纳米多孔介质中$^4$ He的4D-PDKEEPAAA超流相变和耗散
4D-XY Superfluid Transition and Dissipation in $^4$He Confined in Nanoporous Media
摘要：
$^4$ He被限制在纳米多孔Gelsil玻璃中是一个独特的、强关联的玻色系统，通过控制压力表现出量子相变（QPT）。先前的研究表明，QPT发生在四维（4D）XY临界，出现在零温度极限的超流密度。然而，$P-T$相图也表明，4D XY性质出现在有限的温度。在这里，我们已经确定了超流密度的临界指数的$^4$他在两个凝胶样品，具有孔径约为3 nm，使用新开发的机械谐振器技术。幂律拟合$ρ_{\mathrm s} \propto \left| 1 - T/T_{\mathrm c} \right| ^ζ$中的临界指数$ζ$，其中$T_{\mathrm c}$是超流转变温度，对于本实验中实现的所有压力，发现为1.0 $\pm$ 0.1，0.1 $<$ $P$ $<$ 2.4 MPa。$ζ$的这一值为有限温度超流转变属于4D XY普适类提供了决定性的证据。4D XY临界性的出现被解释为在$T_{\mathrm c}$上方存在许多纳米级超流体液滴，即所谓的局域玻色-爱因斯坦凝聚体（LBEC）。由于$^4$ He原子在LBEC之间移动的能量成本很大，LBEC序参数的相位不仅在空间（3D）维度上波动，而且在虚时间（$+1$ D）维度上波动，导致在$T_{\mathrm c}$附近的温度下的4D XY临界性，该温度由系统在虚时间维度上的有限尺寸确定。低于$T_{\mathrm c}$，宏观超流性通过LBEC序参数的相的排列在Gelsil的纳米孔中生长。在$T_{\mathrm c}$以下观察到的过量耗散峰通过该相位匹配过程很好地解释。
英文摘要：
$^4$He confined in nanoporous Gelsil glass is a unique, strongly correlated Bose system exhibiting quantum phase transition (QPT) by controlling pressure. Previous studies revealed that the QPT occurs with four - dimensional (4D) XY criticality, which appears in the zero-temperature limit of the superfluid density. However, the $P-T$ phase diagram also suggested that 4D XY nature appears at finite temperatures. Here, we have determined the critical exponent of the superfluid density of $^4$He in two Gelsil samples that have pore diameter to be about 3 nm, using a newly developed mechanical resonator technique. The critical exponent $ζ$ in the powerlaw fitting $ρ_{\mathrm s} \propto \left| 1 - T/T_{\mathrm c} \right| ^ζ$, where $T_{\mathrm c}$ is the superfluid transition temperature, was found to be 1.0 $\pm$ 0.1 for all pressures realized in this experiment, 0.1 $<$ $P$ $<$ 2.4 MPa. This value of $ζ$ gives a decisive evidence that the finite-temperature superfluid transition belongs to 4D XY universality class. The emergence of the 4D XY criticality is explained by the existence of many nanoscale superfluid droplets, the so called localized Bose - Einstein condensates (LBECs), above $T_{\mathrm c}$. Due to the large energy cost for $^4$He atoms to move between the LBECs, the phase of the LBEC order parameters fluctuates not only in spatial (3D) but imaginary time ($+1$D) dimensions, resulting in the 4D XY criticality by a temperature near $T_{\mathrm c}$, which is determined by the finite size of the system in the imaginary time dimension. Below $T_{\mathrm c}$, macroscopic superfluidity grows in the nanopores of Gelsil by the alignment of the phases of the LBEC order parameters. An excess dissipation peak observed below $T_{\mathrm c}$ is well explained by this phase matching process.
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