Robust population transfer of spin states by geometric formalism

Abstract

Accurate population transfer of uncoupled or weakly coupled spin states is crucial for many quantum information processing tasks. In this paper, we propose a fast and robust scheme for population transfer which combines invariant-based inverse engineering and geometric formalism for robust quantum control. Our scheme is not constrained by the adiabatic condition and therefore can be implemented fast. It can also effectively suppress the dominant noise in spin systems, which together with the fast feature guarantees the accuracy of the population transfer. Moreover, the control parameters of the driving Hamiltonian in our scheme are easy to design because they correspond to the curvature and torsion of a three-dimensional visual space curve derived by using geometric formalism for robust quantum control. We test the efficiency of our scheme by numerically simulating the ground-state population transfer in ${}^{15}$N nitrogen vacancy centers and comparing our scheme with stimulated Raman transition, stimulated Raman adiabatic passage and conventional shortcuts to adiabaticity based schemes, three types of popularly used schemes for population transfer. The numerical results clearly show that our scheme is advantageous over these previous ones.

Accepted by Physical Review A

References in corpus (14)

• Shortcut to adiabatic passage in two and three level atoms
• Dynamic polarization of single nuclear spins by optical pumping of NV color centers in diamond at room temperature
• Coherent Population Trapping of an Electron Spin in a Single Negatively Charged Quantum Dot
• Fast population transfer engineering of three-level systems
• Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states
• Shortcut to adiabatic population transfer in quantum three-level systems: effective two-level problems and feasible counter-diabatic driving
• Fast quantum state engineering via universal SU(2) transformation
• Robust stimulated Raman exact passage using shaped pulses
• Performance of superadiabatic stimulated Raman adiabatic passage in the presence of dissipation and Ornstein-Uhlenbeck dephasing
• Resonant shortcuts for adiabatic rapid passage with only $z$-field control
• Optimal robust stimulated Raman exact passage by inverse optimization
• Optimal quantum optical control of spin in diamond
• Adiabatic population transfer of dressed spin states with quantum optimal control
• Detecting magnetic fields using Nitrogen-Vacancy Centers