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arXiv:cond-mat/0508448 · Physical Review Letters

Parametric Control of a Superconducting Flux Qubit

Shiro Saito, Takayoshi Meno, Masahito Ueda, Hirotaka Tanaka, Kouichi Semba, Hideaki Takayanagi

Published Mar 13, 2006• 54 citations
arXivHTMLPDF

Abstract

Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multiphoton Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a high quality testing ground for exploring nonlinear quantum phenomena of macroscopically distinct states.

DOI
10.1103/physrevlett.96.107001

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Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multiphoton Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a high quality testing ground for exploring nonlinear quantum phenomena of macroscopically distinct states.
The quantum state of a flux qubit was successfully pulse controlled by using a resonant microwave. We observed Ramsey fringes by applying a pair of phase-shifted π∕2 microwave pulses without introducing detuning. With this method, the qubit state can be rotated on an arbitrary axis in the x-y plane of the Bloch sphere in a rotating frame. We successfully observed qubit Larmor precession stroboscopically with an angular velocity of 2π×11.4Grad∕s. In combination with Rabi pulses, this method enables us to achieve full control of single qubit rotation with shorter operation time.
We study electromagnetically induced interference at superconducting qubits. The interaction between qubits and electromagnetic fields can provide additional coupling channels to qubit states, leading to quantum interference in a microwave driven qubit. In particular, the interwell relaxation or Rabi oscillation, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the qubits and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic frequency of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi oscillation, Rabi oscillation induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the qubit, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation, in not only the flux qubit but also the systems with no crossover structure, e.g. phase qubits.
Abstract We propose a versatile scheme for multiphoton frequency up/down conversion in flux superconducting qubit circuits, driven by a pair of microwaves tuned near and far off the qubit resonance. Flux qubits can be engineered with strong anharmonicity such that the two lowest eigenstates are energetically well separated from the higher ones. We demonstrate the high order non-linear transitions between the two lowest levels in the three-photon regime, by coupling the qubit to bichromatic microwave fields with the same Rabi frequencies. Both up and down conversions are presented and accurately interpreted with many-mode Floquet formalism. An intuitive graph theoretic approach elucidates the physics of multiphoton pumping and population trapping. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide range of frequencies. The proposed design and theoretical approach are applicable in maintaining the inter-connectivity of future superconducting quantum machines.
Interaction between quantum two-level systems (qubits) and electromagnetic fields can provide additional coupling channels to qubit states. In particular, the interwell relaxation or Rabi oscillations, resulting, respectively, from the multi- or single-mode interaction, can produce effective crossovers, leading to electromagnetically induced interference in microwave driven qubits. The environment is modeled by a multimode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the qubits and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic frequency of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi oscillations, Rabi-oscillation-induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the qubit, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation in qubits either with or without crossover structure.
We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux qubit, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like oscillation of the retrapping probability in one of the wells has a frequency ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase qubit. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor oscillation and microwave-driven Rabi oscillation are rather similar. Due to the higher frequency of the Larmor oscillations, the microwave-free qubit manipulation allows for much faster coherent operations.