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The current noise spectrum of a single-electron transistor (SET) coupled to a nano-mechanical resonator is calculated in the classical regime. Correlations between the charge on the SET island and the position of the resonator give rise to a distinctive noise spectrum which can be very different from that of the uncoupled SET. The current noise spectrum of the coupled system contains peaks at both the frequency of the resonator and double the resonator frequency, as well as a strong enhancement of the zero-frequency noise. The heights of the peaks are controlled by the strength of the coupling between the SET and the resonator, the damping of the resonator, and the temperature of the system.
We investigate the effect of a quantised vibrational mode on electron tunneling through a chain of three quantum dots. The outer dots are coupled to voltage leads, but the position of the central dot is not rigidly fixed. Motion of the central dot modulates the size of the tunneling barriers in opposite ways so that electron tunneling is correlated with the position of the oscillator. We treat the electronic part of the problem using a simple Coulomb-blockade picture, and model the vibration of the central dot as a quantum oscillator. We calculate the eigenspectrum of the system as a function of the energy level shift between the outer dots. Using a density matrix method, we include couplings to external leads and calculate the steady-state current through the device. The current shows marked resonances which correspond to avoided-le...
Comment: Submitted to New Journal of Physics: Special Issue "Mechanical Systems at the Quantum Limit"
Comment: Submitted to New Journal of Physics: Special Issue "Mechanical Systems at the Quantum Limit"
We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower amplitude noise than states of the same average amplitude excited by a pure harmonic drive; for sufficiently low thermal noise a sub-Poissonian resonator state can be produced. We also calculate the linewidth narrowing that occurs in the limit-cycle states, and show that while the minimum is set by direct phase diffusion, diffusion due to the optical spring effect can dominate if the cavity is not driven exactly at a side-band resonance.
In an electromechanical which-path device electrons travelling through an Aharonov-Bohm ring with a quantum dot in one of the arms are dephased by an interaction with the fundamental flexural mode of a radio-frequency cantilever, leading to a reduction in the visibilty of the interference fringes. However, at finite temperatures time-averaged measurement of the current leads to a fringe visibility which is reduced partly by dephasing of the electrons and partly by a thermal smearing effect. The balance between thermal smearing and dephasing predicted by a calculation depends very strongly on the choice of cantilever basis states used. The interaction between the cantilever and its environment is expected to select the coherent state basis for the cantilever and hence lead to a dephasing rate which is substantially lower than that whi...
Comment: Brief Review, to appear in the American Journal of Physics, http://www.kzoo.edu/ajp/
We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium which persist for times of order t...
We analyze the spectral properties of a resonator coupled to a superconducting single electron transistor (SSET) close to the Josephson quasiparticle resonance. Focussing 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 phas...
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