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IEEE Transactions on Applied Superconductivity

Dressed States of Josephson Phase Qubit Coupled to an LC Circuit

M. Wulf, Thomas Ohki, Xingxiang Zhou, M. J. Feldman

Published Jun 1, 2005• 6 citations
Publisher

Abstract

We study the dynamics of a current biased Josephson phase qubit capacitively coupled to an LC circuit. We find that the eigenstates of this system are dressed states that are entangled states between the phase qubit and the LC resonator. We demonstrate that these dressed states can be probed by measuring the avoided crossing in the spectrum of the system. We present our experimental setup to investigate them. This system is interesting not only in demonstrating entanglement, the essential element for quantum information processing (QIP), but also in serving as a first step toward a solid-state analog of cavity QED.

DOI
10.1109/tasc.2005.850083

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We study the dynamics of a current biased Josephson phase qubit capacitively coupled to an LC circuit. We find that the eigenstates of this system are dressed states that are entangled states between the phase qubit and the LC resonator. We demonstrate that these dressed states can be probed by measuring the avoided crossing in the spectrum of the system. We present our experimental setup to investigate them. This system is interesting not only in demonstrating entanglement, the essential element for quantum information processing (QIP), but also in serving as a first step toward a solid-state analog of cavity QED.
We consider a circuit-QED setup that allows for controllable couplings between bosonic modes that locally interact with noisy qubits. In this setup, two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, are put in interaction by coupling the latter to a current-biased Josephson junction, working as a coupler. We solve this problem exactly and we proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits, which are also subjected to Markovian dephasing. We show that this analysis might serve the context for a first experimental assessment of non-Markovianity in a multi-element solid-state device.
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.
We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to another qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for the first experimental assessment of non-Markovianity in a multielement solid-state device.
We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.
The integration of superconducting qubits and resonators in one circuit offers a promising solution for quantum information processing (QIP), which also realizes the on-chip analogue of cavity quantum electrodynamics (QED), known as circuit QED. In most prototype circuit designs, qubits are active processing elements and resonators are peripherals. As resonators typically have better coherence performance and more accessible energy levels, it is proposed that the entangled qubit–resonator hybrid can be used as a processing element. To achieve such a goal, an accurate measurement of the hybrid is first necessary. Here we demonstrate a joint quantum state tomography (QST) technique to fully characterize an entangled qubit–resonator hybrid. We benchmarked our QST technique by generating and accurately characterizing multiple states, e.g. | gN 〉 + | e ( N − 1)〉 where (| g 〉 and | e 〉) are the ground and excited states of the qubit and (|0〉,...,| N 〉) are Fock states of the resonator. We further provided a numerical method to improve the QST efficiency and measured the decoherence dynamics of the bipartite hybrid, witnessing dissipation coming from both the qubit and the N -photon Fock state. As such, the joint QST presents an important step toward actively using the qubit–resonator element for QIP in hybrid quantum devices and for studying circuit QED.