Overview
This research introduces a quantum control strategy designed for stroboscopic steady states and limit cycles within periodically driven dissipative systems. These steady orbits are established asymptotically when a control sequence is repeated infinitely. The proposed formalism focuses on identifying control sequences capable of directing a dissipative quantum system toward a steady orbit that passes through pre-defined waypoints.
Research Context
Periodically driven dissipative systems can evolve into steady orbits, manifesting as fixed loops on their dynamical manifolds. In quantum mechanics, these steady orbits are relevant in several applications. Examples include cooling engines, which are used to initialize quantum devices, and coherent oscillators, such as lasers and masers. They are also found in precision metrology devices, including atomic clocks, optical magnetometers, and spin magnetometers. Furthermore, steady orbits are pertinent in magnetic resonance contexts, specifically in steady-state free precession and dynamic nuclear polarization.
The control of steady orbits and stroboscopic steady states presents a promising objective for quantum optimal control. However, the numerical complexity associated with existing methods has been a significant barrier. Traditional gradient ascent pulse engineering (GRAPE), for instance, relies on explicit numerical propagation in the time domain. Its application to infinite loops, characteristic of asymptotic steady states, proves prohibitive due to this computational demand.
Approach
The proposed strategy addresses the numerical complexity challenge inherent in controlling stroboscopic steady states and limit cycles. It is designed for situations where these states are approached asymptotically through the infinite repetition of a control sequence. The formalism distinguishes itself from both Floquet-Lindblad state engineering and effective Hamiltonian theories. Instead of focusing on engineering an effective Hamiltonian or state, it directly seeks control sequences.
These control sequences are intended to drive a dissipative quantum system towards a specific steady orbit. A key feature of this approach is its ability to ensure the steady orbit passes through user-specified waypoints. This method has a numerical complexity scaling that is comparable to GRAPE. The software implementation of this strategy has been realized within the Spinach library.
Findings
- An efficient quantum control strategy for stroboscopic steady states and limit cycles was proposed.
- This strategy identifies control sequences that steer a dissipative quantum system to a steady orbit passing through user-specified waypoints.
- The formalism differs from established methods such as Floquet-Lindblad state engineering and effective Hamiltonian theories.
- The numerical complexity scaling of this new approach is equivalent to that of GRAPE.
- The method has been implemented in the Spinach library.