Parametric resonance in tunable superconducting cavities

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the SQUID attached to the cavity, and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum statistical properties of the noise are addressed such as squeezing spectra, second order coherence, and two-mode entanglement.Comment: 25 pages, 17 figure

The Schr\"odinger-Langevin equation with and without thermal fluctuations

The Schr\"odinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SL equation ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SL equation as an effective open quantum system formalism is possible and discuss some of its limitations.Comment: 38 pages, 31 figure

Analysis and design of wideband voltage controlled oscillators using self-oscillating active inductors.

Voltage controlled oscillators (VCOs) are essential components of RF circuits used in transmitters and receivers as sources of carrier waves with variable frequencies. This, together with a rapid development of microelectronic circuits, led to an extensive research on integrated implementations of the oscillator circuits. One of the known approaches to oscillator design employs resonators with active inductors electronic circuits simulating the behavior of passive inductors using only transistors and capacitors. Such resonators occupy only a fraction of the silicon area necessary for a passive inductor, and thus allow to use chip area more eectively. The downsides of the active inductor approach include: power consumption and noise introduced by transistors. This thesis presents a new approach to active inductor oscillator design using selfoscillating active inductor circuits. The instability necessary to start oscillations is provided by the use of a passive RC network rather than a power consuming external circuit employed in the standard oscillator approach. As a result, total power consumption of the oscillator is improved. Although, some of the active inductors with RC circuits has been reported in the literature, there has been no attempt to utilise this technique in wideband voltage controlled oscillator design. For this reason, the dissertation presents a thorough investigation of self-oscillating active inductor circuits, providing a new set of design rules and related trade-os. This includes: a complete small signal model of the oscillator, sensitivity analysis, large signal behavior of the circuit and phase noise model. The presented theory is conrmed by extensive simulations of wideband CMOS VCO circuit for various temperatures and process variations. The obtained results prove that active inductor oscillator performance is obtained without the use of standard active compensation circuits. Finally, the concept of self-oscillating active inductor has been employed to simple and fast OOK (On-Off Keying) transmitter showing energy eciency comparable to the state of the art implementations reported in the literature

A time-variant analysis of the 1/f^(2) phase noise in CMOS parallel LC-Tank quadrature oscillators

This paper presents a study of 1/f/sup 2/ phase noise in quadrature oscillators built by connecting two differential LC-tank oscillators in a parallel fashion. The analysis clearly demonstrates the necessity of adopting a time-variant theory of phase noise, where a more simplistic, time-invariant approach fails to explain numerical simulation results even at the qualitative level. Two topologies of 5-GHz parallel quadrature oscillators are considered, and compact but nevertheless highly general, closed-form formulas are derived for the phase noise caused by the losses in the LC-tanks and by the noisy currents in the MOS transistors. A large number of spectreRF simulations, covering a wide range of working conditions for the oscillators, is used to validate the theoretical analysis