arXiv subjects

Benedikt B. Brandt

Publications and source records attributed to Benedikt B. Brandt.

6 recordsLinked to original sources

arXiv2019

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

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 non-interacting biphotons emanating from EPR-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. 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.

cond-mat.quant-gas↗

arXiv2018

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

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 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.

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arXiv2017

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

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 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 non-interacting 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 multi-well traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit "shortsightedness", with the main contribution coming from nearest-neighboring particles.

cond-mat.quant-gas↗

arXiv2017

Bottom-up configuration-interaction emulations of ultracold fermions in entangled optical plaquettes: building blocks of unconventional superconductivity

A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schroedinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of Lithium-6 atoms in a single square plaquette in the hole-pairing regime, and by analyzing the entanglement (symmetry-preserving) and disentanglement physics (via symmetry-breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy RVB states contribute only partially to the exact many-body solutions, and the CI results map onto a Hubbard Hamiltonian, but not onto the double-occupancy-excluding t-J one. For the double-plaquette case, effects brought about by breaking the symmetry between two weakly-interacting plaquettes, either by distorting, or by tilting and detuning, one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored.

cond-mat.quant-gas↗

arXiv2016

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models

Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly-correlated behavior of ultracold strongly-repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric double wells reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T$_c$ superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, double wells suggest three-cold-atom DW quantum computing qubits.

cond-mat.quant-gas↗

arXiv2015

Double-well ultracold-fermions computational microscopy: Wave-function anatomy of attractive-pairing and Wigner-molecule entanglement and natural orbitals

"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale 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 Feynman's 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 a 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 nano-clustered and condensed-matter phases and ultracold-atoms quantum information.

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