Dynamical symmetry breaking with optimal control: reducing the number of pieces

Abstract

We analyse the production of defects during the dynamical crossing of a mean-field phase transition with a real order parameter. When the parameter that brings the system across the critical point changes in time according to a power-law schedule, we recover the predictions dictated by the well-known Kibble-Zurek theory. For a fixed duration of the evolution, we show that the average number of defects can be drastically reduced for a very large but finite system, by optimising the time dependence of the driving using optimal control techniques. Furthermore, the optimised protocol is robust against small fluctuations.

Published version

References in corpus (11)

• Universal adiabatic dynamics across a quantum critical point
• Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Optimal non-linear passage through a quantum critical point
• Kibble-Zurek mechanism in a quenched ferromagnetic Bose-Einstein condensate
• Vortex quantum creation and winding number scaling in a quenched spinor Bose gas
• Spontaneous nucleation of structural defects in inhomogeneous ion chains
• Optimal control of atom transport for quantum gates in optical lattices
• Theory of defect production in nonlinear quench across a quantum critical point
• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Cooling through optimal control of quantum evolution

Cited by in corpus (8)

• An information theoretical analysis of quantum optimal control
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• Universal dynamics of inhomogeneous quantum phase transitions: suppressing defect formation
• Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains
• Harnessing non-adiabatic excitations promoted by a quantum critical point
• Optimal suppression of defect generation during a passage across a quantum critical point
• Counterdiabatic control in the impulse regime
• Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions