Quantum capacitive phase detector

We discuss how a single Cooper-pair transistor may be used to detect the superconducting phase difference by using the phase dependence of the input capacitance from gate to the ground. The proposed device has a low power dissipation because its operation is in principle free from quasiparticle generation. According to the sensitivity estimates the device may be used for efficient qubit readout in a galvanically isolated and symmetrized circuit.Comment: 5 pages, published for

The Inductive Single-Electron Transistor (L-SET)

We demonstrate a sensitive method of charge detection based on radio-frequency readout of the Josephson inductance of a superconducting single-electron transistor. Charge sensitivity $1.4 \times 10^{-4}e/\sqrt{Hz}$, limited by preamplifier, is achieved in an operation mode which takes advantage of the nonlinearity of the Josephson potential. Owing to reactive readout, our setup has more than two orders of magnitude lower dissipation than the existing method of radio-frequency electrometry. With an optimized sample, we expect uncoupled energy sensitivity below $\hbar$ in the same experimental scheme.Comment: 10 page

Charge sensitivity of the Inductive Single-Electron Transistor

We calculate the charge sensitivity of a recently demonstrated device where the Josephson inductance of a single Cooper-pair transistor is measured. We find that the intrinsic limit to detector performance is set by oscillator quantum noise. Sensitivity better than $10^{-6}$e$/\sqrt{\mathrm{Hz}}$ is possible with a high $Q$-value $\sim 10^3$, or using a SQUID amplifier. The model is compared to experiment, where charge sensitivity $3 \times 10^{-5}$e$/\sqrt{\mathrm{Hz}}$ and bandwidth 100 MHz are achieved.Comment: 3 page

Quantum states of a mesoscopic SQUID measured using a small Josephson junction

We have experimentally studied the energy levels of a mesoscopic superconducting quantum interference device (SQUID) using inelastic Cooper-pair tunneling. The tunneling in a small Josephson junction depends strongly on its electromagnetic environment. We use this fact to do energy-level spectroscopy of a SQUID loop by coupling it to a small junction. Our samples with strong quasiparticle dissipation are well described by a model of a particle localized in one of the dips in a cosine potential, while in the samples with weak dissipation we can see formation of energy bands.Peer reviewe

Current-phase relation and Josephson inductance in a superconducting Cooper-pair transistor

We have investigated the Josephson inductance LJ of a superconducting Cooper pair transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a ∼200 pH strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of EJ/EC=1.75, is integrated over the phase, we obtain a current-phase relation, which is strongly nonsinusoidal near the charge degeneracy point.Peer reviewe

Continuous-Time Monitoring of Landau-Zener Interference in a Cooper-Pair Box

Landau-Zener (LZ) tunneling can occur with a certain probability when crossing energy levels of a quantum two-level system are swept across the minimum energy separation. Here we present experimental evidence of quantum interference effects in solid-state LZ tunneling. We used a Cooper-pair box qubit where the LZ tunneling occurs at the charge degeneracy. By employing a weak nondemolition monitoring, we observe interference between consecutive LZ-tunneling events; we find that the average level occupancies depend on the dynamical phase. The system’s unusually strong linear response is explained by interband relaxation. Our interferometer can be used as a high-resolution Mach-Zehnder–type detector for phase and charge.Peer reviewe

Macroscopic quantum tunneling in nanoelectromechanical systems

The experimental observation of quantum phenomena in mechanical degrees of freedom is difficult, as the systems become linear toward low energies and the quantum limit, and thus reside in the correspondence limit. Here we investigate how to access quantum phenomena in flexural nanomechanical systems which are strongly deflected by a voltage. Near a metastable point one can achieve a significant nonlinearity in the electromechanical potential at the scale of zero-point energy. The system can then escape from the metastable state via macroscopic quantum tunneling (MQT). We consider two model systems suspended atop a voltage gate, namely, a graphene sheet and a carbon nanotube. We find that the experimental demonstration of the phenomenon is currently possible but demanding, since the MQT crossover temperatures fall in the milli-Kelvin range. A carbon nanotube is suggested as the most promising system.Peer reviewe

Strong gate coupling of high-Q nanomechanical resonators

The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2 \pi) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electrodes, in suspended aluminum films. We measured the thermomechanical vibrations down to a temperature of 25 mK, and we obtained a low number of about twenty phonons at the equilibrium bath temperature. The mechanical properties of Al were excellent after FIB cutting and we recorded a quality factor of Q ~ 3 x 10^5 for a 67 MHz resonator at a temperature of 25 mK. Between 0.2K and 2K we find that the dissipation is linearly proportional to the temperature.Comment: 6 page