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arXiv:cond-mat/0609294

Multiple and single measurements of a mesoscopic quantum system with two permitted states

A. A. Burlakov, Vladimir L. Gurtovoi, S. V. Dubonos, А. В. Никулов, V. A. Tulin

Published Sep 12, 2006• 1 citation
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Abstract

Mesoscopic loop is proposed in many works as possible solid-state quantum bit, i.e. two-state quantum system. The quantum oscillations of resistance and of rectified voltage observed on asymmetric superconducting loops give evidence of the two states at magnetic flux divisible by half of the flux quantum. But our measurements of quantum oscillations of the critical current of these loops have given results coming into irreconcilable contradictions with result of the observations of the quantum oscillations of resistance.

DOI
10.48550/arxiv.cond-mat/0609294

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Mesoscopic loop is proposed in many works as possible solid-state quantum bit, i.e. two-state quantum system. The quantum oscillations of resistance and of rectified voltage observed on asymmetric superconducting loops give evidence of the two states at magnetic flux divisible by half of the flux quantum. But our measurements of quantum oscillations of the critical current of these loops have given results coming into irreconcilable contradictions with result of the observations of the quantum oscillations of resistance.
Multiple and single measurements of quantum states of mesoscopic superconducting loops are carried out in order to investigate a possibility of macroscopic quantum superposition and of creation of a superconductor quantum register. Asymmetric superconducting rings are used in order to be convinced that single measurement gives result corresponding to one of permitted states and multiple one gives an average value on these states. We have measured magnetic dependencies of resistance, rectified voltage and critical current on these rings. The observed quantum oscillations of the resistance and the rectified voltage, corresponding to multiple measurement of quantum states, give evidence of two permitted states at the magnetic flux inside the ring divisible by half of the flux quantum. But the observed quantum oscillations of the critical current, corresponding to single measurement, not only does not confirm these two quantum states, but are in a direct contradiction with the observed oscillations of the resistance. It is assumed that the observed contradiction between the results of measurements made on the same ring can testify to violation of the principle of realism on the mesoscopic level that is a necessary condition for an opportunity of creation of a quantum computer.
Voltage biasing of a single superconducting weak link results in coherent electromagnetic oscillation at the frequency $\ensuremath{\nu}=\frac{V}{{\ensuremath{\Phi}}_{0}}$; simultaneous voltage biasing of two weak links in a superconducting ring produces two strongly coupled oscillators at the same frequency. The electromagnetic phase difference is the difference in the gauge-invariant quantum phases across the two contacts. Because of the quantization of the superconducting ring, this phase difference is $\frac{2\ensuremath{\pi}〈\ensuremath{\Phi}〉}{{\ensuremath{\Phi}}_{0}}$, where $〈\ensuremath{\Phi}〉$ is the time-averaged magnetic flux in the superconducting circuit and ${\ensuremath{\Phi}}_{0}$ is the flux quantum. We can characterize the coupled system in terms of normal modes, and we have experimentally observed these modes of oscillation at 30 MHz. This provides a means of understanding the earlier observations of quantum interference in the resistive state.
We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.
Superconducting loop interrupted by one or three Josephson junctions is considered in many publications as a possible quantum bit, flux qubit, which can be used for creation of quantum computer. But the assumption on superposition of two macroscopically distinct quantum states of superconducting loop contradict to the fundamental law of angular momentum conservation and the universally recognized quantum formalism. Numerous publications devoted to the flux qubit testify to an inadequate interpretation by many authors of paradoxical nature of superposition principle and the subject of quantum description.
Connection between an intrinsic breach of symmetry of equilibrium motion and violation of the second law is accentuated. An intrinsic breach only of clockwise - counter-clockwise symmetry of a circular equilibrium motion can be logical under equilibrium conditions, whereas a breach of right-left symmetry should be always an actual violation of the second law. The reader's attention is drawn to experimental evidence of an intrinsic breach of the clockwise - counter-clockwise symmetry of a circular equilibrium motion, well known as the persistent current. The persistent current is observed in mesoscopic normal metal, semiconductor and superconductor loops and the clockwise - counter-clockwise symmetry is broken because of the discrete spectrum of the permitted states of quantum charged particles in a closed loop. The quantum oscillations of the dc voltage observed on a segment of an asymmetric superconducting loop is experimental evidence of the intrinsic breach of the right-left symmetry and an actual violation of the second law.
Superconducting circuits, photonic cavities, and tiny mechanical oscillators are versatile systems in which quantum dynamics can be observed and controlled. These various technologies can be combined, and the resulting “circuits” are often referred to as nano-electromechanical or optomechanical systems. In the context of quantum physics, such devices are referred to as “mesoscopic” because they contain a large number of atoms. This terminology distinguishes them from the “microscopic” systems of atom-optics, such as single ions [364] and atoms [545, 233, 26], and the spins of individual nuclei [412]. Nano-engineered systems provide an especially powerful arena for exploring quantum measurement and control because of their potential to realize complex circuits. In this chapter we explain how to treat these systems and describe in detail a common method used to measure them. Superconducting circuits The electrical circuits that we describe in this chapter are quite different from those that use normal conductors, such as copper wire at room temperature. Normal conductors are subject to strong dissipation and decoherence from the environment. As a result the dynamical degrees of freedom of the circuits, the currents and voltages, behave as classical variables. In superconducting circuits, the resistance, and thus the dissipation, is so small that the currents and voltages behave as quantum mechanical degrees of freedom. Of course, the current in a wire is actually composed of many elementary particles that each obey quantum mechanics. Why then should the current act like a single quantum degree of freedom? A mechanical analogy is useful here. Recall that even though a macroscopic pendulum is composed of many particles, when one talks about the motion of the pendulum one means the motion of the center-of-mass of its constituent particles. Since the center of mass is merely a linear combination of the coordinates of each particle, it is itself a valid quantum mechanical coordinate with a conjugate momentum. In a similar way the total current in a superconducting wire is a collective degree of freedom that obeys quantum mechanics.