玻色-爱因斯坦凝聚的Gardiner声子：$q$变形玻色子的物理实现
Gardiner's phonon for Bose-Einstein Condensation: A physical realization of the $q$-deformed Boson
摘要：
Gardiner声子提出了一种粒子数守恒的近似方法来描述玻色-爱因斯坦凝聚（BEC）（C.W. Gardiner，Phys.Rev.A56，1414（1997））被证明是$q$变形玻色子的物理实现，该变形玻色子是在量子群理论中抽象发展的。在此基础上，从$q$变形的Fock空间出发，分析了射频场驱动下BEC原子的相干输出。证明了玻色对易关系的$q$ -变形对应于凝聚原子粒子数为$N$的非理想玻色对易关系。直到1/N阶，未捕获原子的相干输出态使不确定性关系最小化，就像在BEC的理想情况下的相干态一样，$N$接近无穷大或$q=1-2/N$接近1。
英文摘要：
The Gardiner's phonon presented for a particle-number conserving approximation method to describe the dynamics of Bose-Einstein Condesation (BEC) (C.W. Gardiner, Phys. Rev. A 56, 1414 (1997)) is shown to be a physical realization of the $q$-deformed boson, which was abstractly developed in quantum group theory. On this observation, the coherent output of BEC atoms driven by a radio frequency (r.f) field is analyzed in the viewpoint of a $q$-deformed Fock space. It is illustrated that the $q$-deformation of bosonic commutation relation corresponds to the non-ideal BEC with the finite particle number $N$ of condensated atoms. Up to order 1/N, the coherent output state of the untrapped atoms minimizes the uncertainty relation like a coherent state does in the ideal case of BEC that $N$ approaches infinity or $q=1-2/N$ approaches one.
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