The single Cooper-pair box (SCB) is a mesoscopic superconducting circuit which can be used to observe quantum effects. In this thesis, we attempt to improve our understanding of certain processes limiting the performance of the SCB, and work toward practical solutions. In particular, we focus on improving our understanding of nonequilibrium quasiparticle tunneling in the SCB.
The single Cooper-pair box (SCB) is a mesoscopic superconducting circuit which can be used to observe quantum effects. In this thesis, we attempt to improve our understanding of certain processes limiting the performance of the SCB, and work toward practical solutions. In particular, we focus on improving our understanding of nonequilibrium quasiparticle tunneling in the SCB.
The aluminum single Cooper-pair box (SCB) qubit has demonstrated potential as a candidate for quantum computing. Measurements of coherent manipulation of the relevant SCB states have been demonstrated with various charge and quantum capacitance readout methods. We performed studies of quasiparticle dynamics in an SCB that yielded poisoning probabilities and rates of quasiparticle tunneling processes. Attempts to prevent poisoning with a differential SCB isolated from ground and other quasiparticle sources revealed the possibility for quasiparticle generation on superconducting islands of diminutive size. We have gone on to conduct more advanced measurements of coupled qubits as an important step towards the realization of multi-qubit systems and other precursors that are pivotal in the evolution of reliable quantum computing.
This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.
In this thesis the single Cooper pair box (SCB) is investigated with a radio frequency single electron transistor (RF-SET). The RF-SET is used as an electrometer to detect the charge of the SCB. The SCB can be regarded as a quantum two-level system and could therefore be a possible qubit. Both the SCB and the RF-SET have been fabricated with e-beam lithography followed by two-angle shadow evaporation of aluminium. The system has been measured in a dilution refrigerator at temperatures of ~30 mK. A charge sensitivity of 2.3 μe/square root of Hz was measured for an optimized RF-SET with a bandwidth of 7 MHz, operated in the superconducting state. In a phase sensitive measurement of the RF-SET reflected signal, the gate dependence of the quantum capacitance, due to avoided level crossing, was detected in a superconducting SET. Coulomb staircases for the SCB were obtained by changing the charge of the SCB by ramping a gate voltage and continuously measuring the charge with the RF-SET. To prevent quasiparticle poisoning of the SCB island, we have used a method of graded gaps. Here we exploit the greater reduction of the superconducting gap for the connecting leads with an external magnetic field applied, resulting in a higher gap for the island. This creates an effective barrier against quasiparticle tunnelling. The charging energy and the Josephson coupling energy of the SCB were measured with microwave spectroscopy. The SCBs were fabricated in a SQUID geometry, which made it possible to tune the Josephson coupling energy of the box. This tuning was verified through microwave spectroscopy. The effect of tuning could also be seen in the pure 2e Coulomb staircase, as a predicted smearing of the staircase, which was in excellent agreement with the independent spectroscopy data. Coherent quantum oscillation of the SCB charge state was measured by applying nonadiabatic DC-pulses to the SCB gate. The measured amplitude of the charge oscillations was higher than 70%. The deviation from 100% can be explained by the initial charge state purity and the finite rise time of the pulses. The longest decoherence time of the charge oscillations was T2 = 9 ns at the charge degeneracy point. It was found to be limited by relaxation. Away from the degeneracy point the decoherence time was limited by pure dephasing, due to low frequency charge fluctuators.
In this work we consider measurements on quantum systems emphasizing\non read-out of superconducting qubits. The qubit is always coupled to an\nenvironment, containing a macroscopic number of degrees of freedom. This\nperturbs the qubit and destroys the phase coherence of the quantum state.\nOne tries to minimize this destructive effect by encoding the quantum information in quantum states which do not couple strongly to the dominant\nnoise sources. It is therefore necessary to design read-out methods that can\ndistinguish these states.\n\nWe focus primarily on the single Cooper-pair box (SCB) charge qubit, whose\nproperties are based on the Josephson effect and Coulumb blockade in superconducting electrical circuits. By encoding the information in the qubit\nenergy eigenstates, it is possible to protect it from the most dangerous decoherence source - charge fluctuations in the environment. We investigate\nthe measurement setup, where the SCB is coupled to a lumped element LCoscillator whose resonance frequency is orders of magnitude smaller than the qubit energy splitting. In this regime the SCB will act as an effective positive or negative capacitance, depending on the quantum state. This quantum capacitance then shifts the oscillator resonance frequency, which can be detected in a homodyne phase measurement.\n\nWe have found that reading out a charge qubit by measuring its quantum\ncapacitance in this manner is quantum limited, independently of the oscillator\nquality factor Q. Moreover, we have found that the low-Q oscillator\nis advantageous for the measurement in two ways: first, such an oscillator\nbetter protects the qubit from thermal dephasing, and, second, it allows to\nincrease the speed of the read-out, making it possible to distinguish the qubit states in a single shot measurement.
During this thesis, we have used superconducting circuits with Josephson junctions, derived from the Cooper pair box, in order to implement quantum bits (qubits). To implement two-qubit gates, we have developed a new circuit, the quantroswap, which consists in two capacitively coupled Cooper pair box, each of them being manipulated and read separately. We have demonstrated coherent exchange of energy between them, but we have also observed a problem of qubit instability. In order to avoid this spurious effect, we have implemented another circuit based on a charge insensitive split Cooper pair box coupled to a non-linear resonator for readout-out purpose. We have measured large coherence time, and obtained large readout fidelity (90%) using the bifurcation phenomenon. For metrological purpose, microwave reflectometry measurement on a quantronium also allowed us to relate an applied current I to the frequency f=I/2e of induced Bloch oscillations.
According to a proposal, a phenomenon associated with excitation of quasiparticles in certain superconducting quantum devices would be exploited as a means of detecting photons with exquisite sensitivity. The phenomenon could also be exploited to perform medium-resolution spectroscopy. The proposal was inspired by the observation that Coulomb blockade devices upon which some quantum logic gates are based are extremely sensitive to quasiparticles excited above the superconducting gaps in their leads. The presence of quasiparticles in the leads can be easily detected via the charge states. If quasiparticles could be generated in the leads by absorption of photons, then the devices could be used as very sensitive detectors of electromagnetic radiation over the spectral range from x-rays to submillimeter waves. The devices in question are single-Cooper-pair boxes (SCBs), which are mesoscopic superconducting devices developed for quantum computing. An SCB consists of a small superconducting island connected to a reservoir via a small tunnel junction and connected to a voltage source through a gate capacitor. An SCB is an artificial two-level quantum system, the Hamiltonian of which can be controlled by the gate voltage. One measures the expected value of the charge of the eigenvectors of this quantum system by use of a radio-frequency single-electron transistor. A plot of this expected value of charge as a function of gate voltage resembles a staircase that, in the ideal case, consists of steps of height 2 e (where e is the charge of one electron). Experiments have shown that depending on the parameters of the device, quasiparticles in the form of "broken" Cooper pairs present in the reservoir can tunnel to the island, giving rise to steps of 1 e. This effect is sometimes called "poisoning." Simulations have shown that an extremely small average number of quasiparticles can generate a 1-e periodic signal. In a device according to the proposal, this poisoning would be turned to advantage. Depending on the wavelength, an antenna or other component would be used to couple radiation into the reservoir, wherein the absorption of photons would break Cooper pairs, thereby creating quasiparticles that, in turn, would tunnel to the island, creating a 1-e signal. On the basis of conservative estimates of device parameters derived from experimental data and computational simulations that fit the data, it has been estimated that the noise equivalent power of a device according to the proposal could be as low as 6 10(exp -22) W/Hz(exp 1/2). It has also been estimated that the spectroscopic resolution (photon energy divided by increment of photon energy) of such a device in visible light would exceed 100.