Hamiltonian for coupled flux qubits

An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary "free" 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a "fast variable" which can be eliminated adiabatically. However, the commonly used junction phases are_not_ appropriate "slow variables", and instead one introduces degrees of freedom which are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L->0. Fortunately, they merely renormalize the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.Comment: REVTeX4, 16pp., one figure. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. Informal note. v2: completely rewritten; correction of final result and major expansion. v3: added numerical verification plus a discussion of Ref. [2

One-sided Cauchy-Stieltjes Kernel Families

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-infinitely divisible laws without the first moment. We also determine the domain of means, advancing the understanding of Cauchy-Stieltjes kernel families also for compactly supported generating measures

A Pathwise Ergodic Theorem for Quantum Trajectories

If the time evolution of an open quantum system approaches equilibrium in the time mean, then on any single trajectory of any of its unravelings the time averaged state approaches the same equilibrium state with probability 1. In the case of multiple equilibrium states the quantum trajectory converges in the mean to a random choice from these states.Comment: 8 page

Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator

I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously-monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.Comment: 16 pages, 3 figures, submitted to PRE; expanded introduction and conclusion, corrected typos, new figure

Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.Comment: REVTeX4, 4pp., 4 EPS figure files. v3: changed title, fixed typos; final, to appear in PR

Quantum Manipulations of Small Josephson Junctions

Low-capacitance Josephson junction arrays in the parameter range where single charges can be controlled are suggested as possible physical realizations of the elements which have been considered in the context of quantum computers. We discuss single and multiple quantum bit systems. The systems are controlled by applied gate voltages, which also allow the necessary manipulation of the quantum states. We estimate that the phase coherence time is sufficiently long for experimental demonstration of the principles of quantum computation.Comment: RevTex, 15 pages,4 postscript figures, uuencoded, submitted to Phys. Rev. Lett., estimates of the experimental parameters correcte

Direct Josephson coupling between superconducting flux qubits

We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.Comment: REVTeX 4, 4 pages, 5 figures; v2: completely rewritten, added finite-temperature results and proposals for ferromagnetic galvanic couplin