Efficient Generation Of Many-body Singlet States In Optical Superlattices

Bose-Einstein condensate,abbreviated as BEC,is a novel material form.Most of the particles of this state occupied the same quantum state.In a BEC system,interaction between particles brings many interesting phenomena,such as spin-exchanging between particles,phase transition between insulator and superfluid,vortex and so on.The many-body singlet state is a quantum state with the total spin equaling to zero and being with the two-body largest entanglement.It has important applications in the field of quantum simulation,quantum computation and high precision measurement.In addition,the many-body singlet states can be used to solve some questions that without classical solutions.Such as,the N-strangers problem,the secret sharing problem and the liar detection problem could be solved by using N-Particle N-Level singlet state.In this paper,we propose a protocol to generate the many-body singlet with the spin-1 antiferromagnetic bosons being trapped in an optical superlattice,and we will demonstrate the results via the numerical simulation.In the first chapter,firstly,we introduce the history of development of Bose-Einstein condensate and the experimental verification.Secondly,we introduce some theoretical knowledge of optical trap and optical lattice.Finally,the theoretical methods for dealing with many-body bosons system are introduced,which includes the mean field theory and quantum multi-body theory.In the second chapter,we first introduce the physical model of we are studying,namely the standard Bose-Hubbard model.Secondly,in order to generate the many-body spin singlet states,the stepwise adiabatic merging method is introduced in details.In the third chapter,we discuss the preparation conditions for the evolutional process.The results of evolution are demonstrated in chapter 4 firstly,then we discuss that whether this protocol can be implemented under current experimental conditions.The optical lattice has the good characters in regulating wells-sharp and changing the form of interaction,then the two-well optical lattices be served as the unit in our simulation.We consider the system of many spin-1 antiferromagnetic bosons trapped in the supperlattice.We raise the potential bias to generate the many-body singlet states via a series of stepwise adiabatic merging protocol.Our results show that the fidelity of 16-body singlet state is high as 90%.Next,the picture of generalized spin-squeezing parameter dependence on time is given.The obvious oscillation of generalized spin-squeezing parameter shows it is a good experimental observable and can be severed as a key sign for convincing the generated states are the true singlet states.Finally,we estimate the value of parameters of the simulation under considering the BEC experiments,which fully demonstrate that our protocol can be used to generate the many-body singlet states in current experiments.