Hybrid density matrix approach as a factorization scheme for many-body systems: Illustrated by a quantum dot–continuum system

2015 ◽  
Vol 91 (15) ◽  
Author(s):  
Sandra C. Kuhn ◽  
Marten Richter
Keyword(s):  
Quantum Dot ◽  
Density Matrix ◽  
Matrix Approach ◽  
Many Body ◽  
Factorization Scheme ◽  
Many Body Systems

scholarly journals Quantum interface of an electron and a nuclear ensemble

Science ◽  
2019 ◽  
Vol 364 (6435) ◽  
pp. 62-66 ◽  
Author(s):  
D. A. Gangloff ◽  
G. Éthier-Majcher ◽  
C. Lang ◽  
E. V. Denning ◽  
J. H. Bodey ◽  
...  
Keyword(s):  
Quantum Dot ◽  
Nuclear Spin ◽  
Building Blocks ◽  
Spin Excitation ◽  
Many Body ◽  
Quantum Objects ◽  
All Optical ◽  
Spin Qubit ◽  
Many Body Systems ◽  
Optical Rotations

Coherent excitation of an ensemble of quantum objects underpins quantum many-body phenomena and offers the opportunity to realize a memory that stores quantum information. Thus far, a deterministic and coherent interface between a spin qubit and such an ensemble has remained elusive. In this study, we first used an electron to cool the mesoscopic nuclear spin ensemble of a semiconductor quantum dot to the nuclear sideband–resolved regime. We then implemented an all-optical approach to access individual quantized electronic-nuclear spin transitions. Lastly, we performed coherent optical rotations of a single collective nuclear spin excitation—a spin wave. These results constitute the building blocks of a dedicated local memory per quantum-dot spin qubit and promise a solid-state platform for quantum-state engineering of isolated many-body systems.

scholarly journals REDUCED DENSITY MATRIX AND ENTANGLEMENT ENTROPY OF PERMUTATIONALLY INVARIANT QUANTUM MANY-BODY SYSTEMS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243009 ◽  
Author(s):  
VLADISLAV POPKOV ◽  
MARIO SALERNO
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Reduced Density Matrix ◽  
Diagonal Form ◽  
Temperature Phase ◽  
Many Body ◽  
Permutational Symmetry ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.

scholarly journals A Simple Derivation of the Bloch Equations for Localized Moment E.S.R. in Metals in the Presence of Anisotropy

1973 ◽  
Vol 26 (4) ◽  
pp. 475 ◽  
Author(s):  
DA Smith
Keyword(s):  
Electron Spin Resonance ◽  
Density Matrix ◽  
Matrix Approach ◽  
Many Body ◽  
Bloch Equations ◽  
Simple Derivation ◽  
Local Moments ◽  
Conduction Electrons ◽  
Spin Resonance ◽  
Body Techniques

A density-matrix approach is used to derive the coupled Bloch equations for the electron spin resonance of localized moments and conduction electrons in metals, including anisotropy fields acting on the local moments. The equations agree with those obtained elsewhere by more sophisticated many-body techniques. In particular, it is demonstrated explicitly that relaxation proceeds towards instantaneous equilibrium.

scholarly journals Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach

2014 ◽  
Vol 90 (12) ◽  
Author(s):  
Roberto Rosati ◽  
Rita Claudia Iotti ◽  
Fabrizio Dolcini ◽  
Fausto Rossi
Keyword(s):  
Density Matrix ◽  
Single Particle ◽  
Matrix Approach ◽  
Many Body

DENSITY-MATRIX RENORMALISATION GROUP FOR DYNAMIC CORRELATION FUNCTIONS

2003 ◽  
Vol 17 (28) ◽  
pp. 5453-5457
Author(s):  
E. JECKELMANN
Keyword(s):  
Density Matrix ◽  
Variational Problem ◽  
Correlation Functions ◽  
Renormalisation Group ◽  
Many Body ◽  
Dynamic Correlation ◽  
Many Body Systems ◽  
The One ◽  
Low Dimensional ◽  
Insulating Phase

The calculation of dynamic correlation functions in quantum systems is formulated as a variational problem. For low-dimensional many-body systems this variational problem can be solved numerically using the density-matrix renormalisation group (DMRG). This dynamic DMRG method is demonstrated on the linear optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model at half filling. The full optical spectrum of this model can be calculated almost exactly for chains with more than 100 sites, which is large enough to investigate the spectral properties in the thermodynamic limit. The accuracy of the method is illustrated by comparison with analytical results in the field-theoretical regime and in the strong-coupling limit.

scholarly journals Many-Body Systems and Quantum Chaos: The Multiparticle Quantum Arnol’d Cat

2019 ◽  
Vol 4 (3) ◽  
pp. 72
Author(s):  
Giorgio Mantica
Keyword(s):  
Hamiltonian System ◽  
Density Matrix ◽  
Quantum Chaos ◽  
Reduced Density Matrix ◽  
Von Neumann Entropy ◽  
Physical Parameters ◽  
Many Body ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the physical parameters, with special regard to increasing the mass of the cat particle.

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