Quantum gas mixtures in different correlation regimes

García-March, Miguel Ángel; Busch, Thomas

doi:10.1103/physreva.87.063633

Cited by 34 publications

(44 citation statements)

References 52 publications

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“…To numerically calculate the properties of the ground and excited states of the systems, we employ the second-quantized exact diagonalization algorithm described in [33], which makes use of the expansion of the second-quantized field operator of A in terms of many modes, that is, Hamiltonian we obtain the eigenenergies and the ground and excited states, which we express as expansions in terms of the of Fock vectors j = i=1 c j i i . To obtain the wave function in first quantization from the numerically calculated one in second quantization by direct diagonalization, we consider all possible permutations of the two indistinguishable atoms over the single-particle basis used in the many-mode expansion of the field operator, Eq.…”

Section: Appendix A: Direct Diagonalization Methodsmentioning

confidence: 99%

“…To numerically evaluate the energy spectra of Hamiltonian (1) we employ the exact diagonalization method described in [33] and outlined in Appendix A.…”

Section: Distinguishability and Degeneracies In The Energy Spectramentioning

confidence: 99%

“…The intra-and interspecies interactions, which describe all the interaction processes in these mixtures, can be controlled experimentally by means of Feshbach and confinement induced resonances [26][27][28]. By playing with both the intra-and interspecies interactions one can explore different physical phenomena, like phase separation on small atom mixtures [29][30][31][32][33]. 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].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Appendix A: Direct Diagonalization Methodsmentioning

confidence: 99%

“…To numerically evaluate the energy spectra of Hamiltonian (1) we employ the exact diagonalization method described in [33] and outlined in Appendix A.…”

Section: Distinguishability and Degeneracies In The Energy Spectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…For N B N A the TG-BEC gas is known to be phase separated [14], with the B component being located in the center of the trap and the A component occupying the outer regions. In this case the occupation of the lowest lying natural orbital for species B is of the order of N B , which implies that the component is Bose condensed and fully phase coherent.…”

mentioning

confidence: 99%

“…To calculate the ground-state properties we use direct diagonalization of the Hamiltonian [14] and the diffusion Monte Carlo (DMC) method [15]. The phase-separated TG-BEC is realized with g B = 0 and g AB = 500hωa 0 (diagonalization) or g AB → ∞ (DMC).…”

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confidence: 99%

Sharp crossover from composite fermionization to phase separation in microscopic mixtures of ultracold bosons

et al. 2013

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We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very diverse quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. Starting from the composite fermionization regime, in which the interactions between both components are large and neither gas is phase coherent, our results show that a phase-separated state can be reached by increasing the interaction in one of the species. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting one is expelled to the edges of the trap. The crossover is sharp, as can be witnessed in the system's energy and in the occupation of the lowest natural orbital of the weakly interacting species. We show that such a transition is a few-atom effect which disappears for a large population imbalance. Ensembles of a few interacting ultracold trapped atoms constitute unique quantum systems. They can be exceptionally well isolated from the environment, minimizing the role of decoherence, and are perfect candidates for the study of states with strong quantum correlations. Moreover, they are extremely versatile, as precise control over the shape of the trapping potential and the atom-atom interactions is routinely available in current experiments. Since at these energy scales often all degrees of freedom other than the positions can be ignored, they provide a simple system which still shows a great diversity of phenomena [1,2]. Experimentally, the loading of a small number of fermionic or bosonic atoms into a single trap has been achieved [3], and mixtures have been realized in optical lattice potentials [4]. Also, the strongly correlated low-dimensional Tonks-Girardeau (TG) gas has been achieved experimentally, which also requires low densities [5]. These systems constitute a natural ground for studies of squeezing and entanglement, with applications, for example, in precision measurements [6,7], thus leading to the great interest in their experimental realization.In this article, we predict a sharp crossover between two very different regimes in microscopic, two-component mixtures of repulsively interacting bosons at zero temperature, corresponding to different interaction strengths between atoms of the same and different species when trapped in a onedimensional (1D) trap. In the first regime the interactions between the atoms of different species are strong, while the interactions between the atoms of the same species are weak. This is the so-called composite fermionization limit [8,9], which shows strong anticorrelations between unlike atoms, similar to the ones between like atoms in the standard TG gas [10]. Since the occupation number of the lowest natural orbital for each species, A and B, scales more rapidly than N A,B but more slowly than N A,B , neither of them is fully Bose * magarciamarch@ecm.ub.edu condensed. The second limit is obtained when the interact...

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Stationary modes for vector nonlinear Schrödinger-type equations: A numerical procedure for complete search and its mathematical background

Alfimov,

Fedotov,

Kutsenko

et al. 2023

Physica D: Nonlinear Phenomena

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Quantum gas mixtures in different correlation regimes

Cited by 34 publications

References 52 publications

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

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

Sharp crossover from composite fermionization to phase separation in microscopic mixtures of ultracold bosons

Stationary modes for vector nonlinear Schrödinger-type equations: A numerical procedure for complete search and its mathematical background

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