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arXiv:0810.2406 · Physical Review B

Time-resolved charge detection with cross-correlation techniques

Bruno Küng, Oliver Pfäffli, Simon Gustavsson, Thomas Ihn, K. Ensslin, M. Reinwald, W. Wegscheider

Published Jan 13, 2009• 18 citations
arXivHTMLPDF

Abstract

We present time-resolved charge-sensing measurements on a GaAs double quantum dot with two proximal quantum point-contact (QPC) detectors. The QPC currents are analyzed with cross-correlation techniques, which enable us to measure dot charging and discharging rates for significantly smaller signal-to-noise ratios than required for charge detection with a single QPC. This allows us to reduce the current level in the detector and therefore the invasiveness of the detection process and may help to increase the available measurement bandwidth in noise-limited setups.

DOI
10.1103/physrevb.79.035314

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We present time-resolved charge-sensing measurements on a GaAs double quantum dot with two proximal quantum point-contact (QPC) detectors. The QPC currents are analyzed with cross-correlation techniques, which enable us to measure dot charging and discharging rates for significantly smaller signal-to-noise ratios than required for charge detection with a single QPC. This allows us to reduce the current level in the detector and therefore the invasiveness of the detection process and may help to increase the available measurement bandwidth in noise-limited setups.
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.
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 report on charge sensing measurements of a GaAs semiconductor quantum dot device using a radio frequency quantum point contact (rf-QPC). The rf-QPC is fully characterized at 4K and millikelvin temperatures and found to have a bandwidth exceeding 20MHz. For single shot charge sensing, we achieve a charge sensitivity of ∼2×10−4e∕Hz referred to the neighboring dot’s charge. The rf-QPC compares favorably with rf single electron transistor electrometers and promises to be an extremely useful tool for characterizing and measuring semiconductor quantum systems on fast time scales.
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.
The dynamic capture of electrons in a semiconductor quantum dot (QD) by raising a potential barrier is a crucial stage in metrological quantized charge pumping. In this work, we use a quantum point contact (QPC) charge sensor to study errors in the electron capture process of a QD formed in a GaAs heterostructure. Using a two-step measurement protocol to compensate for 1/f noise in the QPC current, and repeating the protocol more than 106 times, we are able to resolve errors with probabilities of order 10−6. For the studied sample, one-electron capture is affected by errors in ∼30 out of every million cycles, while two-electron capture was performed more than 106 times with only one error. For errors in one-electron capture, we detect both failure to capture an electron and capture of two electrons. Electron counting measurements are a valuable tool for investigating non-equilibrium charge capture dynamics, and necessary for validating the metrological accuracy of semiconductor electron pumps.