Optimal quantum measurement of finite-dimensional systems and coherent anti-Stokes Raman spectroscopy

Quantum measurement is a fundamental problem in quantum control theory and experiments. It can obtain unknown information of quantum systems, and can also change state of the systems inevitably. Both the outcome and back action could be used to control quantum systems. This paper presents recent research progress about optimal control of state transformation in finite-dimensional quantum systems by back action of non-selective quantum measurement, and optimal control of signal and background of CARS (coherent anti-Stokes Raman spectroscopy) by phase shaping technique. In measurement sequence control of finite-dimensional quantum systems, the necessary condition for critical points of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities, and analytical and numerical solutions in several cases are explored. In the CARS control, it is found that the maximal resonant signal and minimal background at a specific frequency can be achieved by shaping the probe pulse only while keeping pump and Stokes pulses in transform limited forms (TLFs). An arctan-type phase function is obtained for the probe pulse to simultaneously enhance the resonant signal and suppress the background. For broadband background elimination, we find that the optimal phase shaping scheme of probe pulse is quasi-time-delay while keeping the pump and Stokes pulses in TLFs. These conclusions could help design control strategies of quantum devices.