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The fluctuations and the distribution of the conductance peak spacings of a quantum dot in the Coulomb-blockade regime are studied and compared with the predictions of random matrix theory (RMT). The experimental data were obtained in transport measurements performed on a semiconductor quantum dot fabricated in a GaAs-AlGaAs heterostructure. It is found that the fluctuations in the peak spacings are considerably larger than the mean level spacing in the quantum dot. The distribution of the spacings appears Gaussian both for zero and for non-zero magnetic field and deviates strongly from the RMT-predictions.PACS numbers: 73.20. Dx,73.23.Hk,05.45.+b Advanced nanofabrication techniques have made it possible to confine small numbers of electrons electrostatically within the two-dimensional electron gas (2DEG) of a semiconductor heterostructure [1,2]. Both the electric charge and energy of such "quantum dots" are quantised and hence such structures are sometimes referred to as "artificial atoms" [3,4]. In transport measurements the charging of these electron islands with single electrons leads to the observation of periodic conductance oscillations in the Coulomb-blockade regime [1]. These reflect the electrostatic coupling of the quantum dot to its environment and, additionally, they contain information about the eigenenergies and eigenfunctions of the electrons in the dot. Due to irregularities in the electrostatic confinement potential and electron-electron interactions, the corresponding classical motion of the electrons in the quantum dot can be expected to be chaotic (nonintegrable) [5,6,7]. Consequently, recent experiments have considered the peak height distribution [8,9], parametric conductance correlations [9] and level statistics [10] of a quantum dot in the Coulomb-blockade regime to test the concepts developed for the quantum mechanical description of classically chaotic systems ("quantum chaos" [11,12]). In particular random matrix theory (RMT) 1

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We present an experimental study of the fluctuations of Coulomb blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon MOSFET structure using stacked gates. This permits variation of the number of electrons on the quantum dot without significant shape distortion. The ratio of charging energy to single particle energy is considerably larger than in comparable GaAs/AlGaAs quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single particle level spacing and thus clearly contradict the expectation of random matrix theory.PACS numbers: 73.23. Hk,05.45.+b,73.20.Dx The spectral properties of many quantum mechanical systems whose classical behavior is known to be chaotic are remarkably well described by the theory of random matrices (RMT) [1]. This has been experimentally confirmed, for example, in measurements of slow neutron resonances of nuclei [2] and in microwave reflection spectra of billiard shaped cavities [3]. Electron transport experiments performed on semiconductor quantum dots in the Coulomb blockade (CB) regime [4] provide a further possibility to check RMT predictions. The classical motion of electrons in these structures can be assumed to be chaotic due to an irregular potential landscape produced by impurities, an asymmetric confinement potential [5], and/or electron-electron interactions [6]. The transport properties of quantum dots are inherently related to their energy spectra and electronic wavefunctions and thus the connection with RMT is readily made [5,7].Indeed, experiments on the distribution of conductance peak heights of quantum dots in the Coulomb blockade regime have shown good agreement with the predictions of RMT [8,9]. On the other hand, the distribution of the CB peak spacings have been found to deviate from the expectations of RMT [10][11][12]. The results suggest that the peak spacings are not distributed according to the famous Wigner surmise. Furthermore, there is no indication of spin degeneracy which would result in a bimodal peak spacing distribution [12]. In Refs. [10,11] the fluctuations of the peak spacings are considerably larger than expected from RMT, whereas the experiments presented in Ref.[12] yield smaller peak spacing fluctuations, which, however, are still larger than those predicted by RMT.The deviations from the RMT predictions have been frequently interpreted as fluctuations in the charging energy. As the charging energy reflects the Coulomb interactions both between the electrons on the dot as well as between the dot and its environment, the dependence of the fluctuations on the interaction strength is of fundamental interest. Numerical studies suggest that the fluctuations are proportional to the charging energy rather than to the single particle level spacing [10,13,14]. This is also found theoretically for the c...

We have used ultracold atoms to characterize the magnetic field near the surface of copper conductors at room temperature carrying currents between 0.045 A and 2 A. In addition to the usual circular field we find an additional, 1000 − 10000 times smaller longitudinal field. The field changes its strength periodically with a period of 200 − 300 µm.