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arXiv:cond-mat/0209315 · Fortschritte der Physik

Rabi oscillations, Ramsey fringes and spin echoes in an electrical circuit

D. Vion, A. Aassime, Audrey Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, Michel Devoret

Published Apr 24, 2003• 38 citations
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Abstract

Abstract We present a superconducting tunnel junction circuit which behaves as a controllable atom, and whose ground and first excited state form an effective spin 1/2. By applying microwave pulses, we have performed on this circuit experiments demonstrating the controlled manipulation of the spin : Rabi precession, Ramsey interferences, and spin echoes.

DOI
10.1002/prop.200310063

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Abstract We present a superconducting tunnel junction circuit which behaves as a controllable atom, and whose ground and first excited state form an effective spin 1/2. By applying microwave pulses, we have performed on this circuit experiments demonstrating the controlled manipulation of the spin : Rabi precession, Ramsey interferences, and spin echoes.
We have designed and operated a novel superconducting tunnel junction circuit which behaves as a controllable atom, with a ground and first excited state forming an effective spin 1/2. These two states are the symmetric and antisymmetric combinations of two charge configurations of a Cooper pair box. Any spin orientation corresponding to an arbitrary superposition of these two states can be prepared by applying NMR-like microwave pulses to the gate of the box. The spin state is readout by measuring the voltage response to a probe current pulse applied to the bridge formed by the two junctions of the box and an additional large, shunting junction. In a sample whose transition period is 60 ps, coherent superpositions decay with a 0.5 μs time constant, as measured by a Ramsey fringes experiment. This result is a step towards the realization of a solid-state quantum information processor.
We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the "quantronium." An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout subcircuit. The measured quality factor of quantum coherence Qphi approximately 25,000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
Quantum tunneling is the phenomenon that makes superconducting circuits "quantum". Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information processing. Here, we report a direct observation of quantum interference induced by such tunneling and its dynamics in a planar superconducting circuit through Wigner tomography. We experimentally elucidate all essential properties of this quantum interference, such as mapping from Fock states to cat states, a temporal oscillation due to the pump detuning, as well as its characteristic Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as manipulations of the observed quantum interference. Our findings lay the groundwork for further studies on quantum properties of superconducting Kerr parametric oscillators and their use in quantum information technologies.
In addition to Rabi, Ramsey, and spin echo experiments for a single qubit, we have successfully demonstrated the conditional operations with more complex pulse sequences of a qubit interacting with an LC harmonic oscillator. Rabi oscillations between |e,0〉 ↔ |g,1〉 (red sideband) and |g,0〉 ↔ |e,1〉 (blue sideband) were observed, where we noted coupled state as |qubit, LC‐oscillator〉. If we consider an LC‐oscillator as a quantum information bus, this is a first step to demonstrate the Cirac‐Zoller scheme in a field of macroscopic superconducting circuit.
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 present an analytical and computational study of resonances and transient responses in a classical Josephson junction system. A theoretical basis for resonances in a superconducting loop with three junctions is presented, outlining both the direct relationship between the dynamics of single- and multijunction systems and the direct relationships between observations of the classical counterparts to Rabi oscillations, Ramsey fringes, and spin-echo oscillations in this class of systems. We show simulation data along with analytical analyses of the classical model, and the results are related to previously reported experiments conducted on three junction loops. We further investigate the effect of off-resonant microwave perturbations to, e.g., the Rabi-type response of the Josephson system, and we relate this response back to the nonlinear and multivalued resonance behavior previously reported for a single Josephson junction. The close relationships between single and multijunction behaviors demonstrate the underlying dynamical mechanism for a whole class of classical counterparts to expected quantum-mechanical observations in a variety of systems, namely, the resonant and transient behavior of a particle in an anharmonic potential well with subsequent escape.