Electrical readout of spin qubits requires fast and sensitive measurements, which are hindered by poor impedance matching to the device. We demonstrate perfect impedance matching in a radio-frequency readout circuit, using voltage-tunable varactors to cancel out parasitic capacitances. An optimized capacitance sensitivity of 1.6 aF= ffiffiffiffiffiffi Hz p is achieved at a maximum source-drain bias of 170-μV rootmean-square and with a bandwidth of 18 MHz. Coulomb blockade in a quantum-dot is measured in both conductance and capacitance, and the two contributions are found to be proportional as expected from a quasistatic tunneling model. We benchmark our results against the requirements for single-shot qubit readout using quantum capacitance, a goal that has so far been elusive.

In an optomechanical setup, the coupling between cavity and resonator can be increased by tuning them to the same frequency. We study this interaction between a carbon nanotube resonator and a radio-frequency tank circuit acting as a cavity. In this resonant regime, the vacuum optomechanical coupling is enhanced by the dc voltage coupling the cavity and the mechanical resonator. Using the cavity to detect the nanotube's motion, we observe and simulate interference between mechanical and electrical oscillations. We measure the mechanical ring down and show that further improvements to the system could enable the measurement of mechanical motion at the quantum limit.

We present a thermometry scheme to extract the temperature of a 2DEG by monitoring the charge occupation of a weakly tunnel-coupled 'thermometer' quantum dot using a quantum point contact detector. Electronic temperatures between 97 mK and 307 mK are measured by this method with an accuracy of up to 3 mK, and agree with those obtained by measuring transport through a quantum dot. The thermometer does not pass a current through the 2DEG, and can be incorporated as an add-on to measure the temperature simultaneously with another operating device. Further, the tuning is independent of temperature.PACS numbers: 81.05. Ea,85.35.Gv,07.20.Dt,73.23.Hk,73.63.Kv The two-dimensional electron gas in GaAs/AlGaAs hetero-structures has diverse applications at cryogenic temperatures. For example, both gate-defined quantum dots and non-abelian fractional quantum hall states are candidates for a solid state quantum computer 1,2 . Almost all these applications require a low operating temperature, which is achieved by cooling the device using a dilution refrigerator or a helium-3 system. These external cooling mechanisms rely on the lattice cooling the electron gas via an exchange of phonons. In the mK range and lower, phonon coupling decreases with temperature, and this reduces the ability of external cooling mechanisms to cool the 2-DEG, limiting the minimum achievable temperature 3-5 . In practice, the electron gas is heated by unintended noise in the measurement set up to a temperature higher than the lattice. In many cases, the background electron temperature of an operating device is needed to analyze its behavior. This temperature has to be measured before or after the main experiment, an approach which cannot take into account any drift in electron temperature which occurs during the experiment. Our work describes the implementation of a thermometer which can perform an accurate and non-invasive temperature measurement 6,7 . The thermometer does not draw current from the sample being measured, which minimizes any back-action on the main experiment.Several low temperature thermometers have recently been realized using modern microlithography and nanolithography techniques 8 . For example, a fast NIS (normal metal-insulator-superconductor) junction thermometer, which operates at RF frequencies, has measured temperatures from 300 mK to 950 mK 9 . A 'Shot Noise Thermometer' (SNT) which extracts the electron temperature from the electrical shot noise through a tunneling junction between two metal electrodes has been shown to operate over a temperature range of 30 mK to 300 K with an accuracy of 0.1 % in the middle two decades of that range 10 . A 'Coulomb Blockade Thermometer' (CBT) a) am877@cam.ac.uk which relies on the temperature-dependent conductance of an array of tunneling junctions in an Al/Al 2 O 3 /Al structure, and which has an operating range of 20mK to tens of Kelvin with an absolute accuracy of 1% 11,12 , has been developed into a commercial product. The CBT can also operate in a magnetic field, which is an impor...

The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.The co-existence in carbon nanotubes of spin and valley angular momenta opens a host of possibilities for quantum information [1][2][3][4], coherent coupling to mechanics [5,6], and on-chip entanglement [7,8]. Spin-orbit coupling [9] provides electrical control, but introduces a relaxation channel. However, measurements of dephasing and decoherence [10][11][12] show that spin and valley qubit states couple surprisingly strongly to lattice nuclear spins and to uncontrolled electric fields, e.g. from thermal switchers. Realising these possibilities requires such effects to be mitigated. Here we study leakage current in a Pauli blockaded double quantum dot to identify spin-orbit and hyperfine contributions to spin-valley relaxation [3,13,14]. By suspending the nanotube, we decouple it from the substrate [11]. Measuring a spinvalley qubit defined in the double dot, we find dephasing and decoherence rates nearly independent of temperature, and show that charge noise cannot explain the observed dephasing, supporting the conclusion that despite the low density of 13 C spins, hyperfine interaction causes rapid dephasing in nanotubes [10,11].The measured device [ Fig. 1(a-b)] is a carbon nanotube suspended by stamping between two contacts and over five gate electrodes G1-G5 [3,[15][16][17]. Gate voltages V G1 − V G5 , together with Schottky barriers at the contacts, define a double quantum dot potential. The dot potentials are predominantly controlled by gates G1 (for the left dot) and G4-5 (for the right dot), while the interdot tunnel barrier is controlled by gates G2-3. For fast manipulation, gates G1 and G5 are connected via tees to waveform generator outputs and a vector microwave source. The device is measured in a magnetic field B = (B X , B Y , B Z ), with Z chosen along the nanotube and X normal to the substrate. Experiments were in a dilution refrigerator at 15 mK unless stated.To map charge configurations of the double quantum dot, we measure the current I through the nanotube with source-drain bias V SD = 8 mV applied between the contacts [ Fig. 1(c)]. As a function of V G1 and V G4 , the honeycomb Coulomb peak pattern is characteristic of a double quantum dot, with honeycomb vertices marking transitions between particular electron or hole occupations [18]. A horizontal stripe of suppressed current around V G4 = 200 mV indicates depl...

We report microwave-driven photon-assisted tunneling in a suspended carbon nanotube double quantum dot. From the resonant linewidth at a temperature of 13 mK, the charge dephasing time is determined to be 280 ± 30 ps. The linewidth is independent of driving frequency, but increases with increasing temperature. The moderate temperature dependence is inconsistent with expectations from electron-phonon coupling alone, but consistent with charge noise arising in the device. The extracted level of charge noise is comparable with that expected from previous measurements of a valley-spin qubit, where it was hypothesized to be the main cause of qubit decoherence. Our results suggest a possible route towards improved valley-spin qubits.