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Shortcuts to adiabaticity from linear response theory
Thiago V Acconcia1, Marcus V S Bonança1, Sebastian Deffner2
1Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas - Unicamp, Rua Sérgio Buarque de Holanda 777, 13083-859 Campinas, São Paulo, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
Shortcuts to adiabaticity achieve ideal final states in finite time. Researchers found these shortcuts for weak perturbations using linear response theory, identifying specific protocols for rapid, precise state transitions.
Area of Science:
- Quantum mechanics
- Thermodynamics
- Non-equilibrium physics
Background:
- Adiabatic processes are fundamental in quantum mechanics, enabling systems to reach specific final states without excitations.
- Achieving true adiabaticity requires infinitely slow transformations, which is often impractical.
- Shortcuts to adiabaticity offer a way to reach the same final states in finite time.
Purpose of the Study:
- To investigate the existence and characteristics of shortcuts to adiabaticity for weak perturbations.
- To develop a theoretical framework for identifying and implementing these shortcuts.
- To quantify the energy cost (excess work) associated with finite-time driving.
Main Methods:
- Application of linear response theory to analyze system dynamics under weak perturbations.
- Development and utilization of phenomenological response functions.
- Analysis of specific quantum systems: the quantum parametric oscillator and a spin-1/2 system in a time-dependent magnetic field.
Main Results:
- Demonstrated that shortcuts to adiabaticity can be found for weak perturbations.
- Derived a simple expression for excess work, quantifying non-equilibrium excitations.
- Identified finite-time zeros of excess work as indicators for the existence of shortcuts.
- Proposed a family of protocols enabling shortcuts for specific, short driving times.
Conclusions:
- Shortcuts to adiabaticity are achievable for weak perturbations, offering practical alternatives to infinitely slow adiabatic processes.
- Excess work serves as a crucial metric for identifying and optimizing shortcut protocols.
- The proposed protocols provide a pathway for rapid and efficient state preparation in quantum systems.
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