High fidelity control of a many-body Tonks--Girardeau gas with an effective mean-field approach

Abstract

Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and non-interacting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks--Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques.

8 pages, 5 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Tools for quantum simulation with ultracold atoms in optical lattices
• Fast atomic transport without vibrational heating
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• High-fidelity rapid ground-state loading of an ultracold gas into an optical lattice
• An efficient non-linear Feshbach engine
• Probing Quantum Speed Limits with Ultracold Gases
• A Feshbach engine in the Thomas-Fermi regime
• Exact ground states of quantum many-body systems under confinement
• Spin squeezing in internal bosonic Josephson junctions via enhanced shortcuts to adiabaticity
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Effective self-similar expansion of a Bose-Einstein condensate: Free space vs confined geometries
• Shortcuts to adiabaticity in superconducting circuits for fast multi-partite state generation
• Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases

Cited by in corpus (3)

• Twist-and-turn dynamics of spin squeezing in bosonic Josephson junctions: Enhanced shortcuts-to-adiabaticity approach
• Universal principles for sudden-quench quantum Otto engines
• Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions