Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the network is decomposed into a product of three matrices that can be generated by Hamiltonians.
We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering matrix, and show that an application of the quantum scattering matrix on an input state is equivalent to applying the inverse of classical scattering matrix on the annihilation operators describing the optical modes. We show how to construct the point-coupling Hamiltonian corresponding to a general l…
Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports
最近，提出了标准光学多端口的推广[Phys. Rev. A 93，043845（2016）]。这些方向无偏的多端口允许光子反转方向并从输入端口向后退出，为任意图形结构上的量子行走提供了现实的线性光学散射顶点。在这里，它表明，这些多端口的阵列允许模拟的范围内的离散时间哈密顿系统。描述的例子，包括空间和内部自由度的情况下，模拟。由于输入端口也兼作输出端口，因此与执行相同功能的前馈网络相比，节省了大量资源。该模拟仅使用线性光学器件以可扩展的方式实现，并且可以以简单的方式推广到更高维的系统，从而提供了离散时间量子系统的图形模型的具体实验可实现的实现。
The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different $N$ states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our r…
Exceptional points (EPs) have recently attracted considerable attention in the study of non-Hermitian systems and in applications such as sensors and mode switching. In particular, nontrivial topological structures of EPs have been studied intensively in relation to encircling EPs. Thus, EP generation is currently an important issue in several fields. To generate multiple EPs, multiple levels or composite physical systems have been employed with Hermitian couplings. In this study, we generate multiple EPs on two-level systems in a single microcavity by adopting the non-Hermitian coupling of a …
Photon carries linear momentum and angular momentum simultaneously. Within the light-matter interaction process, exchange of linear momentum results in optical forces, whereas exchange of angular momentum leads to optical torques. Use of optical forces (light pressure or damping) have been long and wide in quantum optomechanics, however, those of optical torque and optical angular momentum are not. Here we propose a theoretical framework based on optical angular momentum and optical torques to derive the Hamiltonians of cavity orbital and spin angular momentum optomechanical systems, respectiv…
A number of new L$\acute{e}$vi-Leblond type equations admitting four component spinor solutions have been proposed. The pair of linearized equations thus obtained in each case lead to Hamiltonians with characteristic features like L-S coupling and supersymmetry. The relevant momentum operators have often been understood in terms of Clifford algebraic bases producing Schr$\ddot{o}$dinger Hamiltonians with L-S coupling. As for example Hamiltonians representing Rashba effect or three dimensional harmonic oscillator have been constructed. The supersymmetric nature of one dimensional oscillator has…
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first order contribution to the transmission or equal-time N-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature i.e. it only depends on the Hamiltonian trajectory and not on the precise nature of the modulation…
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half-partition …
We investigate a Bose Einstein condensate held in a 1D optical lattice whose phase undergoes a fast oscillation using a statistical analysis. The averaged potential experienced by the atoms boils down to a periodic potential having the same spatial period but with a renormalized depth. However, the atomic dynamics also contains a \emph{micromotion} whose main features are revealed by a Kolmorogov-Smirnov analysis of the experimental momentum distributions. We furthermore discuss the impact of the micromotion on a quench process corresponding to a proper sudden change of the driving amplitude w…
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these first results in several ways. First, we numerically benchmark the working conditions of the analog simulator, and find less demanding experimental setups where chemistry-like behaviour in three-dim…
A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides
本文提出了一种多模哈密顿方程来求解光波导中的光声相互作用问题。我们建立了一个哈密顿表示的声场，然后引入一个完整的系统与一个简单的光声耦合，包括光弹/电致伸缩和辐射压力/移动边界效应。海森堡运动方程用于获得耦合模方程的量子化包络运营商的光场和声场。我们表明，得到的耦合系数与以前建立的耦合系数一致，但我们的形式主义比以前的工作[C. Wolff等人，Physical Review A 92，013836（2015）]。
Optical characterization of excited-state spin Hamiltonians and clock transitions at telecommunication wavelength in Tm3+:YAlO3
Department of Applied Physics, University of Geneva（日内瓦大学应用物理系）；PSI Center for Photon Science, Paul Scherrer Institute（保罗谢尔研究所光子科学中心）；Laboratory for Solid State Physics and Quantum Center, ETH Zurich（苏黎世联邦理工学院固体物理与量子中心）；Institute of Physics, EPF Lausanne（洛桑联邦理工学院物理研究所）
Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices
在量子动力学的突现本征态解[Phys. Rev. X 7，021012（2017）]中，人们可以构造一个局部算符（突现哈密顿量），其时间演化态是本征态。在这里，我们表明，这样的解决方案存在的膨胀动力学的Tonks-Girardeau气体在光晶格后关闭幂律（例如，谐波或四次）限制势，其是不涉及升压算子的几何猝灭。对于系统，最初是在基态，并在膨胀过程中进行动态费米子化，我们表明，他们仍然在基态的紧急本地哈密顿量在任何时候。另一方面，对于非零初始温度下的系统，膨胀动力学可以描述为构造涌现局部哈密顿量的吉布斯系综（涌现吉布斯系综）。
