Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.

Journal of Optics B Quantum and Semiclassical OpticsOct 5, 200417 citations

Probing Correlated Quantum Many-Body Systems at the Single-Particle Level

Manuel Endres

Springer thesesJan 1, 201412 citations

Quantum metrology with alkaline-earth atom arrays

Nelson Darkwah Oppong

Programmable arrays of alkaline-earth atoms have emerged as a versatile experimental platform for quantum science. Together with Rydberg interactions, control at the single-particle level makes such atom arrays ideal systems for studying how quantum entanglement can be harnessed to improve the performance of optical atomic clocks. In this talk, I will discuss recent work from JILA, where we have achieved this goal by engineering Rydberg interactions to prepare entangled states with metrological gain.Programmable arrays of alkaline-earth atoms have emerged as a versatile experimental platform for quantum science. Together with Rydberg interactions, control at the single-particle level makes such atom arrays ideal systems for studying how quantum entanglement can be harnessed to improve the performance of optical atomic clocks. In this talk, I will discuss recent work from JILA, where we have achieved this goal by engineering Rydberg interactions to prepare entangled states with metrological gain.

Optical and Quantum Sensing and Precision Metrology IIMar 19, 20250 citations

Many-Particle Quantum Systems

Philip L. Bowers

Cambridge University Press eBooksAug 27, 20200 citations

Describing Many-Particle Quantum Systems

Mattia Walschaers

Springer thesesJan 1, 20180 citations

Single-Particle Green Function Approach and Correlated Atomic or Molecular Orbitals

Liqiang Wei

In this paper, we propose a generic and systematic approach for study of the electronic structure for atoms or molecules. In particular, we address the issue of single particle states, or orbitals, which should be one of the most important aspects of a quantum many-body theory. We argue that the single-particle $\it{Green}$ function provides a most general scheme for generating these single particle states or orbitals. We call them the $\it{correlated}$ atomic or molecular orbitals to make a distinction from those determined from $\it{Hartree-Fock}$ equation. We present the calculation of the single particle properties (i.e., the electron affinities $(EA's)$ and ionization potentials $(IP's)$ ) for the $H_{2}O$ molecule using the correlated molecular orbitals in the context of quantum chemistry with a second-order self energy. We also calculate the total ground state energy with a single $Slater$ wavefunction determined only from the hole states. Comparisons are made with available experimental data as well as with those from the $\it{Hartree-Fock}$ or density functional theory $(DFT)$ calculations. We conclude that the correlated atomic or molecular orbital approach provides a strictest and most powerful method for studying the single-particle properties of atoms or molecules. It also gives a better total energy than do the $\it{Hartree-Fock}$ and $\it{DFT}$ even at the single $\it{Slater}$ determinant level. It promises that a correlation theory based on the correlated atomic or molecular orbitals will become an approach which possesses the advantages and also overcomes their shortcomings of current quantum chemistry methods based on either the conventional quantum many-body theory or the $DFT$ .In this paper, we propose a generic and systematic approach for study of the electronic structure for atoms or molecules. In particular, we address the issue of single particle states, or orbitals, which should be one of the most important aspects of a quantum many-body theory. We argue that the single-particle $\it{Green}$ function provides a most general scheme for generating these single particle states or orbitals. We call them the $\it{correlated}$ atomic or molecular orbitals to make a distinction from those determined from $\it{Hartree-Fock}$ equation. We present the calculation of the single particle properties (i.e., the electron affinities $(EA's)$ and ionization potentials $(IP's)$) for the $H_{2}O$ molecule using the correlated molecular orbitals in the context of quantum chemistry with a second-order self energy. We also calculate the total ground state energy with a single $Slater$ wavefunction determined only from the hole states. Comparisons are made with available experimental data as well as with those from the $\it{Hartree-Fock}$ or density functional theory $(DFT)$ calculations. We conclude that the correlated atomic or molecular orbital approach provides a strictest and most powerful method for studying the single-particle properties of atoms or molecules. It also gives a better total energy than do the $\it{Hartree-Fock}$ and $\it{DFT}$ even at the single $\it{Slater}$ determinant level. It promises that a correlation theory based on the correlated atomic or molecular orbitals will become an approach which possesses the advantages and also overcomes their shortcomings of current quantum chemistry methods based on either the conventional quantum many-body theory or the $DFT$.

arXiv:physics/0412174Dec 29, 20040 citations

\it{Green}

function provides a most general scheme for generating these single particle states or orbitals. We call them the

\it{correlated}

atomic or molecular orbitals to make a distinction from those determined from

\it{Hartree-Fock}

equation. We present the calculation of the single particle properties (i.e., the electron affinities

(EA's)

and ionization potentials

(IP's)

) for the

H_{2}O

molecule using the correlated molecular orbitals in the context of quantum chemistry with a second-order self energy. We also calculate the total ground state energy with a single

Slater

wavefunction determined only from the hole states. Comparisons are made with available experimental data as well as with those from the

\it{Hartree-Fock}

or density functional theory

(DFT)

calculations. We conclude that the correlated atomic or molecular orbital approach provides a strictest and most powerful method for studying the single-particle properties of atoms or molecules. It also gives a better total energy than do the

\it{Hartree-Fock}

and

\it{DFT}

even at the single

\it{Slater}

determinant level. It promises that a correlation theory based on the correlated atomic or molecular orbitals will become an approach which possesses the advantages and also overcomes their shortcomings of current quantum chemistry methods based on either the conventional quantum many-body theory or the

DFT