Quantum Dynamics of a Resonator Driven by a Superconducting Single-Electron Transistor: A Solid-State Analogue of the Micromaser

Abstract

We investigate the behavior of a quantum resonator coupled to a superconducting single-electron transistor tuned to the Josephson quasiparticle resonance and show that the dynamics is similar in many ways to that found in a micromaser. Coupling to the SSET can drive the resonator into non-classical states of self-sustained oscillation via either continuous or discontinuous transitions. Increasing the coupling further leads to a sequence of transitions and regions of multistability.PACS numbers: 85.85.+j, 85.35.Gv, 74.78.Na Systems where a mesoscopic conductor such as a single-electron transistor is coupled to a nanomechanical resonator have been studied intensively because the current through the conductor can be extremely sensitive to the motion of the resonator and hence may be used to monitor its position with almost quantum-limited precision [1,2,3,4]. Furthermore, where either the coupling between the electrons and the resonator is non-linear [5] or the electronic transport occurs via a resonance [4], dynamic instabilities in the resonator can occur leading to self-sustained oscillations. The way a nanomechanical resonator can be driven into states of finite amplitude oscillation by successive interactions with a current of electrons in a conductor parallels the behavior of quantum optical systems, such as the micromaser, in which an electromagnetic cavity is pumped by interactions with a steady stream of individual two-level atoms [6]. This contrasts with a standard laser (a nanomechanical version of which was envisioned in [7]) where an oscillator interacts simultaneously with many two-level systems.In a superconducting single-electron transistor (SSET) transport can occur via resonant processes involving both coherent motion of Cooper pairs and incoherent quasiparticle tunneling, the simplest of which is the Josephson quasiparticle (JQP) resonance [8]. In the vicinity of a JQP resonance, the dynamics of a resonator coupled linearly to the SSET is very sensitive to the bias point [3,4,9]. For bias points on one side of the resonance, the SSET acts on the resonator like a thermal bath and its current can monitor the position of the resonator with exquisite sensitivity. In contrast, biasing on the opposite side of the JQP resonance can drive the resonator into states of self-sustained oscillation [4].In this Letter we explore the quantum dynamics of a resonator coupled to a SSET and show that it is analogous to that of a micromaser. Less noisy than a laser, a micromaser [6,10] can generate number-squeezed states of the cavity and exhibits not a single threshold transition, but a series of transitions between different dynamical states. Although the SSET-resonator system and micromaser differ in the details of the interactions between their respective sub-components, we find a num- ber of important similarities in their dynamics, many of which first arise when the resonator is sufficiently fast to match the time-scale of the electrical transport. Previous theoretical studies of this system have concentrat...

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