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arXiv:cond-mat/0604608 · Physical Review Letters

Using a Quantum Dot as a High-Frequency Shot Noise Detector

Eugen Onac, Franck Balestro, L. H. Willems van Beveren, Udo Hartmann, Yuli V. Nazarov, Leo P. Kouwenhoven

Published May 1, 2006• 133 citations
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Abstract

We present the experimental realization of a quantum dot (QD) operating as a high-frequency noise detector. Current fluctuations produced in a nearby quantum point contact (QPC) ionize the QD and induce transport through excited states. The resulting transient current through the QD represents our detector signal. We investigate its dependence on the QPC transmission and voltage bias. We observe and explain a quantum threshold feature and a saturation in the detector signal. This experimental and theoretical study is relevant in understanding the backaction of a QPC used as a charge detector.

DOI
10.1103/physrevlett.96.176601

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We present the experimental realization of a quantum dot (QD) operating as a high-frequency noise detector. Current fluctuations produced in a nearby quantum point contact (QPC) ionize the QD and induce transport through excited states. The resulting transient current through the QD represents our detector signal. We investigate its dependence on the QPC transmission and voltage bias. We observe and explain a quantum threshold feature and a saturation in the detector signal. This experimental and theoretical study is relevant in understanding the backaction of a QPC used as a charge detector.
Charge detection at microsecond time-scales has far reaching consequences in both technology and in our understanding of electron dynamics in nanoscale devices such as quantum dots. Radio-frequency superconducting single electron transistors (RF-SET) and quantum point contacts (QPC) are ultra sensitive charge sensors operating near the quantum limit. The operation of RF-SETs outside the superconducting gap has been a topic of study; the sub-gap operation, especially in the presence of large quantum fluctuations of quasiparticles remains largely unexplored, both theoretically and experimentally. We have investigated the effects of quantum fluctuations of quasiparticles on the operation of RF-SETs for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, sub-gap RF-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Such RF-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.\nWe have operated a QPC charge detector in a radio frequency mode that allows fast charge detection in a bandwidth of several megahertz. The noise limiting the sensitivity of the charge detector is not the noise of a secondary amplifier, but the non-equilibrium device noise of the QPC itself. The noise power averaged over a measurement bandwidth of about 10MHz around the carrier frequency is in agreement with the theory of photon-assisted shot noise. Frequency-resolved measurements, however show several significant discrepancies with the theoretical predictions. The measurement techniques developed can also be used to investigate the noise of other semiconductor nanostructures such as quantum dots in the Kondo regime.\nA study of the noise characteristics alone can not determine whether the device is operating at the quantum limit; a characterization of back action is also necessary. The inelastic current through a double quantum dot system (DQD) is sensitive to the spectral density of voltage fluctuations in its electromagnetic environment. Electrical transport studies on a DQD system electrostatically coupled to an SET shows qualitative evidence of back-action of SET. The design and fabrication of a few electron DQD device with integrated RF-SET and QPC charge sensors for the study of back action of the sensors and real-time electron dynamics in the DQD are also discussed.
We study theoretically transitions of a double quantum-dot qubit caused by nonequilibrium charge fluctuations in a nearby quantum point contact (QPC) used as a detector. We show that these transitions are related to the fundamental Heisenberg backaction associated with the measurement, and use the uncertainty principle to derive a lower bound on the transition rates. We also derive simple expressions for the transition rates for the usual model of a QPC as a mesoscopic conductor, with screening treated at the RPA level. Finally, numerical results are presented which demonstrate that the charge noise and shot noise backaction mechanisms can be distinguished in QPCs having nonadiabatic potentials. The enhanced sensitivity of the charge noise to the QPC potential is explained in terms of interference contributions similar to those which cause Friedel oscillations.
We derive an analytical expression for the backaction dephasing rate, which characterizes the disturbance induced by coupling with an environment containing a quantum dot detector (QDD). In this paper, we show in an explicit form that the charge noise induces backaction dephasing. In equilibrium, this backaction dephasing induced by the charge noise can be explained as a relaxation by an inelastic electron-electron scattering in Fermi-liquid theory. Unlike the quantum point contact, the backaction dephasing rate increases or decreases with the bias at low bias and finite-temperature condition. This behavior depends on the QDD energy level with respect to the Fermi energy and the asymmetry of the QDD coupling to the reservoirs. In the high bias voltage regime, the dephasing rate becomes insensitive to the bias because of the saturation of the charge noise.
Charge sensing with quantum point-contacts (QPCs) is a technique widely used in semiconductor quantum-dot research. Understanding the physics of this measurement process, as well as finding ways of suppressing unwanted measurement back-action, are therefore both desirable. In this article, we present experimental studies targeting these two goals. Firstly, we measure the effect of a QPC on electron tunneling between two InAs quantum dots, and show that a model based on the QPC’s shot-noise can account for it. Secondly, we discuss the possibility of lowering the measurement current (and thus the back-action) used for charge sensing by correlating the signals of two independent measurement channels. The performance of this method is tested in a typical experimental setup.
We have operated a quantum point contact (QPC) charge detector in a radio frequency (RF) mode that allows fast charge detection in a bandwidth of tens of megahertz. We find that the charge sensitivity of the RF-QPC is limited not by the noise of a secondary amplifier, but by non-equilibrium noise f the QPC itself. We have performed frequency-resolved measurements of the noise within a 10 MHz bandwidth around our carrier wave. When averaged over our bandwidth, we find that the noise is in good agreement with the theory of photon-assisted shot noise. Our measurements also reveal strong frequency dependence of the noise, asymmetry with respect to the carrier wave, the appearance of sharp local maxima that are correlated with mechanical degrees of freedom in the sample, and noise suppression indicative of many-body physics near the 0.7 structure.
We performed real-time observation of charge states in a double quantum dot (QD) by monitoring the current passing through an adjacent quantum point contact (QPC). The position of the QPC was chosen in such a way that the Coulomb coupling of the QPC to one QD is made stronger than to the other QD, so that the QPC current can clearly resolve the charge states of the double QD. With a response time of ∼200 µs, we also investigated the energy relaxation time T 1 of the double QD by applying rectangular voltage pulses to the double QD. We confirmed that T 1 can be made sufficiently longer than the response time of the QPC.