Quantum nanoelectromechanics with electrons, quasi-particles and Cooper pairs: effective bath descriptions and strong feedback effects

Abstract

Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, and how they can lead to a regime of strong electromechanical feedback, where despite a weak SET -oscillator coupling, the motion of the oscillator strongly effects the tunneling of the Cooper pairs. We show that in this regime, the oscillator is characterized by an energy-dependent effective temperature. Finally, we discuss the strong analogy between back-action effects of incoherent Cooperpair tunneling and ponderomotive effects in an optical cavity with a moveable mirror; in our case, tunneling Cooper pairs play the role of the cavity photons.

Self-consistent theory of molecular switching

“…25 It can also be traced to the "quantum" nature of the charge noise, i.e., a slight asymmetry between the charge noise at positive and negative frequencies. [32][33][34] As a result, the dynamics of the mode x becomes essentially classical, described by the Langevin equation, 14…”

Noise in a superconducting single-electron transistor resonator driven by an external field

“…In particular, as well as providing an additional source of noise for the resonator, the SSET can also act to provide an additional source of damping. [14][15][16][17][18] In these situations, this effective damping will have a significant effect on the noise properties of the resonator even when the resonator is strongly driven. Furthermore, the SSET can cause the total resonator damping of the resonator to become negative and hence the resonator can be driven into a self-oscillating laserlike state even in the absence of external driving.…”

“…Furthermore, the SSET can cause the total resonator damping of the resonator to become negative and hence the resonator can be driven into a self-oscillating laserlike state even in the absence of external driving. [14][15][16][17][18] In this section we review how the systematic response of the SSET can act as an amplitude-dependent damping of the resonator and present some simple analytic approximations before describing how this influences the cavity noise spectrum. We show that the calculation of charge noise presented in Sec.…”

“…Equation ͑34͒ is then reduced to the previously known effective damping. [16][17][18] This expression is valid in the limit, ⑀ J Ӷ⌫ and extends to all resonator frequencies 32 rather than just 0 Ӷ⌫. In Fig.…”

“…Such back-action dynamics have also received considerable attention in the context of a mesoscopic conductor used to investigate the behavior of a mechanical resonator. [6][7][8][9][10][11][12][13] One system that is of particular interest is that of a superconducting single-electron transistor ͑SSET͒ coupled to a resonator, either mechanical [14][15][16][17][18][19][20] or composed of a superconducting stripline. 21 The coherent transport through this device at the Josephson quasiparticle resonance 22,23 ͑JQP͒ allows a very low-noise current and, at the same time, the sensitivity of the SSET to charge means that the resonator-SSET coupling is significant.…”