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Physical Review Letters

Demonstration of absolute magnetic-flux quantization in a superconducting circuit

Blas Cabrera, C. E. Cunningham, D.P. Saroff

Published Apr 24, 1989• 10 citations
Publisher

Abstract

We have demonstrated experimentally that magnetic-flux quantization in a superconducting circuit is obeyed in an absolute sense, and have ruled out the possibility of a fractional quantum of magnetic flux. We use an optically switched superconducting microbridge to destroy and reestablish the phase coherence of the order parameter around a superconducting circuit. Changes in the vector potential while the global phase coherence is destroyed are still observed when the coherence is reestablished, even though the magnetic field is inacessible to the superconductor.

DOI
10.1103/physrevlett.62.2040

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We have demonstrated experimentally that magnetic-flux quantization in a superconducting circuit is obeyed in an absolute sense, and have ruled out the possibility of a fractional quantum of magnetic flux. We use an optically switched superconducting microbridge to destroy and reestablish the phase coherence of the order parameter around a superconducting circuit. Changes in the vector potential while the global phase coherence is destroyed are still observed when the coherence is reestablished, even though the magnetic field is inacessible to the superconductor.
We propose a nonlocal flux-transfer experiment in which a quantized magnetic-field excitation confined within one toroidal superconducting structure is coherently transferred to a spatially separated toroid without magnetic-field occupation of the intervening region. The transfer arises from quantized Aharonov-Bohm-type vector potential coupling mediated by a superconducting loop threading the toroids, which, however, remains in the ground state, acting only through a global fluxoid constraint. A direct experimental signature would be the observation of correlated, time-resolved flux exchange between remote toroids in a SQUID readout. We analyze an apparent signaling paradox related to this interaction as a probe of the broader question of whether spatiotemporal quantum coherence is fundamentally bounded. The proposed setup can provide an experimental testbed for addressing foundational questions such as the existence of an objective collapse of a wavefunction or the fundamental limits of macroscopic quantum coherence which is relevant to large scale quantum computers.
We developed a minimal method of forming and detecting a fractional magnetic flux quantum in a two-component superconductor fabricated using an ultra-thin niobium bilayer that sandwiches a Josephson barrier. The fractional quantum created by cooling a bilayer disk in the magnetic field survived after turning off the magnetic field. The survived quantum was confirmed by the change in the critical current of a superconducting quantum interference device (SQUID) placed on the bilayer disk. By replacing a flux qubit with the SQUID, we can use the fractional flux quantum as the flux bias for the flux qubit. This method enables the investigation of fractional quantization and the related topology.
The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as charge and flux. Although this approach is highly successful, it leaves open why these macroscopic variables should obey quantum commutation relations and how this behavior emerges from the superconducting state. In this work, starting from the microscopic pairing Hamiltonian underlying BCS superconductivity, we derive the low-energy effective Hamiltonian of a circuit-QED architecture containing a superconducting transmission line with distributed capacitive and inductive elements. We establish quantitative relations between macroscopic observables, including current and voltage, and the spatially local superconducting phase, as well as the microscopic parameters of the electron-phonon system. We then extend the third quantization of the superconducting order parameter, introduced in Paper (I) for the global phase, to the spatially local case. This gives a macroscopic field quantization of the superconducting phase. We show that, after restriction to the low-energy excitation subspace, the local superconducting phase becomes a genuine quantum dynamical variable. Thus, the quantum behavior of transmission-line resonators need not be postulated at the macroscopic level, but follows from the third quantization of the superconducting order parameter. These results suggest that capacitive and inductive superconducting circuit elements share the same microscopic origin, providing a unified framework for superconducting circuit quantization.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.
Superconducting circuits containing Josephson junctions have previously been shown to exist in superpositions of states of electric charge and of superconducting phase. This superposition manifests itself in so-called Rabi oscillations between the two energy levels produced by the superposition. In his Perspective, Clarke highlights the report of Chiorescu et al. , who demonstrate that a superconducting ring containing three Josephson junctions also exhibits Rabi oscillations, and thus exists in a superposition of magnetic flux states. The experiments are elegant demonstrations of coherence in superconducting circuits, and are potentially of interest as quantum bits in a future computer.