Quantum Parameter-estimation Theory Based On Cavity Bose-Einstein Condensate Systems

In the past decades, quantum metrology has become a fast developing dis-cipline, which is to estimate accurately the value of an unknown parameter or several unknown paremeters. Quantum parameter estimation which plays a key role in quantum metrology is closely related to atomic frequency standard, atomic clocks and quantum imaging, quantum radar etc. The theory of quantum pa-rameter estimation tells us that every estimated parameter has a lower bound of the error of estimation which is determined by the inverse of quantum Fisher information. Therefore, how to attain this precision limit is the most important task in quantum metrology. In the realistic experiments, the achievable accuracy of parameter estimation is based on four aspects:probe states, parameterization process, measurements and data processing. This thesis, we focus on two aspects: the parameterization in the presence of decoherence and the measurement.The structure of this thesis is arranged as follows:In the first chapter, we review the basic background of quantum parameters estimation, and simply introduce the basic steps of the experiment and experiment devices of quantum parameter estimation. Besides, we present some recent results of quantum parameter estimation about noisy system.In the second chapter, we mainly introduce some basic theoretical knowledge of quantum parameter estimation. First, we introduce quantum Cramer-Rao theorem, and according to quantum Cramer-Rao theorem, we get the concept of quantum Fisher information. Then, we introduce two important limits:the standard quantum limit and Heisenberg limit. Finally, we give the quantum Fisher informatin and parity measurement scheme of some special quantum states.In the third chapter, we investigate the single parameter estimation of one qubit in cavity BEC system. First of all, we give quantum state at time t about the qubit in cavity BEC system and calculate quantum Fisher information under the state.We find that the single parameter estimation precision will decay over time in the cavity BEC system.Moreover, the cavity BEC system is a quantum phase transition environment. Near phase transition point, we find parameter estimation precision is extremely damaged. Therefore, to protect the parameters estimation precision, we try to avoid parameter estimation near the phase transition point.In the fourth chapter, we investigate quantum parameter estimation of two qubits in cavity BEC system. We give the quantum state of the two qubits af-ter interaction with the cavity BEC system, where we assume the initial state of the two qubits is X-type state. Based on the quantum state, we discuss re-spectively single parameter and double parameters estimation in the cavity BEC system. Comparing parameter estimation of single qubit, For two qubits, there is a decoherence-free subspace and the parameter estimation precision keep a stable value, which is a good news for the parameter estimation in the noisy environ-ment. For The two parameters estimation, we give the expression of quantum Fisher information matrix elements. Comparing parameters estimation simulta-neously and parameters estimation individually, we find the maximum estimation precision of parameters estimation simultaneously is always less than or equal to parameters estimation individually. Especially, for some initial states, he max-imum estimation precision of parameters estimation simultaneously is less than parameters estimation individually, but after evolution in the cavity BEC system, Compared with the parameters estimation individually,Parameters estimation si-multaneously save a lot of measuring steps. we find the maximum precision of the two parameters estimation becomes equal, which has a certain guiding significance for the experiment of double parameters estimation.In Chapter Five, we present a summary and outlook.