Related papers: Quantized amplitudes in a nonlinear resonant elect…
An anharmonic oscillator when driven with a fast, frequency chirped voltage pulse can oscillate with either small or large amplitude depending on whether the drive voltage is below or above a critical value-a well studied classical…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…
A quantum coherent capacitor subject to large amplitude pulse cycles can be made to emit or reabsorb an electron in each half cycle. Quantized currents with pulse cycles in the GHz range have been demonstrated experimentally. We develop a…
The problem of resonant excitation of a harmonic oscillator the energy levels of which are slightly shifted under the action of a random potential is solved. It is shown that, in this case, there exists a threshold magnitude of the exciting…
Modelling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic…
A nonlinear resonant circuit comprising a SQUID magnetometer and a parallel capacitor is studied as a readout scheme for a persistent-current (PC) qubit. The flux state of the qubit is detected as a change in the Josephson inductance of the…
Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating…
In this report, we lay the foundation for amplitude noise and phase noise analysis in nonlinear devices. We build a theoretical framework that helps us to analyze extremely difficult problems which include both nonlinearity and noise of…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
Objective: To increase the impedance signal amplitude produced during neural activity using a novel approach of implementing a parallel resistor inductor capacitor (RLC) circuit across the current source used in electrical impedance…
We discover presence of a hitherto unexplored type of resonance in a parametrically excited Van der Pol oscillator. The oscillator also possesses a state of anti-resonance. In the weak non-linear limit, we explain how to practically get a…
We investigate a simple variation of the series RLC circuit in which anti-parallel diodes replace the resistor. This results in a damped harmonic oscillator with a nonlinear damping term that is maximal at zero current and decreases with an…
Oscillation and frequency modulation have been leveraged for applications in detection (or sensing), data processing, and telemetry. This work provides a theoretical analysis of oscillation phenomena with negative impedance implemented…
This article presents a novel method for studying RLC series circuits using two smartphones, one used as a signal generator and the other as an oscilloscope. We measure the voltage at the external resistor as a function of frequency when…
We calculate the noise spectrum of the output signal of a quantum detector during continuous measurement of a two-level system (qubit). We generalize the previous results obtained for the regime of high voltages (when $eV$ is much larger…
We have developed a system for contactless measurement of nonlinear conductivity in the radio-frequency band, and over a wide temperature range. A non-resonant circuit is used to electrically excite the sample, and the induced signal is…
It is known that placing a mechanical oscillator in a superposition of coherent states allows, in theory, a measurement of a linear force whose sensitivity increases with the amplitude of the mechanical oscillations, a uniquely quantum…
We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…