Picosecond coherent electron motion in a silicon single-electron source

Abstract

Understanding ultrafast coherent electron dynamics is necessary for application of a single-electron source to metrological standards 1 , quantum information processing 2 , including electron quantum optics 3 , and quantum sensing 4,5 .While the dynamics of an electron emitted from the source has been extensively studied 6-11 , there is as yet no study of the dynamics inside the source. This is because the speed of the internal dynamics is typically higher than 100 GHz, beyond state-of-the-art experimental bandwidth 2 . Here, we theoretically and experimentally demonstrate that the internal dynamics in a silicon singleelectron source comprising a dynamic quantum dot can be detected, utilising a resonant level with which the dynamics is read out as gate-dependent current oscillations. Our experimental observation and simulation with realistic parameters show that an electron wave packet spatially oscillates quantum-coherently at ∼ 200 GHz inside the source. Our results will lead to a protocol for detecting such fast dynamics in a cavity and offer a means of engineering electron wave packets 12 . This could allow high-accuracy current sources [13][14][15][16] , high-resolution and high-speed electromagnetic-field sensing 4 , and high-fidelity initialisation of flying qubits 17,18 .Owing to recent demonstrations of high-accuracy GHz operation 13-16 , a single-electron pump with a tunable-barrier quantum dot (QD) becomes promising for application to ondemand single-electron sources 1 . Because of the fast dynamic movement of the QD, there can occur nontrivial electron dynamics, such as non-adiabatic excitation 19 and subsequent coherent time evolution. While the non-adiabatic excitation could degrade the pumping accuracy, a spatial movement of an electron wave packet due to the coherent time evolution can be used for engineering a wave packet emitted from the QD 12 , which could make possible electron quantum optics experiments and high-speed quantum sensing with high resolution.In addition, understanding of the fast electron dynamics could offer insight into quantum computing with QDs. However, the existing standard measurement technique 20-22 does not have enough bandwidth to detect fast dynamics beyond 100 GHz. In order to overcome the limitation and detect the fast dynamics in the QD, we use a temporal change in a tunnel rate between a resonant level in a tunnel barrier and a QD, which is induced by the dynamic change of the QD potential.First of all, we explain how coherent oscillations of an electron in a single-electron pump 2 occur. A single-electron pump with a tunable-barrier QD consists of the entrance (Fig. 1a, left) and exit (right) potential barriers, formed by applying gate voltages V ent and V exit , respectively 23 . An AC voltage V ac (t) with frequency f in is added to dynamically tune the entrance barrier. The QD energy level is also tuned owing to the cross coupling. When the energy level E qd n (n = 1, 2, · · ·) of the QD with n electrons is lower than the Fermi level E f , electrons can be load...

Unusual Quantum Transport Mechanisms in Silicon Nano-Devices

“…Hence, the mainstay of these experiments relies on the ability to obtain a synchronized control of all the tunneling rates; the ones that control the movement of electrons from the source to the ones of the levels of the localized state (i.e., Γ in,i ) and the ones related to the movement of electrons from the localized state to the drain (i.e., Γ out,i ) [ 12 , 13 ]. Of course, the different relaxation rates internal to the localized state will also play a fundamental role in these experiments [ 12 , 13 , 15 , 25 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ]. Here, it is important to mention that these experiments are mostly performed with source-drain bias at 0 V or in a region for which changes in the values of the source-drain bias are non-influent [ 12 , 13 , 14 , 15 ], i.e., the situation has given rise to the assumption that these pumping experiments represent a violation of an ideal definition of Ohm’s law [ 38 ].…”

“…However, as soon as the E C of a QD increase to a value like the ones observed naturally in isolated single atom systems, for example by electrostatic confinements [ 14 , 47 ], these errors can also be suppressed in QDs electron pumps operating at temperatures ~4.2 K [ 14 , 15 ]. Another mechanism of errors that can affect single electron pumps, when they operate slightly above the 100 MHz frequencies of excitation, is the one related to non-adiabatic effects [ 45 , 48 ]. These errors are related to the poor efficiency in the achievement of the second step of the pumping cycle, as described in Figure 7 b, i.e., the isolation step.…”

“…Another mechanism of errors that can affect single electron pumps, when they operate slightly above the 100 MHz frequencies of excitation, is the one related to non-adiabatic effects [ 45 , 48 ]. These errors are related to the poor efficiency in the achievement of the second step of the pumping cycle, as described in Figure 7 b, i.e., the isolation step.…”

“…As such, it is important to outline that the high performances observed in SAP’s are linked to the indirect band gap properties characteristic of silicon materials. It is also important to associate the non-adiabatic effects observed for f = 1/ τ between 100 MHz [ 48 ] and a few GHz [ 45 ] to a recent set of results hinting to the ability of studying the ultra-fast coherent dynamics of electrons in highly reproducible silicon CMOS compatible devices [ 45 ]. The alternative way to operate a SAP described above can be relatively error-free, unless these systems are excited to frequencies considerably higher than the GHz ones [ 12 , 13 ].…”

“…For a system where a QD pump is operating at ultra-fast frequencies of excitations (up to 3.55 GHz), it has been shown that the ideal behavior of the pump can sometimes be affected by errors that appear when an impurity-trap state can compete with the main QD in the capture and in the emission of the electrons [ 15 ]. Note that the eventual presence of impurity-trap states in the gate stack of silicon devices is a well-known fact [ 1 , 4 , 45 ]. This novel frequency dependent mechanism [ 15 ], has not been completely explained, and it is a reminder that for silicon CMOS compatible technology, although extremely controlled and reliable [ 4 , 5 ], it is still possible to observe some unexpected behaviors.…”