We propose and study a universal approach for the reconstruction of quantum states of many body systems from symmetry analysis. The concept of minimal complete set of quantum correlation functions (MCSQCF) is introduced to describe the state reconstruction. As an experimentally feasible physical object, the MCSQCF is mathematically defined through the minimal complete subspace of observables determined by the symmetry of quantum states under consideration. An example with broken symmetry is analyzed in detail to illustrate the idea.
Many-body wavefunctions usually lie in high-dimensional Hilbert spaces. However, physically relevant states, i.e, the eigenstates of the Schrödinger equation are rare. For many-body systems involving only pairwise interactions, these eigenstates form a low-dimensional subspace of the entire Hilbert space. The geometry of this subspace, which we call the eigenstate moduli problem is parameterized by a set of 2-particle Hamiltonian. This problem is closely related to the $N$-representability conditions for 2-reduced density matrices, a long-standing challenge for quantum many-body systems. Despi…
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting p…
Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we…
We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability. This allows us to show that all 1RDMs with a purely fractional occupation number spectrum ($0 < n…
Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（彭达夫斯基玻色-爱因斯坦凝聚中心，意大利国家研究委员会无机研究所和特伦托大学物理系）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń（尼古拉·哥白尼大学托伦分校物理、天文学和信息学院物理研究所）
In many of the approximate functionals in one-body reduced density matrix (1RDM) functional theory, the approximate two-body reduced density matrix (2RDM) in the natural orbital representation only depends on the natural occupation numbers. In Phys. Rev. A 92, 012520 (2015) Wang and Knowles initialised a discussion of to what extent this simplification is valid, by introducing two different H$_4$ geometries with identical natural occupation numbers, but different 2RDMs. Gritsenko has argued that this feature is due symmetry [Phys. Rev. A 97, 026501 (2018)]. This work aims to contribute to the …
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $Ω[\mathbf{G}]$ regarded as variational functional of the Green's function $G$ based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger-Ward form. By restricting the input Green's function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To es…
Beijing Normal University（北京师范大学）；Capital Normal University（首都师范大学）
Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work, we demonstrate that convolutional neural network (CNN) can learn from the coefficients of local reduced density matrices to estimate the physical parameters of the many-body Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualiz…
