Complementary Relationship Between Fringe Visibility And Path Information In An Asymmetric Mach-Zehnder Interferometer

The particle-like property and the wave-like property are inherent properties of microscopic particles.They exist at the same time,but they cannot observed.In the same experiment,once interference fringes are observed,the particle-like will property disappear.Conversely,when the path of the particle is accurately obained,the wave-like property will disappear.This is Bohr's principle of comple-mentarity which is related to wave-particle duality.Many studies on the quantifi-cation of wave-particle duality and their complementarity are based on symmetric Mach-Zehnder interferometers.But Mach-Zehnder interferometers are not neces-sarily symmetric.And the study of asymmetric Mach-Zehnder interferometers is more universal.So we studied the complementarity of particle and volatility in an asymmetric Mach-Zehnder interferometer.The difference from the symmetric Mach-Zehnder interference experimental device is the asymmetry of the second beam splitter.We use the fringe visibility to quantify the wave-like property,use the path information to quantify the particle properties,and explore the comple-mentary relationship between the fringe visibility and path information.The main research contents are as follows:1.The visibility of fringes of asymmetric Mach-zehnder interferometer was studied.It is found that the fringe visibility of asymmetric Mach-Zehnder inter-ferometer is not only affected by the initial state of particle and detector,but also by the second asymmetric beam splitter.There is an upper limit on the fringe visibility,that is,V?C,and the maximum value C is obtained only when the initial state of incident particles is pure,and the parameter satisfies cos?=-S_x.2.We obtain the path information of asymmetric Mach-Zehnder interferom-eter by the minimum error discrimination method.The path information is found to be zero in the following cases:?1?The second beam splitter is in the case of total transmission or total reflection,that is?=0 or?=?;?2?S_x=±1,that is single photon only propagates in path a or b;?3?C=1,the detector state does not change.In addition,the size of the I_pathpeak is determined by C,the position of the peak is determined by S_xand?.When cos?=-S_x,the path information reaches the upper limit.3.The the fringe visibility V and the which-path information I_pathin an asymmetric Mach-Zehnder interferometer are studied,complementary relation-ship:V²+I²_path?1.the equation is established to satisfy the following three conditions:?1?the particle is a pure state,?2?cos?=-S_x,?3?C=0 or C=1.