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The question of whether there exists a finite mobility in the standard Holstein model with one vibrational mode on each site remains unclear. In this Communication, we approach this problem by employing the hierarchical equation of motion method to simulate model systems where the vibrational modes are dissipative. It is found that, as the friction becomes smaller, the charge carrier mobility increases significantly and a friction-free limit cannot be obtained. The current autocorrelation functions are also calculated for the friction-free Holstein model, and converged results cannot be obtained with an increase in the number of sites. Based on these observations, we conclude that a finite mobility cannot be defined for the standard Holstein model in the parameter regime explored in this work. [ABSTRACT FROM AUTHOR]

A new Rb fountain clock was built at the National Institute of Metrology with the aim to realize robustness and excellent long-term instability for time keeping. While some basic designs have been adopted from our Cs fountain clocks, new features have been included for improved performance. A double-metal interrogation microwave cavity with a thermal expansion self-compensating mechanism was used to reduce the clock sensitivity to temperature fluctuations for the first time, to our knowledge. Moreover, a compact optical system was developed to ensure robustness. These features dramatically increased the ambient temperature range. The developed Rb fountain clock achieved a typical fractional frequency instability of 1.49×10−13(τ/s)−1/2within 10 days of continuous operation without any intervention, demonstrating the potential for time keeping.

We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system–bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction. [ABSTRACT FROM AUTHOR]

We investigate the numerical stability of the hierarchical equations of motion (HEOM) method applied to systems with the Brownian oscillator (BO) and multimode BO (MBO) spectral densities. It is shown that, with the increase in the system–bath coupling strength, the standard HEOM may become unstable, and a simple increase in the truncation depth of the HEOM cannot remove the instability at long times. To solve this problem, we first show that the high-temperature approximation of the HEOM with the BO spectral density is equivalent to the celebrated quantum Fokker–Planck equation (QFPE). By starting from the HEOM, we then derive a new multidimensional phase space differential equation that generalizes the QFPE to arbitrary temperature. It is further shown that the numerical instability can be removed if the new low-temperature QFPE is expanded in a basis set different than the one that leads to the conventional HEOM. The matrix product state method is also employed to propagate the new equation based on the low-temperature QFPE and to resolve the numerical instability problem for an electron transfer model with the MBO spectral density presented in the recent literature. [ABSTRACT FROM AUTHOR]

We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a promising tool in simulating quantum dynamics in condensed phases. [ABSTRACT FROM AUTHOR]

We report an optical-scanning, dual-fiber, extrinsic Fabry-Perot interferometer system for absolute measurement of microdisplacement. The system involves two air-gapped Fabry-Perot cavities, formed by fiber end faces, functioning as sensing and reference elements. Taking the scanning wavelength as an interconverter to compare the gap length of the sensing head with the reference-cavity length yields the absolute measurement of the sensing-cavity length. The measurement is independent of the wavelength-scanning accuracy, and the reference-cavity length can be self-calibrated simply by one's changing the sensing-head length by an accurate value.

A transportable fountain clock with high reliability is important for high-precision time-frequency measurements. Because of its relatively small cold atoms' collision frequency shift and ease of attaining high quantum state preparation efficiency, the rubidium atomic fountain clock has an indicated higher stability and reliability. This paper reports the design and operation of a transportable rubidium atomic fountain clock developed by the Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Science. After being transported more than 1000 km from Shanghai to the Changping Campus of the National Institute of Metrology, China, the optical platform and other hardware of the fountain clock did not need to be adjusted. The rubidium fountain clock maintained a stability of 4.0 × 10−13τ1/2, reaching 5.0 × 10−16 at 300 000 s. After transportation, the rubidium fountain clock and a cesium fountain clock (NIM5) were operated together against the reference frequency of a hydrogen maser. In three separate operating periods, over a total of nearly three months, the average frequency repeatability of the rubidium fountain was less than 3.8 × 10−15. [ABSTRACT FROM AUTHOR]