Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful technique in studies of quantum phases of matter and quantum information. It can be used to drive a quantum system to a desired (unique) steady state, which can be an exotic phase of matter difficult to stabilize in nature. It can also be used to drive a system to a unitarily-evolving subspace, which can be used to store, protect, and process quantum information. In this paper, we derive a formula for the map corresponding to asymptotic (infinite-time) Lindbladian evolution and use it to study several important features of the unique state and subspace cases. We quantify how subspaces retain information about initial states and show how to use Lindbladians to simulate any quantum channels. We show that the quantum information in all subspaces can be successfully manipulated by small Hamiltonian perturbations, jump operator perturbations, or adiabatic deformations. We provide a Lindblad-induced notion of distance between adiabatically connected subspaces. We derive a Kubo formula governing linear response of subspaces to time-dependent Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the subspaces, resulting from either Hamiltonian/jump-operator perturbations or corrections to adiabatic evolution, is different from the conventional Lindbladian dissipative gap and, in certain cases, is equivalent to the excitation gap of a related Hamiltonian.
Efficient Lindbladian Learning from Constant-Time Pauli Responses
Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机学院前沿计算研究中心）；School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）
Lindbladian approach for many-qubit thermal machines: enhancing the performance with geometric heat pumping by interaction
Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario（罗萨里奥国立大学精确科学、工程与测量学院）；Instituto de Física Rosario (CONICET)（罗萨里奥物理研究所（阿根廷国家科学研究委员会））；Departamento de Sólidos Cuánticos y Sistemas Desordenados, Centro Atómico Bariloche, Instituto de Nanociencia y Nanotecnología CONICET-CNEA and Instituto Balseiro（巴里洛切原子中心量子固体与无序系统系，纳米科学与技术研究所（阿根廷国家科学研究委员会-阿根廷国家原子能委员会）和巴尔塞罗研究所）
Ward-Takahashi Identity and Gauge-Invariant Response Theory for Open Quantum Systems
The University of Tokyo（东京大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所涌现物质科学中心）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理研究所）
Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a fluctuation dissipation theorem for the covariance matrix that connects its linear response at any time to th…
The Geometry of Quantum Complexity in Open Systems
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎大学）；Department of Mathematics, King’s College London（伦敦国王学院数学系）
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.
To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square ($C^2$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this $C^2$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the $\mathbb{Z}_2$ topological number robust to interactions can be measured locally from a correspondence between the pfaff…
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely …
Quantum Hall States response to toroidal geometry deformation
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）；Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院数学分析、几何与动力系统中心）；Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University（特拉维夫大学雷蒙德和贝弗利萨克勒物理与天文学学院）
We study the effects of the quantum geometric tensor, i.e., the Berry curvature and the Fubini-Study metric, on the steady state of driven-dissipative bosonic lattices. We show that the quantum-Hall-type response of the steady-state wave function in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. Looking at this steady-state Hall response, one can map out the full quantum geometric tensor of a sufficiently flat band in momentum space using a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an exa…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase space. We develop a linear response theory for complexity, and demonstrate that the complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. Two immediate significant results follows: i) the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the c…
We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is always negative or zero. We use a one-electron model with tight transverse confinement. In the limit of infinite transverse confinement, the transverse wavefunctions drop out of the hyperpolarizabilities, but their residual effects are essential to include in the sum rules. The effects of geometry are manifested in the projections of the transition moments …
Geometric Response in Open Quantum Systems: Coherence, Curvature, and Susceptibility
University of Houston（休斯顿大学）；Université de Montréal（蒙特利尔大学）；Georgia Institute of Technology（佐治亚理工学院）；Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)（国立理工大学高级研究中心）
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the effective dynamics is determined by torsion, which plays the role of U(1) gauge potential, and find that the topological structure of associated states is defined by orbital spin which originates from 4D space. Strikingly, the response to torsion contributes a quantum Hall effect, and the response to the deformation of torsion contributes Hall viscosity that is per…
Multi-State Geometry of Density Matrices and Rectification Sum Rules
Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Anthony J. Leggett Institute for Condensed Matter Theory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校安东尼·J·利盖特凝聚态理论研究所）
Geometry-calibrated equilibrium sensing for inverse design of nonlocal topological photonic lattices
Nanoscale Magnetic Materials, Institute of Materials Science, Kiel University（基尔大学材料科学研究所）；Kiel Nano, Surface and Interface Science KiNSIS, Christian Albrechts University（克里斯蒂安·阿尔布莱希特大学）
This work focuses on understanding the nonlinear-optical response of a 1-D quantum wire embedded in 2-D space when quantum-size effects in the transverse direction are minimized using an extremely weighted delta function potential. Our aim is to establish the fundamental basis for understanding the effect of geometry on the nonlinear-optical response of quantum loops that are formed into a network of quantum wires. Using the concept of leaky quantum wires, it is shown that in the limit of full confinement, the sum rules are obeyed when the transverse infinite-energy continuum states are includ…
Quantum geometry-driven photogalvanic responses in semi-Dirac systems
School of Basic Sciences, Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔分校基础科学学院）；Department of Physics, National Institute of Technology Silchar（锡拉查国家技术学院物理系）
State--Generator Geometry of Open Quantum Systems: Compatibility and Covariant Transport
University of Houston（休斯顿大学）；Université de Montréal（蒙特利尔大学）；Georgia Institute of Technology（佐治亚理工学院）；Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)（墨西哥国立自治学院高级研究中心）
High magnetic field response of superconductivity dome in quantum artificial High Tc superlattices with variable geometry
Institute of Crystallography, National Research Council, CNR（意大利国家研究委员会晶体学研究所）；Rome International Center for Materials Science Superstripes RICMASS（罗马国际材料科学超晶格RICMASS中心）；Department of Industrial, Electronic and Mechanical Engineering, Roma Tre University（罗马第三大学工业、电子与机械工程系）；Istituto Nazionale di Fisica Nucleare INFN, Sezione Roma Tre（意大利核物理研究所INFN罗马三分部）；National High Magnetic Field Laboratory (NHMFL), Florida State University (FSU)（佛罗里达州立大学国家高磁场实验室）；National High Magnetic Field Laboratory (NHMFL), Los Alamos National Laboratory (LANL)（洛斯阿拉莫斯国家实验室国家高磁场实验室）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
