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arXiv:cond-mat/0312635

Signature of entangled eigenstates in the magnetic response of two coupled flux qubits

Anatoly Yu. Smirnov

Published Dec 24, 2003• 0 citations
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Abstract

We study dissipative dynamics and a magnetic response of two coupled flux qubits interacting with a high quality tank in the framework of the impedance measurement technique (IMT). It is shown that the observation of the difference between a sum of IMT signals from separated qubits and the signal from the system when both qubits are in the degeneracy point (IMT deficit) implies immediately a formation of the entangled two-qubit eigenstates.

DOI
10.48550/arxiv.cond-mat/0312635

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We study dissipative dynamics and a magnetic response of two coupled flux qubits interacting with a high quality tank in the framework of the impedance measurement technique (IMT). It is shown that the observation of the difference between a sum of IMT signals from separated qubits and the signal from the system when both qubits are in the degeneracy point (IMT deficit) implies immediately a formation of the entangled two-qubit eigenstates.
We have studied the low-frequency magnetic susceptibility of two inductively coupled flux qubits using the impedance measurement technique (IMT), through their influence on the resonant properties of a weakly coupled high-quality tank circuit. In a single qubit, an IMT dip in the tank's current-voltage phase angle at the level anticrossing yields the amplitude of coherent flux tunneling. For two qubits, the difference (IMT deficit) between the sum of single-qubit dips and the dip amplitude when both qubits are at degeneracy shows that the system is in a mixture of entangled states (a necessary condition for entanglement). The dependence on temperature and relative bias between the qubits allows one to determine all the parameters of the effective Hamiltonian and equilibrium density matrix, and confirms the formation of entangled eigenstates.
The interaction of flux qubits with a low-frequency tank circuit is studied. It is shown that changes in the state of the interacting qubits influence the effective inductance and resistance of the circuit, which is the essence of the so-called impedance measurement technique. The multiphoton resonant excitations in both single flux qubits and pairs of coupled flux qubits are investigated. In particular, we compare our theoretical results with recent spectroscopy measurements, Landau-Zener interferometry, and the multiphoton fringes.
We propose to investigate flux qubits by the impedance measurement technique (IMT), currently used to determine the current-phase relation in Josephson junctions. We analyze in detail the case of a high-quality tank circuit coupled to a persistent-current qubit, to which the IMT was successfully applied in the classical regime. It is shown that the low-frequency IMT can give considerable information about the level anticrossing, in particular the value of the tunneling amplitude. An interesting difference exists between applying the ac bias directly to the tank and indirectly via the qubit. In the latter case, a convenient way to find the degeneracy point in situ is described. Our design only involves existing technology, and its noise tolerance is quantitatively estimated to be realistic.
We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.
We study theoretically the behavior of a superconducting flux qubit subjected to a series of electromagnetic pulses. The possibility of controlling the system state via changing the parameters of the pulse is studied. We calculated the phase shift in the tank circuit weakly coupled to the qubit which can be measured by the impedance measurement technique. For the flux qubit we consider the possibility of estimating the relaxation rate from the impedance measurements by varying the delay time between the pulses.