M. H. Devoret

Adjustable nanofabricated atomic size contacts

Metallic point contacts and tunnel junctions with a small and adjustable number of conduction channels have been obtained in the last few years using scanning tunneling microscope and break junction techniques. For conventional break junctions, the reported drift of the interelectrode spacing in the tunnel regime is typically of the order of 0.5 pm/min (1 pm=10−12 m). We have nanofabricated break junctions which display a drift smaller than 0.2 pm/h. The improvement results from the scaling down by two orders of magnitude of the device dimensions. We describe the nanofabrication process, which can be adapted to most metals. We have performed measurements on Al, Cu, and Nb devices. The results illustrate the ability of the technique to explore phenomenalike conductance quantization and two level fluctuations. These new adjustable atomic size contacts and tunnel junctions can be integrated in complex circuits.

Evidence for Saturation of Channel Transmission from Conductance Fluctuations in Atomic-Size Point Contacts

Metallic contacts consisting of only a few atoms can be obtained using scanning tunneling microscopy or mechanically controllable break junction [1] techniques. The electrical conductance through such contacts is described in terms of electronic wave modes by the Landauer-Buttiker formalism [2]. Each of the N modes forms a channel for the conductance, with a transmission probability Tn between 0 and 1. The total conductance is given by the sum over these channels G › P N›1 TnG0, where G0 › 2e 2 yh is the quantum of conductance. By recording histograms of conductance values [3] for contacts of simple metals (Na, Au), a statistical preference was observed for conductances near integer values. This statistical preference was interpreted as an indication that transmitted modes in the most probable contacts are completely opened (Tn › 1, i.e., saturation of channel transmission), in analogy with the conductance quantization observed in 2D electron gas devices [4]. Here, we test this interpretation by performing a new type of measurement giving access to the second moment of the distribution of the Tn’s. The atomic contacts are formed by breaking a gold wire at low temperatures, and then finely adjusting the size of the contact between the fresh fracture surfaces using a piezoelectric element [1]. Figure 1 shows the differential conductance, ›Iy›V measured as a function of bias voltage for three atomic-size contacts with different conductance values, using a modulation voltage eV ? kBu (with u the temperature). For each contact, both of the curves for increasing and decreasing bias voltage are given. Measurements such as those of Fig. 1 suggest that the fluctuation pattern changes randomly between contact configurations and that the amplitude of the fluctuations is suppressed for conductance values near G0. In order to establish such a relation, it is necessary to statistically average over a large number of contacts. We do this by measuring the voltage dependence of the conductance s›Gy›V › › 2 Iy›V 2 d and

Miniature electrical filters for single electron devices

In experiments on single electron devices, the electromagnetic noise from parts of the apparatus at temperatures higher than that of the device can dramatically increase the tunnel rates out of the Coulomb‐blocked state and therefore increase the device error rate. The electrical lines must therefore be filtered adequately. We derive simple expressions for calculating the required attenuation coefficient. We describe a wide‐band miniature dissipative filter functioning at cryogenic temperatures. The effective thermalization of an experiment at 30 mK can be obtained by placing four of these filters in series at temperatures ranging from 4 K to 30 mK.

Implementation of a combined charge-phase quantum bit in a superconducting circuit

We discuss a qubit circuit based on the single Cooper-pair transistor (which consists of two ultrasmall Josephson junctions in series) connected in parallel with a large Josephson junction. The switching of this junction out of its zero-voltage state is used to readout the qubit. We report measurements of the discriminating power of the readout process, and we discuss its back-action on the qubit.

Relaxation and frequency shifts induced by quasiparticles in superconducting qubits

As low-loss nonlinear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represents an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and nonequilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible nonequilibrium quasiparticle distribution. We also derive expressions for the shift in qubit frequency in the presence of quasiparticles.

Quantum Coherence of Charge States in the Single Electron Box

A metallic electrode connected to electron reservoirs by tunnel junctions has a series of charge states corresponding to the number of excess electrons in the electrode. In contrast to the charge state of an atomic or molecular ion, the charge states of such an “island” are mesoscopic states involving all the conduction electrons of the island. Island charge states bear some resemblance to the photon number states of the cavity in cavity QED, the phase conjugate to the number of electrons being analogous to the phase of the field in the cavity. For a normal island, charge states decay irreversibly into charge states of lower energies. However, the gound state of a superconducting island connected to superconducting reservoirs can be a coherent superposition of charge states differing by two electrons (i.e., a Cooper pair). We describe an experiment in which this Josephson effect involving only one Cooper pair is measured.

MEASUREMENT METHOD OF THE ANTIPROTON GRAVITATIONAL MASS USING THE SINGLE ELECTRON TRANSISTOR

We propose a non-destructive method to measure the trajectory of a single antiproton in a drift tube using position sensors based on the single electron transistor. We show that this recently developed device has sufficient sensitivity to detect the electric field of a moving charged particle. Comparing the trajectories of antiprotons and H− ions could allow a reliable determination of the gravitational mass of the antiproton.

On the observability of Coulomb blockade and single-electron tunneling

Abstract Coulomb blockade and single-electron tunneling are manifestations, at the macroscopic level, of the granularity of charge. These effects can occur in small capacitance tunnel junction systems, under conditions which are discussed in this article. We examine in particular how the zero-point electromagnetic fluctuations can eventually wash out the single-electron effects.

Observation of the effect of an electromagnetic environment with sharp resonances on the current-voltage characteristics of a small capacitance tunnel junction

Abstract We have measured the current-voltage characteristic of a small capacitance tunnel junction coupled to a transmission line resonator. We calibrate the resonator using the sharp resonances displayed by the junction in the superconducting state, which correspond to the pumping of the modes of the resonator by the AC Josephson current. With this calibration, we explain quantitatively the non-linearity of the junction characteristic in the normal state as being due to the process by which a single electron tunnels by emitting a photon, the basic process of the theory of the effect of the electromagnetic environment on tunneling.

Frequency-determined current with a turnstile device for single electrons

Abstract We have fabricated a device in which the current is to a high accuracy determined by an external frequency f as I=ef. This device consists of an array of ultrasmall tunnel junctions. An rf voltage is applied to a gate and causes the transfer of a single electron per cycle through the array. The locking of the electron transfer is obtained by using Coulomb blockade of electron tunneling.