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IEEE Transactions on Magnetics

Controlled transfer of single charge carriers

C. Urbina, H. Pothier, P. Lafarge, P.F. Orfila, D. Esteve, Michel Devoret, Lambert J. Geerligs, V.F. Anderegg, P. A. M. Holweg, Johan E. Mooij

Published Mar 1, 1991• 30 citations
Publisher

Abstract

Two devices that allow the coherent transfer of single electrons are described. They are based on the electrostatic control of tunnel processes across ultrasmall normal tunnel junctions. When appropriate AC signals are applied to gates a current I=e*f is forced to flow through the devices. There are, however, fundamental differences in their principles which make the pump the only suitable candidate for the controlled transfer of cooper pairs. Although in these experiments the I=e*f relation was verified with only a 1% accuracy, more elaborate versions of these devices could be promising candidates for a current standard.

DOI
10.1109/20.133742

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•Jan 1, 2009•0 citations
Two devices that allow the coherent transfer of single electrons are described. They are based on the electrostatic control of tunnel processes across ultrasmall normal tunnel junctions. When appropriate AC signals are applied to gates a current I=ef is forced to flow through the devices. There are, however, fundamental differences in their principles which make the pump the only suitable candidate for the controlled transfer of cooper pairs. Although in these experiments the I=ef relation was verified with only a 1% accuracy, more elaborate versions of these devices could be promising candidates for a current standard.
Abstract A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an artificial two-level electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed1, 2, 3, 4. The Cooper-pair box has therefore been suggested5, 6, 7 as a candidate for a quantum bit or ‘qubit’—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single-Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non-adiabatically, bringing them into resonance. The resulting state—a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
We introduce and discuss a scheme for Cooper-pair pumping. The scheme relies on the coherent transfer of a superposition of charge states across a superconducting island and is realized by adiabatic manipulation of magnetic fluxes. Differently from previous implementations, it does not require any modulation of electrostatic potentials. We find a peculiar dependence of the pumped charge on the superconducting phase bias across the pump and that an arbitrarily large amount of charge can be pumped in a single cycle when the phase bias is $\ensuremath{\pi}$. We explain these features and their relation to the adiabatic theorem.
Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.
Quantum mechanics constrains conjugate observables from being simultaneously measurable with arbitrary precision. In a Josephson junction, these are the transferred electric charge and the quantum-mechanical phase difference between the superconducting domains. Which of them fluctuates determines the supercurrent: a dissipative trickle of single Cooper pairs in one limit, a coherent dissipationless flow in the other. Bridging both regimes in one device remained elusive because the Josephson and charging energies are fixed at fabrication. Here, we use the tunable tunnel junction of a scanning tunneling microscope at millikelvin temperature to vary their ratio continuously over many orders of magnitude. In this way, we monitor the smooth transition between incoherent and coherent Cooper pair flow in a single junction, revealing the quantum-to-classical transition in a controlled way.
This Thesis studies opportunities to create a quantum standard for the electric current with the help of tunnel junctions. We use two types of tunnel junctions: superconducting Josephson junctions, and NIS junctions where one of the electrodes is normal (N) and the other one superconducting (S). In both cases, tunnel junctions are employed in a single-electron transistor (SET) structure, which is used to transfer a controlled number k of electrons (e) with the repetition frequency f. The magnitude of the resulting current is thus I = kef. First, we study the Cooper pair sluice, where Josephson junctions are connected as two superconducting quantum interference devices (SQUID). A gate electrode is used to control the charge state of the superconducting island formed between the SQUIDs. The sluice is based on tuning the tunneling rates through the SQUIDs with local magnetic fluxes, which allows to control the direction of the charge transfer. Weak traces of current quantization can be observed up to above 1 nA, which is large enough current for many metrological purposes. However, the accuracy of the current is still far from what is required in metrology. We study also a new type of SQUID structure, the balanced SQUID, which could be used to improve the accuracy of the sluice or in, e.g., some quantum computing applications. Second, we employ NIS junctions in the hybrid (SINIS) single-electron transistor with superconducting leads and a normal-metal island. This structure can be used as the SINIS turnstile which lets electrons to flow one by one in the direction determined by the bias voltage. We report the first experimental results on the SINIS turnstile and two methods to improve the accuracy of the current: increasing the charging energy of the island or connecting the turnstile in a resistive environment. We also show that the SINIS turnstile can be used as an electronic radio-frequency refrigerator where tunneling processes cool the electron temperature of the normal-metal island.