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arXiv:1210.6310 · Physical Review B

Tunneling spectroscopy using a probe qubit

A. J. Berkley, A. J. Przybysz, Trevor M. Lanting, R. Harris, Neil G. Dickson, Fabio Altomare, M. H. S. Amin, P. Bunyk, Colin Enderud, Emile Hoskinson, Mark W. Johnson, E. Ladizinsky, R. Neufeld, Chris C. Rich, Anatoly Yu. Smirnov, E. Tolkacheva, Sergey V. Uchaikin, A. B. Wilson

Published Jan 3, 2013• 35 citations
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Abstract

We describe a quantum tunneling spectroscopy technique that requires only low-bandwidth control. The method involves coupling a probe qubit to the system under study to create a localized probe state. The energy of the probe state is then scanned with respect to the unperturbed energy levels of the probed system. Incoherent tunneling transitions that flip the state of the probe qubit occur when the energy bias of the probe is close to an eigenenergy of the probed system. Monitoring these transitions allows the reconstruction of the probed system eigenspectrum. We demonstrate this method on an rf SQUID flux qubit.

DOI
10.1103/physrevb.87.020502

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We describe a quantum tunneling spectroscopy technique that requires only low-bandwidth control. The method involves coupling a probe qubit to the system under study to create a localized probe state. The energy of the probe state is then scanned with respect to the unperturbed energy levels of the probed system. Incoherent tunneling transitions that flip the state of the probe qubit occur when the energy bias of the probe is close to an eigenenergy of the probed system. Monitoring these transitions allows the reconstruction of the probed system eigenspectrum. We demonstrate this method on an rf SQUID flux qubit.
We report measurements of macroscopic resonant tunneling between the two lowest energy states of a pair of magnetically coupled rf-superconducting quantum interference device flux qubits. This technique provides both a direct means of measuring the energy gap of the two-qubit system and a method for probing of the environment coupled to the pair of qubits. Measurements of the tunneling rate as a function of qubit flux bias show a Gaussian line shape that is well matched to theoretical predictions. Moreover, the peak widths indicate that each qubit is coupled to a local environment whose fluctuations are uncorrelated with that of the other qubit.
Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than the target well. The rms amplitude of the noise, which is proportional to the dephasing rate 1/tauphi, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.
Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has recently become possible by qubit tunneling spectroscopy (QTS). In the standard QTS experiments, an incoherent probe qubit is strongly coupled to one of the qubits of the system in such a way that its incoherent tunneling rate provides information about the energy eigenvalues of the original (source) system. In this paper, we generalize QTS by coupling the probe qubit to many source qubits. We show that by properly choosing the couplings, one can perform projective measurements of the source system energy eigenstates in an arbitrary basis, thus performing quantum eigenstate tomography. As a practical example of a limited tomography, we apply our scheme to probe the eigenstates of a kink in a frustrated transverse Ising chain.
Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has recently become possible by qubit tunneling spectroscopy (QTS). In the standard QTS experiments, an incoherent probe qubit is strongly coupled to one of the qubits of the system in such a way that its incoherent tunneling rate provides information about the energy eigenvalues of the original (source) system. In this paper, we generalize QTS by coupling the probe qubit to many source qubits. We show that by properly choosing the couplings, one can perform projective measurements of the source system energy eigenstates in an arbitrary basis, thus performing quantum eigenstate tomography. As a practical example of a limited tomography, we apply our scheme to probe the eigenstates of a kink in a frustrated transverse Ising chain.
It is well known that that superconducting qubits based on Josephson junctions have the advantages of scalability and the qubit states are easy to prepare and control. In addition, demonstration of Rabi oscillations in various superconducting circuits shows that superconducting qubits are promising for scalable quantum information processing. However, despite flexibility of design and fabrication, easier to scale up, and fast gate speed, superconducting qubits usually have much shorter decoherence time than trapped ions, NMR etc. due to the relatively strong interactions between qubits and environment. Recent experiments show that low frequency flux noise is the dominant mechanism of decoherence in superconducting flux qubits. However, despite extensive effort the origin of flux noise is still not well understood. The goal of this work is to identify the source and characterize the property of flux noisein rf SQUID flux qubit through various spectroscopy and time-resolved measurements. Our result show that one can determine all circuit parameters needed for reconstructing qubit Hamiltonian with high accuracy via measurement of macroscopic resonant tunneling (MRT) and photon assisted tunneling (PAT) and that the amount of flux noise in rf SQUID qubits scales linearly with self inductance of the qubits. In addition, we have investigated the dynamics of a three-level flux qubit in incoherent regime. The result demonstrates that treating a multi-level physical qubit, such as the superconducting flux qubit, as an ideal two-level quantum system may be inadequate under certain circumstances.