Spin Squeezing In The Spin-1 Bose-Einstein Condensates

The research about spin squeezing has been widely concerned for the three reasons:First,the rapid development of science and technology has greatly reduced the classical error which includes technical defects,instrument error and so on.The quantum error determined by quantum nature has been the main source of error on measurement.The general existence of the standard quantum limit of Uncertainty principle becomes the essential obstacle to improve the precision of quantum measurement device,and how to suppress its influence on accuracy has a wide application prospect [1].Second,there is an internal close relationship between quantum entanglement and squeezed state,which can effectively improve the quantum signal to noise ratio,so that the study of squeezing is of great significance to quantum information.Third,quantum entanglement is also one of the basic problems in physics.So the study of spin squeezing has important meaning not only on the side of application,but also the side of basic theory.This paper mainly explores the unique squeezed problem in the spin-1 Bose Einstein Condensates,which includes the spin squeezing between the spin components and spin nematic squeezing between spin component and nematic tensor.In the analysis of squeezed question,the angular momentum representation and the particle number representation have different characters,the later has more advantages in the study of this question.In particular,many coupling terms of external field that cannot be represented by the angular momentum creation and annihilation operators,but can be expressed by the particle number representation simply.Then,the special influence of different external field intensities on spin squeezing and nematic tensor squeezing were systematically studied.Besides,the intrinsic relation between the squeezed coefficient and the number of particles through numerical analysis was discussed Finally,the dynamic of squeezed coefficient in BEC and the effect of different field factors on the squeezed coefficient were studied.This paper has five parts,the specific framework is organized as follows:The first part,in order to introduce some basic concepts about spin squeezing,the theory of spin squeezing from the photon system and spin 1/2 system were reviewed firstly,these systems are capable of demonstrating single-mode orthogonal squeezing and spin squeezing in the system of spin 1/2.In this chapter,the background and basic concepts of the spin condensate and spin squeezing are briefly introduced.In the second part,the coherent spin states(CSS)and the squeezed spin states(SSS)are analyzed firstly,and then several different definitions of squeezing coefficient are discussed.The basic method to explore the squeezed question has been extended to the spin-nematic squeezing,and the accomplished methods of the squeezed state are discussed and analyzed.The third part adopts angular momentum representation,particle number representation and numerical analyzation to explore the squeezed question.The advantages of the two representations on squeezing are compared.In this chapter,the spin-nematic squeezing in the spin-1 system was explored,the comparison between the conditions of the two kinds of squeezing was given.During the process of spin-nematic squeezing,spin exchange takes place between different spin components,and the dynamic evolution of the initial index in the process is given.In the fourth part,the main influencing factors on squeezing including the applied magnetic field and the number of particles are taken into account.The theoretical simulation shows the dynamical law of squeezed coefficient and the corresponding initial character under diverse magnetic fields and different number of particles.At the end of this paper,a summary about the main result of this paper was given,and look forward for the future development of squeezed technology.