensional nonlinear code. Both the analytical formulation and the numerical code are based on coupled-mode theory. The oscillator supermode is a combination of transverse modes that keeps its field profile at any point...

The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible onl...