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arXiv:quant-ph/0609122

False qubits II. Entanglement of Josephson junctions

Robert Alicki

Published Sep 16, 2006• 2 citations
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Abstract

The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.

DOI
10.48550/arxiv.quant-ph/0609122

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The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.
There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented, for instance, by Rydberg atoms, Josephson junctions or Bose-Einstein condensates - the systems which should rather emerge in localized semiclassical states. In this note it is shown how, under realistic conditions, the false qubit interpretation can be consistent with the restricted set of experimental data collected for semiclassical systems. The recent experiments displaying semiclassical character of Bose-Einstein condensates and possible quantumness tests for a single system are briefly invoked also.
We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes to be even dominant over the single-qubit tunneling processes in the states of two qubits. It is shown that due to the two-qubit tunneling processes, both the ground state and excited states of the coupled flux qubits can be a Bell type of maximally entangled state, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of magnetic flux and Josephson coupling energies.
We show that two capacitively coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.
I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.
Recent demonstrations of macroscopic quantum coherence in Josephson junction based electronic circuits have opened an entirely new dimension for research and applications in the established field of Josephson electronics. In this article we discuss basic Josephson circuits for qubit applications, methods of quantum description of these circuits, and circuit solutions for qubit couplings. Principles of manipulation and readout of superconducting qubits are reviewed and illustrated with recent experiments using various qubit types.
There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large NNN aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freedom, the second approach yields an essentially classical structure of accessible quantum states which, in particular, implies the absence of entanglement for two coupled JJ's. The arguments in favor of the mean-field theory are presented and different experimental tests including a new proposal are briefly discussed.