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A tunable macroscopic quantum system based on two fractional vortices

Dennis Manuel Heim, Karl Vogel, Wolfgang P. Schleich, D. Koelle, R. Kleiner, E. Goldobin

Published May 13, 2013• 3 citations
Publisher

Abstract

Abstract We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.

DOI
10.18725/oparu-44305

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Abstract We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.
We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.
We propose a concept of a qubit based on two coupled fractional vortices pinned at two artificially created κ\kappaκ discontinuities of the Josephson phase in a long Josephson junction. Each discontinuity can be created by a pair of tiny current injectors with the current IinjI_\mathrm{inj}Iinj​ applied. We map the dynamics of the system to the dynamics of a single particle in a double-well potential and calculate the effective parameters of this potential. By tuning the discontinuities κ∝Iinj\kappa \propto I_\mathrm{inj}κ∝Iinj​ during the experiment we are able to control the parameters of the effective double-well potential as well as to initialize the fractional vortex molecule to a desired state. The system can be used to study macroscopic quantum phenomena involving tailored vortex matter.
The quantum dynamics of population-balanced fractional vortices and population-imbalanced vortices in an effective two-state bosonic system, made of two coupled discrete circuits with few sites, is addressed within the Bose-Hubbard model. We show that, for low on-site interaction, the tunneling of quantized vortices between the rings performs a coherent, oscillating dynamics connecting current states with chiral symmetry. The vortex-flux transfer dually follows the usual sinusoidal particle current of the Josephson effect, in good agreement with a mean-field approximation. Within such a regime, the switch of persistent currents in the rings resembles flux-qubit features and is feasible for experimental realization. On the contrary, strong interatomic interactions suppress the chiral current and lead the system into fragmented condensation.
We consider a symmetric $0\text{\ensuremath{-}}\ensuremath{\pi}$ Josephson junction of length LLL, which classically can be in one of two degenerate ground states $\ensuremath{\uparrow}$ or $\ensuremath{\downarrow}$, corresponding to supercurrents circulating clockwise or counterclockwise around the $0\text{\ensuremath{-}}\ensuremath{\pi}$ boundary. When the length LLL of the junction becomes smaller than the Josephson penetration depth ${\ensuremath{\lambda}}_{J}$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling to the neighboring well. We map this problem to the dynamics of a single particle in a periodic double-well potential and estimate parameters for which macroscopic quantum coherence may be observed experimentally. We conclude that this system is not very promising to build a qubit because (a) it requires very low temperatures to reach the quantum regime, (b) its tiny flux is hard to read out, and (c) it is very sensitive to the asymmetries between the 0 and $\ensuremath{\pi}$ parts of the junction.
We study the mass exchange between two rotating, quantum massive vortices in a two-component Bose-Einstein condensate. The vortices, in the majority component, exhibit a filled core, where the in-filling minority component undergoes a quantum tunneling effect. Remarkably, we observe that the two-vortex system features stable Josephson oscillations, as well as all the nonlinear phenomena, including the macroscopic quantum self-trapping, that characterize a Bosonic Josephson Junction. We propose an analytical model for describing the intervortex tunneling, obtained by implementing the coherent-state representation of the two-mode Bose-Hubbard model. This allows us to give the explicit expression of the model's parameters in terms of the physical macroscopic parameters of the two-vortex system. The comparison of the dynamical scenario predicted by the model with that emerging from the Gross–Pitaevskii equations is very good for sufficiently small atom numbers, while at larger atom numbers it grows less precise, presumably due to the partial exclusion of the many-body interactions from our model. The definition of an effective self-interaction parameter allows us to include the many-body effects, thus restoring a quite good agreement with the numerical results. Interestingly, the recognition of the bosonic Josephson dynamics paves the way to the investigation of new dynamical behaviors in multivortex configurations. Published by the American Physical Society 2024
We investigate the effects of a high-quality resonant cavity on macroscopic quantum tunneling (MQT) of fluxons from both a metastable state to continuum and from one degenerate ground state of a double-well potential to the other. By using a set of two coupled perturbed sine-Gordon equations, we describe the tunneling processes in linear long Josephson junctions and find that MQT in the resonant cavity increases due to potential renormalization, induced by the interaction between the fluxon and the cavity. Enhancement of the MQT rate in the weak-coupling regime is estimated by using the experimentally accessible range of the model parameters. The tunneling rate from the metastable state is found to increase weakly with increasing junction-cavity interaction strength. However, the energy splitting between the two degenerate ground states of the double-well potential increases significantly with increasing both the interaction strength and the frequency of the resonant cavity mode. Finally, we discuss how the resonant cavity may be used to tune the property of Josephson vortex quantum bits.