We study the quantum system of three ultracold one-dimensional identical bosons withδ-contact interaction in a harmonic trap by proposing a method termed the generator coordinate method(GCM)-polynomial ansatz(PA).Bas...We study the quantum system of three ultracold one-dimensional identical bosons withδ-contact interaction in a harmonic trap by proposing a method termed the generator coordinate method(GCM)-polynomial ansatz(PA).Based on the asymptotic property of our system,we describe the wave function as a(pseudo-)polynomial multiplied by the asymptotic Gaussian function,then apply the GCM to this PA description to solve the system.Our results include not only the ground and first excited states,which are in agreement with previous calculations,but also a dozen unex-plored excited states.We present and discuss the eigenenergy spectra and eigenstates,including periodic patterns and degeneracies.Additionally,we reproduce the states and properties at extreme interaction limits,such as Bose–Einstein(BE)condensate,fermionization at Tonks–Girardeau(TG)gas limit and TG/super-TG mapping.展开更多
基金supported by the National Key R&D Program of China(No.2023YFA1606701)supported in part by the National Natural Science Foundation of China under contract Nos.12175042,11890710,11890714,12047514,12147101,12347106。
文摘We study the quantum system of three ultracold one-dimensional identical bosons withδ-contact interaction in a harmonic trap by proposing a method termed the generator coordinate method(GCM)-polynomial ansatz(PA).Based on the asymptotic property of our system,we describe the wave function as a(pseudo-)polynomial multiplied by the asymptotic Gaussian function,then apply the GCM to this PA description to solve the system.Our results include not only the ground and first excited states,which are in agreement with previous calculations,but also a dozen unex-plored excited states.We present and discuss the eigenenergy spectra and eigenstates,including periodic patterns and degeneracies.Additionally,we reproduce the states and properties at extreme interaction limits,such as Bose–Einstein(BE)condensate,fermionization at Tonks–Girardeau(TG)gas limit and TG/super-TG mapping.
