We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least square linea
r fitting method to achieve the quantum Cram{e}r-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
We demonstrate that voltage-controlled negative index can be obtained in self-organized InAs quantum dot systems. As the bias voltage changes, the refractive index can be adjusted and controlled continuously from -7 to 7. Simultaneously, the absorpti
on of light in the system will be very small. The single-negative index materials and the double-negative index materials can be achieved in different bias voltages.
Berry phase in a single quantum dot with Rashba spin-orbit coupling is investigated theoretically. Berry phases as functions of magnetic field strength, dot size, spin-orbit coupling and photon-spin coupling constants are evaluated. It is shown that
the Berry phase will alter dramatically from 0 to $2pi$ as the magnetic field strength increases. The threshold of magnetic field depends on the dot size and the spin-orbit coupling constant.
The voltage-controlled Berry phases in two vertically coupled InGaAs/GaAs quantum dots are investigated theoretically. It is found that Berry phases can be changed dramatically from 0 to 2$pi$ (or 2$pi$ to 0) only simply by turning the external volta
ge. Under realistic conditions, as the tunneling is varied from $0.8eV$ to $0.9eV$ via a bias voltage, the Berry phases are altered obviously, which can be detected in an interference experiment. The scheme is expected to be useful in constructing quantum computation based on geometric phases in an asymmetrical double quantum dot controlled by voltage.
