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arXiv:cond-mat/0308192 · Physical Review Letters

Spectroscopy on Two Coupled Superconducting Flux Qubits

Johannes Majer, F. G. Paauw, A. C. J. ter Haar, C. J. P. M. Harmans, Johan E. Mooij

Published Mar 9, 2005• 240 citations
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Abstract

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a sigma(z)(1)sigma(z)(2) interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the applied magnetic field, we observe the coupling of the qubits. The coupling strength agrees with calculations of the mutual inductance.

DOI
10.1103/physrevlett.94.090501

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We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a sigma(z)(1)sigma(z)(2) interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the applied magnetic field, we observe the coupling of the qubits. The coupling strength agrees with calculations of the mutual inductance.
We have designed and experimentally implemented a circuit of inductively coupled superconducting charge qubits, where a Josephson junction is used as an inductance, and the coupling between the qubits is controlled by an applied magnetic flux. Spectroscopic measurements on the circuit are in good agreement with theoretical calculations. We observed anticrossings which originate from the coupling between the qubit and the plasma mode of the Josephson junction. Moreover, the size of the anticrossing depends on the external magnetic flux, which demonstrates the controllability of the coupling.
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.
The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.
We experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength JJJ whose sign and magnitude can be tuned in situ. To measure the effective JJJ, the ground state of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that JJJ can be tuned from antiferromagnetic through zero to ferromagnetic.
Superconducting qubit networks (SQNs) embedded in a low-dissipative resonator is a promising device allowing one not only to establish the collective quantum dynamics on a macroscopic scale but also to greatly enhance the sensitivity of detectors of microwave photons. A quantum ac Stark effect provided by coupling between an SQN and microwave photons of a resonator, leads to a strong nonlinear interaction between photons. Here, we present a two-tone spectroscopy experiment in which a set of 10 superconducting flux qubits is coupled to the input R- resonator and the output T- transmission line. An external microwave pump field close to the resonance frequency populates macroscopically the resonator mode as a Bose-Einstein condensate, while a second probe beam scans the resonances referred also as Bogoliubov-like excitations. The corresponding excitation frequency measured from the transmission coefficient, |S21(f)| displays an abrupt change of the resonant dip position once the power of the pump field overcomes a critical value Pcr. This sharp shift occurs in a narrow region of pump frequencies, and can be tuned by an applied magnetic field. It is a signature of bistability of the photon number inside the resonator, in agreement with theory.
The authors propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables them to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator can be as large as submillimeters and qubits interact with it via mutual inductance, their scheme makes it possible to construct a quantum gate involving remote qubits.