Time fractals and discrete scale invariance with trapped ions
arXiv:1901.01661 · doi:10.1103/PhysRevA.100.011403
Abstract
We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates itself under a rescaling of distance for some scale factor, and a time fractal is a signal that is invariant under the rescaling of time. These features are reminiscent of the Efimov effect, which has been predicted and observed in bound states of three-body systems. We demonstrate that discrete scale invariance in the trapped ion system can be controlled with two independently tunable parameters. We also discuss the extension to n-body states where the discrete scaling symmetry has an exotic heterogeneous structure. The results we present can be realized using currently available technologies developed for trapped ion quantum systems.
arXiv comment4 + 5 pages (main + supplemental materials), 2 + 3 figures (main + supplemental materials), version to appear in Physical Review A Rapid Communications
References in corpus (18)
- Observation of a Discrete Time Crystal
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Evidence for Efimov quantum states in an ultracold gas of cesium atoms
- Renormalization of the Three-Body System with Short-Range Interactions
- The Three-Boson System with Short-Range Interactions
- Effective Theory of the Triton
- Observation of the Efimov state of the helium trimer
- Universal Properties of the Four-Body System with Large Scattering Length
- The Four-Boson System with Short-Range Interactions
- Anomalies in Quantum Mechanics: the 1/r^2 Potential
- Super Efimov effect of resonantly interacting fermions in two dimensions
- Universal Five- and Six-Body Droplets Tied to an Efimov Trimer
- Efimov Physics around the neutron rich Calcium-60 isotope
- Efimov effect in quantum magnets
- Liberating Efimov physics from three dimensions
- Observing a scale anomaly and a universal quantum phase transition in graphene
- Ground-state properties of unitary bosons: from clusters to matter
- Weakly bound molecules trapped with discrete scaling symmetries
Cited by in corpus (6)
- Projected Cooling Algorithm for Quantum Computation
- Fractional Dynamics with Non-Local Scaling
- Dynamical Fractal in Quantum Gases with Discrete Scaling Symmetry
- Quasienergy operators and generalized squeezed states for systems of trapped ions
- The fractal geometry and the mapping of Efimov states to Bloch states
- Bound-like State in a 1D Self-Similar Delta-Barrier Array