Analogue gravity from Bose-Einstein condensates
Analogue gravity from Bose-Einstein condensates
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DOI：
10.1088/0264-9381/18/6/312
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发表时间：
2001-03-21
影响因子：
3.5
通讯作者：
Visser, M
中科院分区：
文献类型：
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作者：
Barceló, C;Liberati, S;Visser, M
我们分析了使用玻色-爱因斯坦凝聚作为凝聚物质系统的前景，适合于生成一个通用的“有效度量”，并模仿广义相对论的运动学方面。我们扩展了Garay等人（2000 Phys. Rev. Lett. 85 4643，2001 Phys.Rev.A63 023611）。从长远来看，我们要问这样一个系统的最终极限可能是什么。为此，我们考虑非线性薛定谔方程的一个非常一般的版本（具有3张量位置相关质量和任意非线性）。这样的方程可以用于，例如，在讨论玻色-爱因斯坦凝聚在异质和高度非线性系统。我们表明，在低动量线性化激发的相位的凝聚波函数服从（3 + 1）维的d 'Alembertian方程耦合到（3 + 1）维洛伦兹签名的“有效度量”，这是通用的，并依赖于代数的背景场。因此，在低动量时，这个系统就相当于广义相对论中弯曲时空的类比。相反，在高动量，我们演示了如何使用程函近似提取一个良好控制的Bogoliubov样色散关系，并（也许出乎意料地）恢复非相对论性牛顿物理在高动量，玻色-爱因斯坦凝聚似乎是一个非常有前途的模拟系统，用于探测广义相对论的运动学方面。
We analyse prospects for the use of Bose-Einstein condensates as condensed-matter systems suitable for generating a generic 'effective metric', and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al (2000 Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a long-term view, we ask what the ultimate limits of such a system might be. To this end, we consider a very general version of the nonlinear Schrodinger equation (with a 3-tensor position-dependent mass and arbitrary nonlinearity). Such equations can be used, for example, in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We demonstrate that at low momenta linearized excitations of the phase of the condensate wavefunction obey a (3 + l)-dimensional d'Alembertian equation coupling to a (3 + l)-dimensional Lorentzian-signature 'effective metric' that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analogue for the curved spacetime of general relativity. In contrast, at high momenta we demonstrate how one can use the eikonal approximation to extract a well controlled Bogoliubov-like dispersion relation, and (perhaps unexpectedly) recover non-relativistic Newtonian physics at high momenta, Bose-Einstein condensates appear to be an extremely promising analogue system for probing kinematic aspects of general relativity.