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AIP conference proceedings

Coherent Control of Coupled Superconducting Macroscopic Quantum Systems

Kouichi Semba, Shiro Saito, Takayoshi Meno, Jan Johansson, Hideaki Takayanagi

Published Jan 1, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.2355013

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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.
We have observed the coherent exchange of a single energy quantum between a flux qubit and a superconducting LC circuit acting as a quantum harmonic oscillator. The exchange of an energy quantum is known as the vacuum Rabi oscillation: the qubit is oscillating between the excited state and the ground state and the oscillator between the vacuum state and the first excited state. We also show that we can detect the state of the oscillator with the qubit and thereby obtained evidence of level quantization of the LC circuit. Our results support the idea of using oscillators as couplers of solid-state qubits.
Recent experiments on quantum state engineering with superconducting circuits realized concepts originally introduced in the field of quantum optics. Motivated by one such experiment we investigate a Josephson qubit coupled to a slow LC oscillator with frequency much lower than the qubit’s energy splitting. The qubit is ac‐driven to perform Rabi oscillations, and the Rabi frequency is tuned to resonance with the oscillator. The properties of this driven circuit QED system depend strongly on relaxation and decoherence effects in the qubit. We investigate both one‐photon and two‐photon qubit‐oscillator coupling, the latter being dominant at the symmetry point of the qubit. When the qubit driving frequency is blue detuned, we find that the system exhibits lasing behavior; for red detuning the qubit cools the oscillator. Similar behavior is expected in an accessible range of parameters for a Josephson qubit coupled to a nano‐mechanical oscillator. In a different parameter regime, furthering the analogies between superconducting and quantum optical systems, we investigate Sisyphus damping, which is the key element of the Sisyphus cooling protocol, as well as its exact opposite, Sisyphus amplification.
Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in the GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high-quality resonant tank circuit, inductively coupled to the phase qubit. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase qubit), which explicitly account for the back action of a tank circuit. According to the results of our simulations the Rabi oscillations in the MHz range can be detected using the conventional NMR pulse Fourier technique.
I present a general scheme through which the evidence of a superposition involving distinct classical-like states of a macroscopic system can be probed. The scheme relies on a qubit being coupled to a macroscopic harmonic oscillator in such a way that it can be used to both prepare and probe a macroscopic superposition. Two potentially realizable implementations, one with a flux qubit coupled to a LC circuit, and the other with an ion-trap qubit coupled to the collective motion of several ions, are proposed.
We study the coupled-qubit oscillation driven by an oscillating field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.