Based on the entangled state representation and the appropriate bosonic phase operator we develop the superconducting capacitor model in the presence of a voltage bias and a current bias. In so doing, the full Hamiltonian operator theory for a superconducting barrier is established.
This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman's assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.
We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other. Microwave spectroscopy in the 4 to 6 gigahertzrange at 20 millikelvin reveals energy levels that agree well with theoretical results for entangled states. The single qubits are spatially separate, and the entangled states extend over the 0.7-millimeter distance between the two qubits.
The superconducting charge-phase ``quantronium'' qubit is considered in order to develop a model for the measurement process used in the experiment of Vion et al. [Science 296, 886 (2002)]. For this model we propose a method for including the bias current in the readout process in a fundamentally irreversible way, which to first order is approximated by the Josephson junction tilted-washboard potential phenomenology. The decohering bias current is introduced in the form of a Lindblad operator and the Wigner function for the current-biased readout Josephson junction is derived and analyzed. During the readout current pulse used in the quantronium experiment we find that the coherence of the qubit initially prepared in a symmetric superposition state is lost at a time of 0.2ns after the bias current pulse has been applied, a time scale that is much shorter than the experimental readout time. Additionally we look at the effect of Johnson-Nyquist noise with zero mean from the current source during the qubit manipulation and show that the decoherence due to the irreversible bias current description is an order of magnitude smaller than that found through adding noise to the reversible tilted-washboard potential model. Our irreversible bias current model is also applicable to persistent-current-based qubits where the state is measured according to its flux via a small-inductance direct-current superconducting quantum interference device.