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Physical Review Letters

Qubit Assisted Probing of Coherence between Mesoscopic States of an Apparatus

Sougato Bose

Published Feb 15, 2006• 14 citations
Publisher

Abstract

I present a general scheme through which the evidence of a superposition involving distinct states of a mesoscopic system can be probed. The scheme relies on a single qubit being coupled to a mesoscopic harmonic oscillator in such a way that it can be used to both prepare and probe a superposition of states of the oscillator. Two potentially realizable implementations, one with a single flux qubit coupled to an LC circuit, and the other with a single ion-trap qubit coupled to the collective motion of several ions, are proposed.

DOI
10.1103/physrevlett.96.060402

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I present a general scheme through which the evidence of a superposition involving distinct states of a mesoscopic system can be probed. The scheme relies on a single qubit being coupled to a mesoscopic harmonic oscillator in such a way that it can be used to both prepare and probe a superposition of states of the oscillator. Two potentially realizable implementations, one with a single flux qubit coupled to an LC circuit, and the other with a single ion-trap qubit coupled to the collective motion of several ions, are proposed.
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.
In this paper I present a foundational application of a qubit in probing the domain of validity of the quantum superposition principle. I show how a qubit can be coupled to a mesoscopic harmonic oscillator to both create and probe a superposition of states which involves distinct coherent states of the oscillator. Many harmonic oscillator systems are being developed as apparatus for a qubit and I argue that simply setting these oscillators to work in an under‐damped regime is enough to implement the scheme I discuss. I present two realizations: one based on a flux qubit coupled to a LCR circuit and the other based on a ion trap qubit coupled to the vibration of N ions.
We consider a system of two superconducting islands, each of which is coupled to a bulk superconductor via Josephson tunneling. One of the islands represents a "Cooper-pair box", i.e. it is an effective two-level system. The other island has a smaller charging energy and approximates a harmonic oscillator. A capacitive interaction between the islands results in a dependence of the oscillator frequency on the quantum state of the box. Placing the latter in a coherent superposition of its eigenstates and exciting coherent oscillations in the large island will lead to a phase-shift of these oscillations depending on the box quantum state, thereby producing a coherent superposition of two "mesoscopically distinct" quantum states in the large island.
We consider a system of two superconducting islands, each of which is coupled to a bulk superconductor via Josephson tunneling. One of the islands represents a ``Cooper-pair box,'' i.e., it is an effective two-level system. The other island has a smaller charging energy and approximates a harmonic oscillator. A capacitive interaction between the islands results in a dependence of the oscillator frequency on the quantum state of the box. Placing the latter in a coherent superposition of its eigenstates and exciting coherent oscillations in the large island will lead to a phase shift of these oscillations depending on the box quantum state, thereby producing a coherent superposition of two ``mesoscopically distinct'' quantum states in the large island.