Quenching small quantum gases: Genesis of the orthogonality catastrophe

Campbell, Steve; García-March, Miguel Ángel; Fogarty, Thomás; Busch, Thomas

doi:10.1103/physreva.90.013617

Cited by 53 publications

(75 citation statements)

References 73 publications

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“…Finally, it is also possible to generalize our work to Bose-Fermi mixtures [49,50], which can be compared with recent few-body studies of such mixtures [51][52][53][54]. We will consider these generalizations in future work.…”

Section: Discussionmentioning

confidence: 94%

Strongly interacting quantum gases in one-dimensional traps

2015

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Under second-order degenerate perturbation theory, we show that the physics of N particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.

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Section: Discussionmentioning

confidence: 94%

Strongly interacting quantum gases in one-dimensional traps

2015

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“…It exactly cancels the sign coming from the determinant that we pulled out of the sum in Eq. (61). The relative minus sign in front of the sum in Eq.…”

Section: A First Order Perturbation Expansionmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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“…The fact that the third atom is distinguishable is the responsible for the change of sign of the two excited-state wave functions when crossing the lines X = ± √ 3Y , and therefore of the threefold degeneracy occurring for infinite interactions. This has profound implications in the dynamics of the system, for example, after a quench in the AB interactions, where interesting phenomena such as the emergence of orthogonality catastrophe has been found [44]. (18) and (19), respectively.…”

Section: Variable Inter-and Intraspecies Interactionsmentioning

confidence: 99%

“…Other relevant phenomena are the presence of a composite fermionized gas [34][35][36], quantum magnetism [37][38][39], or a crossover between composite fermionization and phase separation [40,41]. Also, these small number bosonic mixtures allow for the study of dynamical phenomena, like the tunneling of one species through the barrier formed by the other species [42,43] or the dynamical emergence of orthogonality catastrophe [44]. This latter, extremely appealing phenomena occurs in a system of two atoms in one species and a third atom in a second species.…”

Section: Introductionmentioning

confidence: 99%

Distinguishability, degeneracy, and correlations in three harmonically trapped bosons in one dimension

et al. 2014

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We study a system of two bosons of one species and a third atom of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter-and intraspecies interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical Ansätze gaining physical insight over the numerically obtained wave functions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wave function when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the interspecies and/or the intraspecies interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit us to build up different correlations in the system and lead to different spatial distributions of the three atoms.

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Quenching small quantum gases: Genesis of the orthogonality catastrophe

Cited by 53 publications

References 73 publications

Strongly interacting quantum gases in one-dimensional traps

Strongly interacting quantum gases in one-dimensional traps

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Distinguishability, degeneracy, and correlations in three harmonically trapped bosons in one dimension

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