Optimal protocols for finite-duration quantum quenches in the Luttinger model

Abstract

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to non-adiabaticity. We study the optimal protocol for swithcing on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\tau$, starting from the non-interacting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\tau /2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high energy modes. In the limit of large $\tau$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.

8 pages, 5 figures

References in corpus (15)

• The Luttinger model following a sudden interaction switch-on
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Quantum quench dynamics of the Luttinger model
• Fast atomic transport without vibrational heating
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Optimal non-linear passage through a quantum critical point
• Luttinger liquid universality in the time evolution after an interaction quench
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• Optimal Control of Majorana Zero Modes
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Controlling quantum critical dynamics of isolated systems
• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system
• Spectral properties of one-dimensional Fermi systems after an interaction quench
• Quantum adiabatic protocols using emergent local Hamiltonians