Evergon Serial Number Generator


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Evergon Serial Number Generator

an electron pulse is launched from the left ohmic contact into the quantum wire containing initially n=28 channels. upon propagation, this charge pulse decomposes onto the n=28 eigenmodes (plasmon modes) due to coulomb interaction. when this pulse passes through the qpc0, only one channel is transmitted, as shown in fig. 3c. after the passage, the electron pulse continues its propagation along the quantum wire containing again the same number n of available channels as before the passage through the selection qpc0. assuming a non-adiabatic passage, the charge pulse should instantaneously fractionalise into a fast plasmon mode and n1 slow modes. very surprisingly, this is not the case. time-resolved measurements of the charge pulse propagation through qpc1, qpc2 and qpc3 allow us to determine the average speed of the charge pulse after passing through the selection qpc0, as shown in fig. 3b, d.

the finite width of the potential barriers between the qpcs leads to a reduction of the velocity of the pulse as compared to the situation where the electrons are transferred across an infinitely narrow potential barrier. the width of the potential barriers between qpcs is given by the effective distance of the qpcs, which depends on the potential setting of the channel selection and potential pick-up qpcs. the transmission probability through the channel selection and potential pick-up qpcs depends on the respective gate voltage setting. to obtain a quantitative model, we first assume that the potential barriers are infinitely narrow. in this case, the transmission probability through the channel selection and potential pick-up qpcs is given by the transmission probability of a channel with a confining potential v~vb, where the qpcs are open. for this situation, we obtain a velocity of the pulse of vp=1.44*104m/s. to obtain a quantitative model, we now include the finite width of the potential barriers between the qpcs by calculating the transmission probability through the respective qpcs. from the measured transmission probabilities of the channel selection and potential pick-up qpcs (c.f. supplementary note 1), we obtain the effective distance of the qpcs. the transmission probabilities of the channel selection and potential pick-up qpcs are determined by the respective gate voltage settings. in order to take into account the influence of the finite width of the potential barriers between the qpcs, we calculate the transmission probability through the channel selection and potential pick-up qpcs for a range of gate voltages. the transmission probability through the channel selection and potential pick-up qpcs obtained from these calculations is then used to model the evolution of the pulse of a self-consistent calculation. the results of these calculations are plotted in fig. 4a. as the gate voltage is increased, the velocity of the pulse decreases. this is due to the increasing impact of the finite width of the potential barriers on the pulse propagation velocity. in the limit of an infinitely narrow potential barrier, the pulse velocity is given by the slope of the velocity of a single channel, which is 1.44104m/s. for the situation of an one-channel qpc, the pulse velocity is given by the slope of the blue solid line in fig. 3d. this corresponds to the result of a self-consistent calculation for a tomonagaluttinger liquid. for the situation of a two-channel qpc, the pulse velocity is given by the red solid line in fig. this is the result of a self-consistent calculation for a tomonagaluttinger liquid with repulsive coulomb interactions. as can be seen, the velocity obtained in the self-consistent calculation agrees well with the velocity that is obtained from the measurement. the inset in fig. 4a shows the pulse velocity as a function of the number of channels. the black dashed line corresponds to the non-interacting fermi liquid. the blue solid line corresponds to the self-consistent calculation for a tomonagaluttinger liquid and the red solid line corresponds to the self-consistent calculation for a tomonagaluttinger liquid with repulsive coulomb interactions. the error bars for the self-consistent calculation are derived from the propagation of the uncertainty of the parameter-free velocity model. the inset also shows the gate voltage at which the velocity of fig.

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