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arXiv:cond-mat/0609627 · Physical Review B

Spectroscopy of three strongly coupled flux qubits

A. O. Niskanen, K. Harrabi, Fumiki Yoshihara, Yasunobu Nakamura, J. S. Tsai

Published Dec 5, 2006• 32 citations
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Abstract

We have carried out spectroscopic measurements of a system of three strongly coupled four-junction flux qubits. The samples studied cover a wide range of parameters with the coupling energy between neighboring qubits varying between $0.75\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ and $6.05\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. The observed complicated spectra agree well with eight-level theory. The experiments are relevant for the realization of a tunable coupling between qubits.

DOI
10.1103/physrevb.74.220503

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We have carried out spectroscopic measurements of a system of three strongly coupled four-junction flux qubits. The samples studied cover a wide range of parameters with the coupling energy between neighboring qubits varying between 0.75GHz0.75\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}0.75GHz and 6.05GHz6.05\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}6.05GHz. The observed complicated spectra agree well with eight-level theory. The experiments are relevant for the realization of a tunable coupling between qubits.
We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.
We study the quantum mechanical behavior of a macroscopic, three-body, superconducting circuit. Microwave spectroscopy on our system, a resonator coupling two large Josephson junctions, produced complex energy spectra well explained by quantum theory over a large frequency range. By tuning each junction separately into resonance with the resonator, we first observe strong coupling between each junction and the resonator. Bringing both junctions together into resonance with the resonator, we find spectroscopic evidence for entanglement between all 3 degrees of freedom and suggest a new method for controllable coupling of distant qubits, a key step toward quantum computation.
Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time T Rabi = 78 ns and energy relaxation time T 1 = 315 ns. We found that the value of T Rabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.
A double-loop four-Josephson-junction (4-JJ) flux qubit has an advantage over a three-Josephson-junction flux qubit in that the energy gap Δ at the symmetry point can be controlled in situ by varying the magnetic flux in one of the two loops. We report the results of a microwave spectroscopy measurement of a 4-JJ qubit. The magnetic fluxes in the two loops were controlled via a magnetic field and control flux. The excitation energy spectra at various values of control flux indicate the tunability of Δ via the control flux. Two branches of the excitation spectra were observed.
A double-loop four-Josephson-junction (4-JJ) flux qubit is a tunable qubit wherein the potential profile can be varied in situ via two applied magnetic fluxes. This provides a high level of control over state transitions. Here, we report the results of spectroscopic measurements on this system. We observed microwave resonances associated with the first and second excited states. A branch of resonances that is most likely attributable to the third excited state was also observed. The excitation energy spectra for these levels were in qualitative agreement with the results of simplified calculations performed using an effective Hamiltonian with two phases. The three lowest levels characterized in this study may allow novel applications, including those proposed theoretically in the past. Our analysis showed that the potential exhibited a crossover from the commonly used double-well regime to the novel single-well regime. This indicates the possibility of manipulation and readout of a 3-JJ (and 4-JJ) qubit in the single-well regime using a simple technique.
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a superconducting quantum interference device. Those two elements allow to engineer qubits Hamiltonians with XX, YY, and ZZ interactions, including ultrastrongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely, the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.