Quantum Correlations in Systems of Indistinguishable Particles

Eckert, K.; Schliemann, John; Bruß, Dagmar; Lewenstein, Maciej

doi:10.1006/aphy.2002.6268

Cited by 367 publications

(657 citation statements)

References 61 publications

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“…In all instances the energy of the triplet states is independent of , as found also for a single well 17 signifying the left and right wells and , the two spin projections). Such states approximate the highly entangled Bell states 10,18 . The energy curves that show a -dependence correspond to singlet states having both fermions in the same well.…”

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confidence: 91%

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

2015

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"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 analoguesimulator 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 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.Key words: ultracold atoms, double-well nano-confinement, Wigner molecule, configuration interaction, entanglement, strong correlated matter *Corresponding Author: uzi.landman@physics.gatech.edu arXiv:1508.02308v3 2 Ingress to the origins of complex physical phenomena often requires experiments whereby theories are tested or suggested through artificial manipulations of physical circumstances. During the past decade, a cornucopia of new tools have emerged resulting from the discovery and advancement of methods for the preparation and trapping of ultracold atomic gases, controlled tuning of the interparticle interactions (via magnetic manipulation of the Feshbach resonance), and the creation of synthetic gauge fields through atom-light interactions in optical lattices of varied geometries and topologies 1,2 . The remarkable pristine nature of these systems, and the exquisite level of control that can be exercised over them, brought forth a realization of Richard Feynman's vision 3 for the construction of physical quantum simulators, capable of an exact simulation, of systems or situations that are computationally or analytically intractable. Indeed, in the past several years we witnessed a surge of realizations of such exact simulations addressing diverse fields (see reviews in refs.1 and 2), including in particular the behavior of strongly interacting fermions where computations are precluded because of the "fermion sign problem." 4 . These systems range from high-Tc superconductivity 1,2 , collosal magnetoresistance 5 and quantum Hall effects 2 to atomic frequency resonators 6 , interferometry 7,8 , matter wave gyroscopes 9 and the development of scalable quantum computers with neutral atoms 10,11 .Progress aiming at a "bottom-up" app...

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confidence: 91%

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

2015

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“…The entanglement of formation (EOF) for mixed states has also been investigated for the single particle state Hilbert space of dimension four. In particular, a formula was identified [9,12] and is similar to the known formula for two-qubit states by Wootters [13].…”

Section: Introductionmentioning

confidence: 65%

“…This is simply due to the fact the LU group is such a small group compared to the entire unitary group U(2 N ). Entanglement theory for identical particle systems has also been considerably developed during the past decade [3,8,9,10,11,12]. Entanglement for identical particle systems cannot be discussed in usual way as for the distinguishable particle case.…”

Section: Introductionmentioning

confidence: 99%

“…This is because the symmetrization for bosonic systems and antisymmetrization for fermionic systems for the wave functions may introduce 'pseudo entanglement' which is not accessible in practice. It is now widely agreed that non-entangled states are reasonably corresponding to the form |v N for bosonic states [11,3,12] (there was indeed suggestion that non-entangled bosonic state corresponds to |v 1 ∨ |v 2 ∨ · · · ∨ |v N [10], however most of the literatures accept |v N ) and to the form of Slater determinants |v 1 ∧ |v 2 ∧ · · · ∧ |v N for fermionic states [3,12].…”

Section: Introductionmentioning

confidence: 99%

“…This thus allows a complete understanding of entanglement properties for bipartite fermionic pure states. Many interesting analogues to the bipartite distinguishable particle case have also been identified, such as concurrence and magic basis [9,12]. The entanglement of formation (EOF) for mixed states has also been investigated for the single particle state Hilbert space of dimension four.…”

Section: Introductionmentioning

confidence: 99%

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Universal Subspaces for Local Unitary Groups of Fermionic Systems

Chen

Djoković

et al. 2014

Commun. Math. Phys.

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Let V = ∧ N V be the N -fermion Hilbert space with M -dimensional single particle space V and 2N ≤ M . We refer to the unitary group G of V as the local unitary (LU) group. We fix an orthonormal (o.n.) basis |v 1 , . . . , |v M of V . Then the Slater determinants e i 1 ,...,i N :Let S ⊆ V be the subspace spanned by all e i 1 ,...,i N such that the set {i 1 , . . . , i N } contains no pair {2k − 1, 2k}, k an integer. We say that the |ψ ∈ S are single occupancy states (with respect to the basis |v 1 , . . . , |v M ). We prove that for N = 3 the subspace S is universal, i.e., each G-orbit in V meets S, and that this is false for N > 3. If M is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N = 3 and M even there is a universal subspace W ⊆ S spanned by M (M − 1)(M − 5)/6 states e i 1 ,...,i N . Moreover the number M (M − 1)(M − 5)/6 is minimal.

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Entanglement Properties of Composite Quantum Systems

Eckert

Gühne

Hulpke

et al. 2003

Quantum Information Processing

Self Cite

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We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much entangled it is, remains one of the most fundamental open questions in quantum information theory. We discuss our recent results related to the problem of separability and distillability for distinguishable particles, employing the tool of witness operators. Finally, we also state our results concerning quantum correlations for indistinguishable particles.

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Quantum Correlations in Systems of Indistinguishable Particles

Cited by 367 publications

References 61 publications

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

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

Universal Subspaces for Local Unitary Groups of Fermionic Systems

Entanglement Properties of Composite Quantum Systems

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