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.
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.
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.
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.
Aiming at elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton joint-coincidence spectral correlations, studied with massless noninteracting biphotons emanating from Einstein-Podolsky-Rosen Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total second-order momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. The general form of this partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science.
The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space, our findings provide impetus for time-of-flight experimental protocols for detecting anyonic statistics via interferometry measurements of massive particles that broaden the scope of the biphoton interferometry of quantum optics.
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.
"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.