Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions

Abstract

Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W -and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order and second-order spin-resolved and spin-unresolved momentum correlations, aiming at matter-wave interference investigations with trapped massive particles in analogy with, and having the potential for expanding the scope of, recent three-photon quantum-optics interferometry. * Constantine.Yannouleas@physics.gatech.edu † Uzi.Landman@physics.gatech.edu arXiv:1902.09439v2 [cond-mat.quant-gas]

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

“…Therefore, demonstrating that this complexity of the theoretical treatment can be handled in an efficient manner through the use of algebraic computer languages constitutes an important step toward the implementation of the bottom-up approach for simulating many-body physics with ultracold atoms. In this respect, the statement above parallels earlier observations that three-particle entanglement extends two-particle entanglement in a nontrivial way [17][18][19].…”

“…Each boson in any of the three wells is represented by a single-particle localized orbital having the form of a displaced Gaussian function [12][13][14]19], which in momentum space is given by…”

“…for the pairs (i = 1, j = 10), (i = 2, j = 9), (i = 3, j = 8), (i = 4, j = 3), (i = 5, j = 2), (i = 6, j = 5), (i = 7, j = 4), (i = 8, j = 7), (i = 9, j = 6), and (i = 10, j = 1) due to the equalities between eigenvectors listed in Eq. (19).…”

“…It is worth noting that the expression (47) above for 3 bosons is similar to the third-order correlation for the triplet states (with total spin S = 3/2 and spin projections S z = 3/2 or S z = 1/2) for 3-fermions trapped in 3 wells, except that in the fermionic case the sign in front of the cosine terms with only 2 momenta in the cosine argument is negative; see Refs. [3,19]…”

Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap

“…[1][2][3][4][5][6][7]), one-dimensional (1D) assemblies of strongly contact-interacting ultracold atoms have attracted much attention in the last few years [8][9][10][11][12][13][14][15][16][17], motivated by rapid experimental advances in the field of trapped ultracold atoms that allow direct verification of theoretical results. In this context, insitu and time-of-flight single-atom measurements of realspace and momentum-space higher-order correlations, respectively, hold a great promise [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”