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Josephson Persistent Current Qubit and Quantum Flux Measurements

Caspar H. van der Wal, Johan E. Mooij, A. C. Wallast, A. C. J. ter Haar, A. C. J. Terhaar, L. M. Vangorkom, C. J. P. M. Harmans, Lin Tian, Hirotaka Tanaka, J. J. Mazo, Terry P. Orlando, Seth Lloyd, Leonid S Levitov

Published Nov 21, 2007• 0 citations
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Abstract

. In circuits of underdamped, small-capacitance Josephson junctions, the charge and phase variables behave quantum mechanically. Superpositions of charge states and flux states have been demonstrated, as well as microwave induced quantum dynamics (see e.g. refs [3, 4]). These e#ects have their origin in the conjugation of the phase and charge variables of Josephson circuits. The qubit design that we present here also contains small-capacitance Josephson junctions. However, even though charge-phase conjugation underlies the quantum behavior of the qubit, it was explicitly designed to be very insensitive to charge e#ects. In practice, random background charges and 1/f charge noise are always present in Josephson circuits, but these charge e#ects have negligible influence on the qubit. The qubit loop contains three Josephson junctions. Two junctions have Josephson coupling E J , the third junction has a coupling of #E J .Weaim

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arXiv:cond-mat/0510843•Physical Review B•Jul 25, 2006•28 citations
. In circuits of underdamped, small-capacitance Josephson junctions, the charge and phase variables behave quantum mechanically. Superpositions of charge states and flux states have been demonstrated, as well as microwave induced quantum dynamics (see e.g. refs [3, 4]). These e#ects have their origin in the conjugation of the phase and charge variables of Josephson circuits. The qubit design that we present here also contains small-capacitance Josephson junctions. However, even though charge-phase conjugation underlies the quantum behavior of the qubit, it was explicitly designed to be very insensitive to charge e#ects. In practice, random background charges and 1/f charge noise are always present in Josephson circuits, but these charge e#ects have negligible influence on the qubit. The qubit loop contains three Josephson junctions. Two junctions have Josephson coupling E J , the third junction has a coupling of #E J .Weaim
In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.
A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.
We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.
A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer, one small loop, and three Josephson junctions. We develop a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. To make the required calculation tractable, we devise a general Born-Oppenheimer approximation which reduces the effective dimensionality in the calculation to one. Contributions to relaxation (T1)({T}_{1})(T1​) and dephasing $({T}_{\ensuremath{\phi}})$ arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We explore T1{T}_{1}T1​ and ${T}_{\ensuremath{\phi}}$ along an optimal line in the space of applied fluxes; along this ``S line'' we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.