Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation

Abstract

Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap is investigated by combining techniques of the variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Control schemes considered in the paper include imaginary trap frequencies at short time scales, i.e., the HO potential replaced by the quadratic repulsive one. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help to address fundamental problems of the quantum speed limit and thermodynamics.

9 pages, 6 figures, to be published in Chaos

References in corpus (15)

• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Fast optimal transition between two equilibrium states
• Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
• Fast ground-state cooling of mechanical resonator with time-dependent optical cavities
• Optimal transport of ultracold atoms in the non-adiabatic regime
• The Quantum Refrigerator: The quest for absolute zero
• Focus on Shortcuts to Adiabaticity
• Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force
• An efficient non-linear Feshbach engine
• Fast generation of spin-squeezed states in bosonic Josephson junctions
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• Design of a Photonic Lattice Using Shortcuts to Adiabaticity
• Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
• Modulated trapping of interacting bosons in one dimension

Cited by in corpus (7)

• Quantum control of frequency tunable transmon superconducting qubits
• Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
• Time-Optimal Quantum Driving by Variational Circuit Learning
• Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases
• Time-optimal variational control of bright matter-wave soliton
• Shortcuts to Adiabatic Soliton Compression in Active Nonlinear Kerr Media
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method