SQUID developments for the gravitational wave antenna MiniGRAIL

We designed two different sensor SQUIDs for the readout of the resonant mass gravitational wave detector MiniGRAIL. Both designs have integrated input inductors in the order of 1.5 muH and are planned for operation in the mK temperature range. Cooling fins were added to the shunt resistors. The fabricated SQUIDs show a behavior that differs from standard DC-SQUIDs. We were able to operate a design with a parallel configuration of washers at reasonable sensitivities. The flux noise saturated to a value of 0.84 muPhi0/radicHz below a temperature of 200 mK. The equivalent noise referred to the current through the input coil is 155 fA/radicHz and the energy resolution yields 62 h

Fabrication and analogue applications of nanoSQUIDs using Dayem bridge junctions

We report here recent work at the U.K. National Physical Laboratory on developing nanoscale SQUIDs using Dayem bridge Josephson junctions. The advantages are simplicity of fabrication, exceptional low-noise performance, toward the quantum limit, and a range of novel applications. Focused ion beam patterned Nb SQUID, possessing exceptionally low noise (∼200 nΦ0/Hz1/2 above 1 kHz), and operating above 4.2 K can be applied to measurement of nanoscale magnetic objects or coupled to nanoelectromechanical resonators, as well as single particle detection of photons, protons, and ions. The limited operating temperature range may be extended by exposing the Dayem bridges to carefully controlled ion beam implantation, leading to nonreversible changes in junction transition temperature.The work reported here was supported in part by the EMRP projects ‘MetNEMS’ NEW-08 and ‘BioQUART’SIB-06. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union

QUBIT COUPLED MECHANICAL RESONATOR IN AN ELECTROMECHANICAL SYSTEM

This thesis describes the development of a hybrid quantum electromechanical system. In this system the mechanical resonator is capacitively coupled to a superconducting transmon which is embedded in a superconducting coplanar waveguide (CPW) cavity. The difficulty of achieving high quality of superconducting qubit in a high-quality voltage-biased cavity is overcome by integrating a superconducting reflective T-filter to the cavity. Further spectroscopic and pulsed measurements of the hybrid system demonstrate interactions between the ultra-high frequency mechanical resonator and transmon qubit. The noise of mechanical resonator close to ground state is measured by looking at the spectroscopy of the transmon. At last, fabrication and tests of membrane resonators are discussed

Characterization of superconducting hardware for implementing quantum stabilizers

Superconducting qubits are one of the leading approaches being investigated for building a scalable quantum computer. In the presence of external noise and perturbations plus local microscopic fluctuations and dissipation in the qubit environment, arbitrary quantum states will decohere, leading to bit-flip and phase-flip errors of the qubit. In order to build a fault-tolerant quantum computer that can preserve and process quantum information in the presence of noise and dissipation, one must implement some form of quantum error correction. Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of groups of qubits. Alternatively, qubits can be designed so that the Hamiltonian includes terms that correspond directly to a stabilizer for protecting quantum information. In this thesis, we demonstrate such a hardware implementation of stabilizers in a superconducting circuit composed of chains of $\pi$-periodic Josephson elements called a plaquette. Each plaquette consists of a superconducting loop with two conventional Josephson junctions and two inductors. We study the phase dependence of the plaquette by incorporating it into a resonant multi-loop circuit and measuring the resonator\u27s frequency as a function of the external magnetic flux through each loop. To demonstrate the implementation of stabilizers in the Hamiltonian we made a superconducting circuit composed of a chain of three plaquettes shunted by a large capacitor. We map out the multidimensional flux space of the device by using on-chip bias lines to tune the magnetic flux through the three plaquettes independently. We measure the flux and charge dependence of the device\u27s energy levels with microwave spectroscopy. We compare these measurements with numerical modeling of the energy level spectrum and obtain good agreement between theory and experiment for the designed and fabricated device parameters. We observe a softening of the energy band dispersion with respect to flux that is exponential in the number of frustrated plaquettes, this corresponds to the device being protected against errors caused by dephasing due to flux noise. The large shunt capacitor suppresses tunneling between the qubit logical states, and thus protects the device against bit-flip errors. A future qubit based on this design will exhibit simultaneous protection against bit-flip and phase-flip errors leading to gate errors that are significantly improved over the current state of the art

Electro-optomechanical equivalent circuits for quantum transduction

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.Comment: 30 pages, 9 figure

Hardware implementation of quantum stabilizers in superconducting circuits

Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of groups of qubits. Alternatively, qubits can be designed so that the Hamiltonian corresponds directly to a stabilizer for protecting quantum information. We demonstrate such a hardware implementation of stabilizers in a superconducting circuit composed of chains of $\pi$-periodic Josephson elements. With local on-chip flux- and charge-biasing, we observe a softening of the energy band dispersion with respect to flux that is exponential in the number of frustrated plaquette elements, in close agreement with our numerical modeling.Comment: 6+30 pages, 4+18 figures, 0+6 tables, published versio

Multiphoton transitions in Josephson-junction qubits (Review Article)

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit-resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-St\"uckelberg interferometry, the multiphoton transitions of both direct and ladder- type character, and creation of the inverse population for lasing.Comment: 20 pages, 15 figure

Development and testing of the gravitational wave antenna MiniGRAIL in its full-featured configuration

The MiniGRAIL detector is a cryogenic 68 cm diameter spherical gravitational wave antenna made of CuAl(6%) alloy with a mass of 1400 Kg and a resonance frequency of 2.9 kHz. Unlike other types of gravitational wave detectors, a single sphere is capable of determining direction and polarization of GW signal, because it has five degenerate modes of oscillation that interact with gravitational waves. This thesis is focused on building the full acquisition system and preparation of MiniGRAIL for a scientific run, with a full read-out configuration at millikelvin temperatures. We have also performed a test run to evaluate the calibration procedure we developed. During the run we have reached a peak strain sensitivity of 3E-20 Hz^(-1/2) at 4.2K. For current system configuration and thermodynamic temperature of the sphere of 20 mK, the estimated peak sensitivity level is 2E-22 Hz^(-1/2) and the minimal detectable Fourier amplitude of gravitational wave burst of 1E-22. In the last chapter of the thesis we present a SQUID-based scheme to measure the displacement of a nanomechanical resonator at cryogenic temperature. We demonstrate its potential by cooling an ultrasoft silicon cantilever to a noise temperature of 25 mK, corresponding to a subattonewton thermal force noise of 0.5 aN/Hz^(1/2).LEI Universiteit LeidenQuantum Matter and Optic