Spectral properties of a resonator driven by a superconducting single-electron transistor

Abstract

We analyze the spectral properties of a resonator coupled to a superconducting single-electron transistor ͑SSET͒ close to the Josephson quasiparticle resonance. Focusing on the regime where the resonator is driven into a limit-cycle state by the SSET, we investigate the behavior of the resonator linewidth and the energy relaxation rate which control the widths of the main features in the resonator spectra. We find that the linewidth becomes very narrow in the limit-cycle regime, where it is dominated by a slow phase-diffusion process, as in a laser. The overall phase-diffusion rate is determined by a combination of direct phase diffusion and the effect of amplitude fluctuations which affect the phase because the resonator frequency is amplitude dependent. For sufficiently strong couplings we find that a regime emerges where the phase diffusion is no longer minimized when the average resonator energy is maximized. Finally we show that the current noise of the SSET provides a way of measuring both the linewidth and energy relaxation rate.

Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

“…30,[47][48][49][50][51][52][53][54][55][56][57][58][59][60] Due to the many oscillator states participating in transport the matrix representations of the involved operators are of large dimensions and it is necessary to resort to numerics. We demonstrate the numerical stability of our recursive algorithm up to very high cumulant orders (∼ 100) and show how oscillations of the cumulants can be used to extract information about the analytic structure of the cumulant generating function.…”

Process tomography for systems in a thermal state

“…This includes systems in some general mixed states and in particular in thermal states. In this respect, we hope that the present method could be beneficial in various experimental systems, such as nanoelectromechanical systems (NEMS) [15,16] and mesoscopic systems.…”

“…where f abc and g abc determine the structure of the basis. Substituting equation (14)- (16) in equation (13) we obtain…”

Coherent properties of nanoelectromechanical systems

“…55 Many groups focused their attention on this regime, employing rate equations to study transport phenomena such as the Franck-Condon blockade, super-Poissonian shot noise, 9,10,12,24 and even peculiar effects such as subPoissonian out-of-equilibrium vibron distributions. 28,29,33,56,57 In the opposite regime of slow vibrations γ 1, electrons are extremely sensitive to the position of the oscillator, which can be treated in a semiclassical approximation. 26,30,31,58 Indeed, Mozyrsky et al have shown 25 that it is the onset of a semiclassical Langevin dynamics.…”

“…23 A great variety of NEMS setups have been investigated theoretically. Typically, the electronic part is composed of a semiconducting, [24][25][26][27][28][29] normal, [30][31][32] or superconducting [33][34][35][36] single quantum dot. 37 Double-dot setups have been studied as well.…”