Many-body interactions in semiconductors probed by optical two-dimensional fourier transform spectroscopy

We study many-body interactions between excitons in semiconductors by applying the powerful technique of optical two-dimensional Fourier transform spectroscopy. A two-dimensional spectrum correlates the phase (frequency) evolution of the nonlinear polarization field during the initial evolution and the final detection period. A single two-dimensional spectrum can identify couplings between resonances, separate quantum mechanical pathways, and distinguish among microscopic many-body interactions.     

Quantum memory assisted probing of dynamical spin correlations

We propose a method to probe time-dependent correlations of nontrivial observables in many-body ultracold lattice gases. The scheme uses a quantum nondemolition matter-light interface, first to map the observable of interest on the many-body system into the light and then to store coherently such information into an external system acting as a quantum memory. Correlations of the observable at two (or more) instances of time are retrieved with a single final measurement that includes the readout of the quantum memory. Such a method brings to reach the study of dynamics of many-body systems in and out of equilibrium by means of quantum memories in the field of quantum simulators.     

The periodically kicked quantum spin

It is shown that the same kind of deterministic chaos that occurs in classical systems can occur in certain quantum mechanical, many-body systems. The example of the physical realization of the periodically kicked quantum spin (PKQS) is considered in detail. The quantum mechanical equations of motion for this system can be converted into the three-dimensional PKQS map, which exhibits deterministic chaos and Arnold diffusion. Although the case of quantum spin s= 1/2 is assumed, it is shown that the same map results for s=1 (but not for s>/=3/2), and for a suitably chosen classical particle with orbital angular momentum. A simple generalization of the PKQS model gives rise to stochastic webs on the surface of the unit sphere very similar to the Zaslavsky stochastic webs in a plane.     

THE COMPOSITE PARTICLE REPRESENTATION THEORY: (I) The Composite Particle Representation Transformation

A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a .generalized transformation. Using this generalization, we were able to construct a special representation called the "Composite Particle Representation". In the composite. particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical .representation which .includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons.from the quark point of view and the Interacting Boson Mode1 in nuclei.     

基于张量网络算法的自旋梯子系统的弦序参量的研究

通过基于矩阵乘积态(MPS)的强关联电子量子自旋梯子格点系统的张量网络(TN)算法,摸索研究自旋梯子量子多体系统的弦序参量,探测系统的量子相变点,刻画系统的量子临界现象,获取系统的量子相图,这为我们提供了一个研究自旋梯子系统的量子多体物理性质强有力的工具和方法:在不知道系统是否缺乏Landau对称性破缺序或者系统是否存在相关的拓扑弦序的情况下,可以先得到系统的基态波函数,如果基态缺乏Landau对称性破缺序,或可以通过其它方式找出系统存在若干非局域的弦序参量,来完整地描述一些拓扑量子相变点,获得系统的量子相图,从而丰富和发展了传统的Landau对称性破缺的相变理论.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Digraph states and their neural network representations

With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.     

量子计算与量子模拟

量子计算和量子模拟在过去的几年里发展迅速,今后涉及多量子比特的量子计算和量子模拟将是一个发展的重点.本文回顾了该领域的主要进展,包括量子多体模拟、量子计算、量子计算模拟器、量子计算云平台、量子软件等内容,其中量子多体模拟又涵盖量子多体动力学、时间晶体及多体局域化、量子统计和量子化学等的模拟.这些研究方向的回顾是基于对现阶段量子计算和量子模拟研究特点的考虑,即量子比特数处于中等规模而量子操控精度还不具有大规模逻辑门实现的能力,研究处于基础科研和实用化的过渡阶段,因此综述的内容主要还是希望管窥今后的发展.     

Circuit QED and sudden phase switching in a superconducting qubit array

Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Self-Consistent Calculations of Probabilities for Transitions between $${3}_{1}^{{-}}$$ and $${2}_{1}^{{+}}$$ One-Phonon States in Tin Isotopes

Physics of Atomic Nuclei - For the first time, a self-consistent method for studying second-order anharmonic effects within quantum many-body theory is applied to calculating probabilities for...     

Temperature dependence near phase transitions in classical and quant. mech. canonical statistics

The free energy of a many-body system, classical as well as quantum mechanical, is represented by a finite Laplace transform of the interaction phase volume for stable potentials for which the thermodynamic limit exists. Possible singular and regular phase transitions are discussed with respect to the temperature dependence and are classified by the behaviour of a limiting density of complex temperature zeros. The phenomenologically known types are reproduced.     

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

ABSTRACT

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H²-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.     

Bidirectional Information Flow Quantum State Tomography

The exact reconstruction of many-body quantum systems is one of the major challenges in modern physics,because it is impractical to overcome the exponential complexity problem brought by high-dimensional quantum manybody systems.Recently,machine learning techniques are well used to promote quantum information research and quantum state tomography has also been developed by neural network generative models.We propose a quantum state tomography method,which is based on a bidirectional gated recurrent unit neural network,to learn and reconstruct both easy quantum states and hard quantum states in this study.We are able to use fewer measurement samples in our method to reconstruct these quantum states and to obtain high fidelity.     

Systematic derivation of order parameters through reduced density matrices

A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the degenerate ground states without the aid of empirical knowledge, and thus opens a way to explore unknown exotic orders. The applicability of this method is demonstrated numerically or rigorously in models that are considered to exhibit dimer, scalar chiral, and topological orders.     

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.     

Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems,by Maciej Lewenstein,Anna Sanpera and Verònica Ahufinger

A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.     

Class of quantum many-body states that can be efficiently simulated

We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that the expectation value of local observables can be computed exactly and efficiently. The multiscale entanglement renormalization ansatz is equivalent to a quantum circuit of logarithmic depth that has a very characteristic causal structure. It is also the ansatz underlying entanglement renormalization, a novel coarse-graining scheme for many-body quantum systems on a lattice.