We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, the sub-gap charge transport takes place via slow tunneling of quasiparticles that link two Josephson-coupled charge manifolds. In between the quasiparticle tunneling events, the CPT behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage. This capacitance has two parts, the geometric capacitance, C geom , and the quantum capacitance C Q . The latter is due to the level anti-crossing caused by the Josephson coupling. It depends parametrically on the gate voltage and is dual to the Josephson inductance. Furthermore, it's magnitude may be substantially larger than C geom . We have been able to detect C Q in our CPT, by measuring the in-phase and quadrature rf-signal reflected from a resonant circuit in which the CPT is embedded.C Q can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.

We have fabricated a Josephson charge qubit by capacitively coupling a single-Cooper-pair box ͑SCB͒ to an electrometer based upon a single-electron transistor ͑SET͒ configured for radio-frequency readout ͑rf-SET͒. Charge quantization of 2e is observed and microwave spectroscopy is used to extract the Josephson and charging energies of the box. We perform coherent manipulation of the SCB by using very fast dc pulses and observe quantum oscillations in time of the charge that persist to Ӎ10 ns. The observed contrast of the oscillations is high and agrees with that expected from the finite E J /E C ratio and finite rise time of the dc pulses. In addition, we are able to demonstrate nearly 100% initial charge state polarization. We also present a method to determine the relaxation time T 1 when it is shorter than the measurement time T meas . DOI: 10.1103/PhysRevB.69.140503 PACS number͑s͒: 85.25.Hv, 74.40.ϩk, 85.35.Gv Although a large number of physical systems have been suggested as potential implementations of qubits, solid-state systems are attractive in that they offer a realistic possibility of scaling to a large number of interacting qubits. Recently there has been considerable experimental progress using superconducting microelectronic circuits to construct artificial two-level systems. A variety of relative Josephson and Coulomb energy scales have been used to construct qubits based upon a single-Cooper-pair box 1,2 and flux qubits based upon a three-junction loop.3,4 Coherence times of the order of 0.5 s have been achieved for a single-Cooper-pair box qubit.2 Rabi oscillations between energy levels of a single large tunnel junction have also been observed. 5,6 Despite the encouraging results, one aspect that is not well understood concerns the contrast of the oscillations, which in all previously reported experiments is smaller than expected.The experimental systems reported so far can also be distinguished by the readout method and the manner of performing single-qubit rotations. The first demonstration of coherent control of a single-Cooper-pair box 1 ͑SCB͒ employed a weakly coupled probe junction to determine the charge on the island. In the more recent experiment reported by Vion et al., 2 the SCB was incorporated into a loop containing a large tunnel junction, for which the switching current depends on the state of the SCB. Switching current measurements of superconducting quantum-interference devices ͑SQUID's͒ have also been used for flux and phase-type qubits.3-6 Nakamura et al. 1 performed single-qubit rotations by applying very fast dc pulses to a gate lead in order to quickly move the SCB into and away from the charge degeneracy point. This technique produces qubit rotations with an operation time that can be of the order of the natural oscillation period. Other experiments utilize microwave pulses to perform NMR-like rotations of the qubit.2,4 -6 The latter approach requires less stringent microwave engineering, since rf rotations can be accomplished with pulses that are more than an order of...

We demonstrate that a continuously measured microelectronic circuit, the Cooper-pair box measured by a radio-frequency single-electron transistor, approximates a quantum two-level system. We extract the Hamiltonian of the circuit through resonant spectroscopy and measure the excited-state lifetime. The lifetime is more than 10(5) times longer than the inverse transition frequency of the two-level system, even though the measurement is active. This lifetime is also comparable to an estimate of the known upper limit, set by spontaneous emission, for this circuit.

We have fabricated an aluminum single-electron transistor and characterized it at frequencies up to 10 MHz by measuring the reflected signal from a resonant tank in which the transistor is embedded. We measured the charge sensitivity of this radio-frequency single-electron transistor to be 3.2×10−6 e/Hz, which corresponds to the uncoupled energy sensitivity of 4.8 ℏ. Our measurements indicate that with further improvements, the radio-frequency single-electron transistor could reach the shot-noise limit estimated to be about 1 ℏ.

Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron–phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the 3He/4He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.