Experimental Demonstrations Of Uncertainty Relations Based On Spin Systems

Quantum systems have many intriguing distinctions from classical systems,and uncertainty relations deal with one of the significant aspects.Uncertainty re-lations in quantum mechanics can be primarily divided into two categories.One category describes the dispersion of the values of observables,and reflects the intrinsic properties of observables and quantum states.This type of uncertainty relation is termed preparation uncertainty relation,and most uncertainty relations in textbooks belong to this type.The other type of uncertainty relation aligns with Heisenberg's original idea,and can be termed measurement uncertainty re-lation,which handles the inaccuracies in measurement.For example,when two incompatible observables are measured sequentially,there are some trade-offs be-tween the error in implementing the first observable and the disturbance exerted on the second observable.Alternatively,when two incompatible observables are approximated by joint measurement,the inaccuracies incurred by the approxima-tion yield to some constraints.In the beginning of this dissertation,the establishment and development of quantum mechanics as well as the concept of uncertainty relations are sketched Next,three typical spin systems,including nuclear magnetic resonance systems,electron paramagnetic resonance systems,and the nitrogen-vacancy centers in diamond,are outlined.The central topics of this dissertation are introduced afterwards.The topics contain three issues as follows.1.Preparation uncertainty relations,especially the uncertainty relations for the triple components of angular momentum and its experimental demonstra-tion,are introduced.This kind of uncertainty relation has been formulated in various ways,such as variance-based and entropic uncertainty relations.The most well-known uncertainty relations deal with two observables,while nontrivial uncertainty relations for three or more observables cannot gen-erally be derived directly from relations for two observables.We perform the experimental demonstration of several uncertainty relations based on variance and standard deviation for the triple components of angular mo-mentum using the single electron spin of a nitrogen-vacancy center.2.Measurement uncertainty relations,especially the uncertainty relations based on the statistical distances between the probability distributions of measure-ment outcomes as well as its experimental demonstration,are introduced.This kind of uncertainty relation has also been formulated in various ways till now.In recent years,some researchers proposed measurement uncer-tainty relations based on the statistical distances between the probability distributions of measurement outcomes.We reformulate and improve such a measurement uncertainty relation for qubit measurement,and conclude that the lower bound of the uncertainty is the incompatibility of target ob-servables.We perform the experimental demonstration with a nuclear spin ensemble manipulated by the nuclear magnetic resonance technique.3.A quantum adiabatic pump based on quantum coherence and its quantum simulation experiment are introduced.Quantum coherence has a close rela-tionship with quantum uncertainty.As a fundamental feature of quantum systems,quantum coherence underlies many remarkable effects.Take a quantum adiabatic pump for instance.If there is no interband coherence in the initial state,the amount of pumping will generally be restricted by the topology of the system.However,if there is interband coherence in the initial state,the coherence will make a non-topological contribution to the pumping.This extra pumping component is extensively tunable by varying the band gaps or the switching-on rate of a pumping protocol.We perform the quantum simulation experiment of the coherence-based quantum adia-batic pump with the single electron spin of the nitrogen-vacancy center,and the experimental results confirm all principal features of this pump.