Measurements of higher-order noise correlations in a quantum dot with a finite bandwidth detector

Abstract

We present measurements of the fourth and fifth cumulants of the distribution of transmitted charge in a tunable quantum dot. We investigate how the measured statistics is influenced by the finite bandwidth of the detector and by the finite measurement time. By including the detector when modeling the system, we use the theory of full counting statistics to calculate the noise levels for the combined system. The predictions of the finite-bandwidth model are in good agreement with measured data. PACS numbers:Current fluctuations in mesoscopic systems have been extensively studied due to the extra information they give in comparison to measurements of the mean current [1]. The focus has traditionally been on investigations of the shot-noise, which for classical systems arises due to the discreteness of the electron charge. The theory of full counting statistics (FCS) was introduced as a new way of examining current fluctuations [2]. With the FCS, fluctuations are studied by counting the number of electrons that pass through a conductor within a fixed period of time. This gives direct access to the probability distribution function p t0 (N ), which is the probability that N electrons are transferred within a time interval of length t 0 . From the distribution function, not only the shot noise but also correlations of higher order can be calculated.The third moment of a tunneling current has been shown to be independent of the thermal noise [3,4], thus making it a potential tool for investigating electronelectron interactions even at elevated temperatures. Higher order moments in strongly interacting systems are predicted to depend heavily on both the conductance [5] and on the internal level structure [6] of the system. Determining higher order moments may therefore give a more complete characterization of the electron transport process. This can be of importance for realizing measurements of electron correlation and entanglement effects in quantum dots [7,8].Experimentally, the third moment of the current distribution function has been measured for a tunnel junction [9] as well as for a single quantum dot (QD) [10,11] and a double QD [3]. In quantum optics, higher order moments are routinely measured in order to study entanglement and coherence effects of the electromagnetic field [12]. Here, we set out to measure the fourth and fifth cumulant of the distribution function for charge transport * Electronic address: simongus@phys.ethz.ch through a QD.In general, experimental measurements of FCS for electrons are difficult to achieve due to the need of a sensitive, high-bandwidth detector capable of resolving individual electrons [13,14,15]. However, a more fundamental complication with the measurements is that most forms of the FCS theory assume the existence of (1) a detector with infinite bandwidth and (2) infinitely long data traces. Since no physical detector can fulfill these requirements, every experimental realization of the FCS will measure a distribution which is influenced by the properties of the detector....

High-order cumulants in the counting statistics of asymmetric quantum dots

“…6,7 With the use of a quantum point contact ͑QPC͒ as a noninvasive charge detector with sufficiently fast time response, FCS became experimentally feasible in QD physics. [8][9][10][11] In a measurement of the fourth and fifth cumulant complex behavior as a function of asymmetry and integration time with local minima was found. 11 A significantly improved experimental technique has made the extraction of very high-order cumulants possible, revealing an oscillating behavior as function of integration time that strongly increases with the order of the moment.…”

“…[8][9][10][11] In a measurement of the fourth and fifth cumulant complex behavior as a function of asymmetry and integration time with local minima was found. 11 A significantly improved experimental technique has made the extraction of very high-order cumulants possible, revealing an oscillating behavior as function of integration time that strongly increases with the order of the moment. 12,13 Such oscillations are also predicted theoretically in quantum optics 15 and particle physics.…”

Conditional statistics of electron transport in interacting nanoscale conductors

“…Results (1) and (2) follow from (3). The function H (0, χ) generates the current cumulants of the QD 27 (the first few of which have been experimentally verified 22,29 ), and H (l, 0) generates the current cumulants of the QPC 28 . The full QPC current distribution was predicted to have an elliptical shape 28 :…”

Wideband Detection of the Third Moment of Shot Noise by a Hysteretic Josephson Junction

“…The noise correlations were observed up to the third order over a bandwidth of a few tens of kHz. The latest remarkable results on observation of the fourth and the fifth moments of current through a quantum dot [9] demonstrated on-chip detection of FCS in the low frequency regime. As regards to highfrequency on-chip detectors of non-Gaussian noise, a Josephson junction (JJ) appears to be a very attractive one according to various theoretical predictions [10 -13].…”