Double Quantum Dots as Detectors of High-Frequency Quantum Noise in Mesoscopic Conductors

Abstract

We propose a measurement setup for detecting quantum noise over a wide frequency range using inelastic transitions in a tunable two-level system as a detector. The frequency-resolving detector consists of a double quantum dot which is capacitively coupled to the leads of a nearby mesoscopic conductor. The inelastic current through the double quantum dot is calculated in response to equilibrium and nonequilibrium current fluctuations in the nearby conductor, including zero-point fluctuations at very low temperatures. As a specific example, the fluctuations across a quantum point contact are discussed. PACS numbers: 73.50.Td, 73.20.Dx, Two-level systems (TLS) coupled to a dissipative environment are canonical model systems to study dephasing in quantum mechanics [1]. The reversed problem is a TLS that measures the characteristics of a specific environment. The transition rate for levels separated by an energy e is a measure of the spectral density of the fluctuations in the environment at a frequency f e͞h. Transitions are allowed when energy can be exchanged with the environment. Recently, two device structures were realized that can be used as tunable TLS. In a superconducting single electron transistor a Cooper pair [2] and in a double quantum dot (DQD) an electron [3] can make inelastic transitions between two discrete energy states. In this work we calculate the rate for inelastic transitions in a DQD coupled to an environment formed by a second mesoscopic device.Small electronic devices have interesting equilibrium and nonequilibrium noise properties which are nonlinear in frequency [4]. In equilibrium, a transition occurs going from low frequencies, where Johnson-Nyquist noise due to thermal fluctuations dominates, to high frequencies where quantum noise due to zero-point fluctuations (ZPF) prevails. When the device is voltage biased, nonequilibrium fluctuations can become dominant. These lead to shot noise in the current, which has been measured near zero frequency [5] and at several high-frequency values where ZPF become dominant [6]. The idea of using a mesoscopic device, quantum point contact (QPC), as an environment for another device, quantum dot, has successfully been used in the so-called "which-path" detector [7]: the dc shot-noise of the QPC modifies the transport properties of the dot, leading to dephasing. Here we propose a setup for studying the effect of broadband fluctuations on the inelastic rate in a TLS. This setup provides a frequencyresolved detection over a large frequency range of the fluctuations in mesoscopic systems. A wide frequency range requires that the frequency dependent impedance of the whole circuit is taken into account. Below, we first describe the basic properties of a DQD, then formulate transition probabilities in terms of the noise spectrum, followed by calculations where the specific environment is formed by a QPC.A DQD is a fully controllable TLS. The separation between levels e ϵ E L 2 E R , the tunnel rates across the left and right barriers, G L , G R , and the tu...

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