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arXiv:0712.3970 · Physical Review Letters

Strong Tunable Coupling between a Superconducting Charge and Phase Qubit

Aurélien Fay, Emile Hoskinson, Florent Lecocq, Laurent-Patrick Lévy, F. W. J. Hekking, Wiebke Guichard, O. Buisson

Published May 6, 2008• 38 citations
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Abstract

We have realized a tunable coupling over a large frequency range between an asymmetric Cooper pair transistor (charge qubit) and a dc SQUID (phase qubit). Our circuit enables the independent manipulation of the quantum states of each qubit as well as their entanglement. The measurement of the charge qubit's quantum states is performed by an adiabatic quantum transfer from the charge to the phase qubit. The measured coupling strength is in agreement with an analytic theory including a capacitive and a tunable Josephson coupling between the two qubits.

DOI
10.1103/physrevlett.100.187003

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We have realized a tunable coupling over a large frequency range between an asymmetric Cooper pair transistor (charge qubit) and a dc SQUID (phase qubit). Our circuit enables the independent manipulation of the quantum states of each qubit as well as their entanglement. The measurement of the charge qubit's quantum states is performed by an adiabatic quantum transfer from the charge to the phase qubit. The measured coupling strength is in agreement with an analytic theory including a capacitive and a tunable Josephson coupling between the two qubits.
We present a theoretical analysis of a superconducting quantum circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc superconduction quantum intereference device (SQUID). Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc SQUID can be viewed as a tunable micrometer-sized resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regime. It describes very precisely the tunable coupling strength measured in this circuit [A. Fay et al., Phys. Rev. Lett. 100, 187003 (2008)] and explains the ``quantronium'' as well as the adiabatic quantum transfer readout.
We present a theoretical analysis of the quantum dynamics of a superconducting circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc-SQUID. Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc-SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc-SQUID can be viewed as a tunable micron-size resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regimes. It describes very precisely the tunable coupling strength measured in this circuit and explains the 'quantronium' as well as the adiabatic quantum transfer read-out.
We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
A protocol to test cross correlations between charge and critical-current noise in the small superconducting contacts of an asymmetric Cooper-pair transistor coupled to a phase qubit is presented. The superconducting circuit behaves as a tunable four-level quantum system that can be prepared in two different configurations where cross-correlation terms are, respectively, absent or present and therefore, in principle, detectable. The measurements of the cross correlations are performed either through the escape probability of the dc superconducting quantum interference device or a quantum-state tomography of a few elements of the reduced density matrix of the four-level quantum system.
We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need two dc SQUID's in the connecting loop and the control fluxes threading the dc SQUID's must be in opposite directions. The coupling strength is analytically calculated as a function of the control flux at the coresonance point.