Modelling assisted tunneling on the Bloch sphere using the Quantum Composer

Abstract

The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing-UP of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.

arXiv comment19 pages, 11 figures, submitted to European Journal of Physics

References in corpus (25)

• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• Single Particle Tunneling in Strongly Driven Double Well Potentials
• Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
• Developing and Researching PhET simulations for Teaching Quantum Mechanics
• Superconducting Qubits: A Short Review
• Interactive learning tutorials on quantum mechanics
• The double well potential in quantum mechanics: a simple, numerically exact formulation
• Swing-up of quantum emitter population using detuned pulses
• SUPER Scheme in Action: Experimental Demonstration of Red-detuned Excitation of a Quantum Dot
• Periodic Quantum Tunneling and Parametric Resonance with Cigar-Shaped Bose-Einstein Condensates
• Tunneling and energy splitting in an asymmetric double-well potential
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• QEngine: An open-source C++ Library for Quantum Optimal Control of Ultracold Atoms
• Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation
• Time-Optimal Control of Collisional $\sqrt{\text{SWAP}}$ Gates in Ultracold Atomic Systems
• Two-level systems with periodic $N$-step driving fields: Exact dynamics and quantum state manipulations
• Engineering Double-Well Potentials with Variable-Width Annular Josephson Tunnel Junctions
• Spatial tomography of individual atoms in a quantum gas microscope
• Quantum Composer: A programmable quantum visualization and simulation tool for education and research
• Student use of a quantum simulation and visualization tool
• Steady-state entanglement in a double-well Bose-Einstein condensate through coupling to a superconducting resonator
• The impact of an interactive visualization and simulation tool on learning quantum physics: Results of an eye-tracking study
• Chaotic Tunneling in a Laser Field
• Parametric Resonance Phenomena in Bose-Einstein Condensates: Enhanced Quantum Tunneling of Coherent Matter Pulses