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arXiv 1401.0952cond-mat.quant-gascond-mat.mes-hall
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超冷玻色气体中极化子的射频谱

Radio frequency spectroscopy of polarons in ultracold Bose gases

Aditya Shashi, Fabian Grusdt, Dmitry A. Abanin, Eugene Demler

摘要:

最近的实验进展使得能够实现浸没在超冷原子的玻色-爱因斯坦凝聚体(BEC)中的移动杂质。在这里,我们考虑具有两个或更多个内部超精细状态的杂质,并研究它们的射频(RF)吸收光谱,这对应于两个不同的超精细状态之间的跃迁。我们计算RF光谱的情况下,当涉及的超精细状态之一与BEC相互作用,而另一个状态是非相互作用的,通过执行非微扰的激发不同数量的声子模式的概率的重新确认。在相互作用的存在下,杂质被BEC的Bogoliubov激发所修饰,并形成极化子。RF信号包含以相对于裸杂质跃迁频率测量的极化子能量为中心的δ函数峰,其权重等于极化子状态中的裸杂质特征的量。RF频谱也有一个广泛的不相干的部分所产生的背景激发的BEC,与一个特征的幂律尾,出现作为一个普遍的物理接触相互作用的结果。我们讨论了直接RF测量,其中杂质最初是在相互作用状态,和反向RF测量,其中杂质最初是在非相互作用状态。在后一种情况下,为了计算RF谱,我们解决了极化子形成的问题:移动杂质动态地被Bogoliubov声子修饰。我们的解决方案的基础上的Bogoliubov声子相干态的含时变分分析,成为精确的杂质时,本地化。此外,我们还表明,这样的一个antenness比较以及与半经典估计的BEC中的移动杂质的传播振幅。我们的技术可以扩展到的情况下,当初始和最终的杂质状态与BEC相互作用。

英文摘要:

Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here we consider impurities with two or more internal hyperfine states, and study their radio-frequency (RF) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate RF spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is non-interacting, by performing a non-perturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The RF signal contains a delta-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The RF spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct RF measurement, in which the impurity is initially in an interacting state, and the inverse RF measurement, in which the impurity is initially in a non-interacting state. In the latter case, in order to calculate the RF spectrum, we solve the problem of polaron formation: a mobile impurity dynamically gets dressed by Bogoliubov phonons. Our solution based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, becomes exact when the impurity is localized. Moreover we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states interact with the BEC.

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