Department of Physics, ETH Zurich, 8093 Zurich, Switzerland.
Phys Rev Lett. 2010 May 7;104(18):180401. doi: 10.1103/PhysRevLett.104.180401. Epub 2010 May 6.
We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Néel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy.
我们使用被囚禁在光晶格中的超冷气体对排斥型费米-哈伯德模型进行了定量模拟。通过将对平衡双占据的精确测量与在广泛参数范围内的理论计算进行比较，我们确定了系统的熵。我们展示了高温级数和动力平均场理论都适用于与实验数据获得定量一致。通过对所有系统误差的综合分析，验证了熵确定的可靠性。在莫特绝缘云的中心，我们得到的每个原子的熵低至 0.77kB，约为奈尔相变处熵的两倍。相应的温度取决于原子数，对于小填充度，达到了与隧道能量相当的值。
