Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Interaction-strength evolution of two-particle momentum correlation maps of two ultracold fermions in a double well

Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman

Published Jan 8, 2018• 0 citations
OpenAlex

Abstract

Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the two-particle density matrix constructed via configuration-interaction (CI) exact diagonalization of the microscopic Hamiltonian, we explored here the systematic evolution of characteristic, damped, interference patterns in the two-particle momentum and spatial correlation maps of two ultracold fermionic atoms trapped in a double-well potential, over the entire range of variation of the contact repulsive interatomic interaction strength. For the singlet ground state the two-particle momentum maps were found to transform from a square-plaid pattern for non-interacting particles, to a system of striped interference fringes, with the most intense fringe lying along the main diagonal indicating bunching. Two-particle momentum correlation maps for low-lying excited states were also analyzed, with the triplet excited state found to exhibit antibunching. A modified Hubbard-type effective model is shown to reproduce well the microscopic CI results. This led to uncovering of analytic expressions capturing the full evolution of the two-particle momentum correlation maps over the entire range of interparticle interactions, from the independent particle limit with a substantial site-double-occupancy fraction, to the Mott insulating regime.

Related papers

Interatomic interaction effects on second-order momentum correlations and Hong-Ou-Mandel interference of double-well-trapped ultracold fermionic atoms

Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman

Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum-information resources. With the use of the second-order density matrix constructed via exact diagonalization of the microscopic Hamiltonian, and an analytic Hubbard-type model, we explore here the systematic evolution of characteristic interference patterns in the two-body momentum and spatial correlation maps of two entangled ultracold fermionic atoms in a double well, for the entire attractive- and repulsive-interaction range. We uncover quantum-statistics-governed bunching and antibunching, as well as interaction-dependent interference patterns, in the ground and excited states, and interpret our results in light of the Hong-Ou-Mandel interference physics, widely exploited in photon indistinguishability testing and quantum-information science.

arXiv:1801.02295•Physical Review A•May 4, 2018•14 citations

Two-point momentum correlations of few ultracold quasi-one-dimensional trapped fermions: Diffraction patterns

Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman

Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of spin resolved patterns exhibited in two-point correlations, accessible directly by experiments, are key for uncovering the symmetry and structure of the many-body wave functions of the trapped system. Using the full configuration interaction method for exact diagonalization of the many-body Hamiltonian of $N=2--4$ fermionic atoms trapped in single, double, triple, and quadruple wells, we analyze both two-point momentum and space correlations, as well as associated noise distributions, for a broad range of interparticle contact repulsion strengths and interwell separations, unveiling characteristics allowing insights into the transition, via an intermediate phase, from the noninteracting Bose-Einstein condensate to the weakly interacting quasi-Bose-Einstein regime, and from the latter to the strong-repulsion Tonks-Girardeau (TG) one. The ab initio numerical predictions are shown to agree well with the results of a constructed analytical model employing localized displaced Gaussian functions to represent the $N$ fermions. The two-point momentum correlations are found to exhibit damped oscillatory diffraction behavior. This diffraction behavior develops fully for atoms trapped in a single well with strong interatomic repulsion in the TG regime, or for atoms in well-separated multiwell traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit ``shortsightedness,'' with the main contribution coming from nearest-neighboring particles.

arXiv:1710.07853•Physical Review A•Nov 30, 2017•14 citations

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman

"Bottom-up" approaches to the many-body physics of fermions have recently demonstrated precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nanoscale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic Hamiltonian, approaching realization of Feynmans' vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational microscopy solutions of the Hamiltonian, uncovering the spectral evolution, wave function anatomy, and entanglement properties of the interacting fermions in the entire parameter range, including crossover from an SW to a DW confinement and a controllable energy imbalance between the wells. We demonstrate attractive pairing and formation of repulsive, highly correlated, ultracold Wigner molecules, well-described in the natural orbital representation. The agreement with the measurements affirms the henceforth gained deep insights into ultracold molecules and opens access to the size-dependent evolution of nanoclustered and condensed-matter phases and ultracold-atoms quantum information.

arXiv:1508.02308•Nano Letters•Sep 9, 2015•28 citations

Two Fermions in a Double Well: Exploring a Fundamental Building Block of the Hubbard Model

Simon Murmann, Andrea Bergschneider, Vincent M. Klinkhamer +3 more

We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.

arXiv:1410.8784•Physical Review Letters•Feb 23, 2015•252 citations

All-order momentum correlations of three ultracold bosonic atoms confined in triple-well traps: Signatures of emergent many-body quantum phase transitions and analogies with three-photon quantum-optics interference

Constantine Yannouleas, Uzi Landman

All-order momentum correlation functions associated with the time-of-flight spectroscopy of three spinless ultracold bosonic interacting neutral atoms confined in a linear three-well optical trap are presented. The underlying Hamiltonian employed for the interacting atoms is an augmented three-site Hubbard model. Our investigations target matter-wave interference of massive particles, aiming at the establishment of experimental protocols for characterizing the quantum states of trapped attractively or repulsively interacting ultracold particles, with variable interaction strength. The advantages and physical insights that can be gained from the results of our study for a comprehensive understanding of the nature of the quantum states of interacting many-particle systems, via analysis of the all-order (that is, first, second, and third) momentum correlation functions for three bosonic atoms in a three-well confinement, are illustrated in the context of time-of-flight inteferometric interrogations of the interaction-strength-induced emergent quantum phase transition from the Mott insulating phase to the superfluid one. Furthermore, our inteferometric interrogations establish strong analogies with the quantum-optics interference of three photons, including the aspects of genuine three-photon interference, which are important to explorations targeting the development and implementation of quantum information applications and quantum computing.

arXiv:2002.00311•Physical Review A•Jun 11, 2020•3 citations

Few-Fermion Systems under a Matterwave Microscope

Vincent M. Klinkhamer

This thesis presents correlation measurements in two different few-fermion systems of ultracold 6Li atoms. The measurements have been performed with a new spatially and spin-resolved imaging method with single-atom sensitivity, with which we can probe coherences of the initial system as correlations in the momenta. First, we study attractively interacting atoms in a single microtrap, which serves as a basis for understanding the expansion dynamics of strongly interacting Fermi gases. We observe correlation features in the relative coordinate for different interaction strengths. We explain several of these features theoretically by calculating the initial interacting state in the microtrap and projecting it on a molecular bound state and scattering waves. Next, we study a small number of repulsively interacting particles in the ground state of a double-well potential. This system constitutes the fundamental building block of the Hubbard model. We observe interference patterns in the coordinates of the individual particles and in their relative coordinates. From the amplitude and phase of these patterns, we extract off-diagonal density matrix elements of the state, which we use to directly show coherence and entanglement in our system.

•Jan 1, 2018•0 citations
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the two-particle density matrix constructed via configuration-interaction (CI) exact diagonalization of the microscopic Hamiltonian, we explored here the systematic evolution of characteristic, damped, interference patterns in the two-particle momentum and spatial correlation maps of two ultracold fermionic atoms trapped in a double-well potential, over the entire range of variation of the contact repulsive interatomic interaction strength. For the singlet ground state the two-particle momentum maps were found to transform from a square-plaid pattern for non-interacting particles, to a system of striped interference fringes, with the most intense fringe lying along the main diagonal indicating bunching. Two-particle momentum correlation maps for low-lying excited states were also analyzed, with the triplet excited state found to exhibit antibunching. A modified Hubbard-type effective model is shown to reproduce well the microscopic CI results. This led to uncovering of analytic expressions capturing the full evolution of the two-particle momentum correlation maps over the entire range of interparticle interactions, from the independent particle limit with a substantial site-double-occupancy fraction, to the Mott insulating regime.
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum-information resources. With the use of the second-order density matrix constructed via exact diagonalization of the microscopic Hamiltonian, and an analytic Hubbard-type model, we explore here the systematic evolution of characteristic interference patterns in the two-body momentum and spatial correlation maps of two entangled ultracold fermionic atoms in a double well, for the entire attractive- and repulsive-interaction range. We uncover quantum-statistics-governed bunching and antibunching, as well as interaction-dependent interference patterns, in the ground and excited states, and interpret our results in light of the Hong-Ou-Mandel interference physics, widely exploited in photon indistinguishability testing and quantum-information science.
Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of spin resolved patterns exhibited in two-point correlations, accessible directly by experiments, are key for uncovering the symmetry and structure of the many-body wave functions of the trapped system. Using the full configuration interaction method for exact diagonalization of the many-body Hamiltonian of N=2−−4N=2--4N=2−−4 fermionic atoms trapped in single, double, triple, and quadruple wells, we analyze both two-point momentum and space correlations, as well as associated noise distributions, for a broad range of interparticle contact repulsion strengths and interwell separations, unveiling characteristics allowing insights into the transition, via an intermediate phase, from the noninteracting Bose-Einstein condensate to the weakly interacting quasi-Bose-Einstein regime, and from the latter to the strong-repulsion Tonks-Girardeau (TG) one. The ab initio numerical predictions are shown to agree well with the results of a constructed analytical model employing localized displaced Gaussian functions to represent the NNN fermions. The two-point momentum correlations are found to exhibit damped oscillatory diffraction behavior. This diffraction behavior develops fully for atoms trapped in a single well with strong interatomic repulsion in the TG regime, or for atoms in well-separated multiwell traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit ``shortsightedness,'' with the main contribution coming from nearest-neighboring particles.
"Bottom-up" approaches to the many-body physics of fermions have recently demonstrated precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nanoscale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic Hamiltonian, approaching realization of Feynmans' vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational microscopy solutions of the Hamiltonian, uncovering the spectral evolution, wave function anatomy, and entanglement properties of the interacting fermions in the entire parameter range, including crossover from an SW to a DW confinement and a controllable energy imbalance between the wells. We demonstrate attractive pairing and formation of repulsive, highly correlated, ultracold Wigner molecules, well-described in the natural orbital representation. The agreement with the measurements affirms the henceforth gained deep insights into ultracold molecules and opens access to the size-dependent evolution of nanoclustered and condensed-matter phases and ultracold-atoms quantum information.
We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.
All-order momentum correlation functions associated with the time-of-flight spectroscopy of three spinless ultracold bosonic interacting neutral atoms confined in a linear three-well optical trap are presented. The underlying Hamiltonian employed for the interacting atoms is an augmented three-site Hubbard model. Our investigations target matter-wave interference of massive particles, aiming at the establishment of experimental protocols for characterizing the quantum states of trapped attractively or repulsively interacting ultracold particles, with variable interaction strength. The advantages and physical insights that can be gained from the results of our study for a comprehensive understanding of the nature of the quantum states of interacting many-particle systems, via analysis of the all-order (that is, first, second, and third) momentum correlation functions for three bosonic atoms in a three-well confinement, are illustrated in the context of time-of-flight inteferometric interrogations of the interaction-strength-induced emergent quantum phase transition from the Mott insulating phase to the superfluid one. Furthermore, our inteferometric interrogations establish strong analogies with the quantum-optics interference of three photons, including the aspects of genuine three-photon interference, which are important to explorations targeting the development and implementation of quantum information applications and quantum computing.
This thesis presents correlation measurements in two different few-fermion systems of ultracold 6Li atoms. The measurements have been performed with a new spatially and spin-resolved imaging method with single-atom sensitivity, with which we can probe coherences of the initial system as correlations in the momenta. First, we study attractively interacting atoms in a single microtrap, which serves as a basis for understanding the expansion dynamics of strongly interacting Fermi gases. We observe correlation features in the relative coordinate for different interaction strengths. We explain several of these features theoretically by calculating the initial interacting state in the microtrap and projecting it on a molecular bound state and scattering waves. Next, we study a small number of repulsively interacting particles in the ground state of a double-well potential. This system constitutes the fundamental building block of the Hubbard model. We observe interference patterns in the coordinates of the individual particles and in their relative coordinates. From the amplitude and phase of these patterns, we extract off-diagonal density matrix elements of the state, which we use to directly show coherence and entanglement in our system.