Kevin Bladh

Coherent dynamics of a Josephson charge qubit

We have fabricated a Josephson charge qubit by capacitively coupling a single-Cooper-pair box (SCB) to an electrometer based upon a single-electron transistor (SET) configured for radio-frequency readout (rf-SET). 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 ≃10 ns. The observed contrast of the oscillations is high and agrees with that expected from the finite EJ/EC 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 T1 when it is shorter than the measurement time

Radio-frequency single-electron transistor: Toward the shot-noise limit

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.

Observation of quantum capacitance in the Cooper-pair transistor

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, it 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 and has two parts, the geometric capacitance, C(geom), and the quantum capacitance C(Q). The latter is due to the level anticrossing caused by the Josephson coupling and is dual to the Josephson inductance. It depends parametrically on the gate voltage and its magnitude may be substantially larger than C(geom). We have detected 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.

Comparison of cryogenic filters for use in single electronics experiments

We have analyzed six different cryogenic filters for applications in single electronics. Each filter is evaluated with respect to its construction, cryogenic compatibility, principle of operation, and performance. The filters were measured at 4.2 K in a 50 Ω environment between 20 kHz and 8 GHz. We have also combined some of the best properties of these filters into a single, highly effective filter that covers the entire frequency spectrum.

Noise performance of the radio-frequency single-electron transistor

We have analyzed a radio-frequency single-electron-transistor (RF-SET) circuit that includes a high-electron-mobility-transistor (HEMT) amplifier, coupled to the single-electron-transistor (SET) via an impedance transformer. We consider how power is transferred between different components of the circuit, model noise components, and analyze the operating conditions of practical importance. The results are compared with experimental data on SETs. Good agreement is obtained between our noise model and the experimental results. Our analysis shows, also, that the biggest improvement to the present RF-SETs will be achieved by increasing the charging energy and by lowering the HEMT amplifier noise contribution.

Backaction effects of a SSET measuring a qubit spectroscopy and ground State measurement

We investigate the backaction of superconducting single-electron transistor (SSET) continuously measuring a Cooper-pair box. Due to the minimized backaction of the SSET, we observe a 2e periodic Coulomb staircase according to the two-level system Hamiltonian of the Cooper-pair box. We demonstrate that we can control the quantum broadening of the ground state in-situ. We perform spectroscopy measurements and demonstrate that we have full control over the Cooper-pair box Hamiltonian. The ability to reduce the backaction is a necessary condition to use the SSET as a quantum state readout for the CPB as a qubit.

Characterization of a single Cooper pair box

We have used a radio-frequency single electron transistor to read-out a single Cooper pair box. We observe a Coulomb staircase with 2e periodicity, but with a shorter step corresponding to odd number ofcharges in the box. From the size of this short step we can extract the even–odd energy di3erence, ˜_, and study its magnetic 5eld dependence. We have also characterized the box with microwave spectroscopy and extracted the charging energy and the Josephson coupling energy to be Ec=kB = 1:65 K and EJ0=kB = 0:69 K..

Similarities between single charge and Josephson effects and devices. A fast and sensitive radio frequency single electron transistor

Abstract There are several dualities between Josephson and single charge tunneling, being conjugate phenomena, where either the phase (flux) or the number (charge) states are well determined while the complementary entity (number, phase) is undetermined. A zero voltage, phase-dependent current flows in the Josephson junction up to a critical current value while no current flows in the Coulomb blockade region, up to a threshold voltage, in a single charge element having high resistance and small Josephson coupling. The dual of the extremely flux sensitive DC superconducting quantum interference device (SQUID) is the single charge transistor (SET). It has an outstanding charge sensitivity but its high impedance severely limits its bandwidth. A superconducting radio frequency version, RF-SET, is related to the common RF-SQUID and its bandwidth is improved orders of magnitude compared to the usual SET. A charge sensitivity of the order of 3×10 −6 e/√Hz has been demonstrated. It can be used, e.g., as a read out of the charge of a quantum “qu-bit”. The latter is, in this case, based upon the charge state of a small island, being a superposition of a charge or not a charge, which can be compared with a flux based qu-bit where currents go clock- or anti-clockwise in a SQUID loop.

Noise in the Single Electron Transistor and its Back Action during Measurement

Single electron transistors (SETs) are very sensitive electrometers and they can be used in a range of applications. In this paper we give an introduction to the SET and present a full quantum mechanical calculation of how noise is generated in the SET over the full frequency range, including a new formula for the quantum current noise. The calculation agrees well with the shot noise result in the low frequency limit, and with the Nyquist noise in the high frequency limit. We discuss how the SET and in particular the radio-frequency SET can be used to read out charge based qubits such as the single Cooper pair box. We also discuss the backaction which the SET will have on the qubit. The back action is determined by the spectral power of voltage fluctuations on the SET island. We will mainly treat the normal state SET but many of the results are also valid for superconducting SETs.