Few-body Bose gases in low dimensions—A laboratory for quantum dynamics

Mistakidis, S.I.; Volosniev, A.G.; Barfknecht, R.E.; Fogarty, T.; Busch, Th.; Foerster, A.; Schmelcher, P.; Zinner, N.T.

doi:10.1016/j.physrep.2023.10.004

Cited by 27 publications

(11 citation statements)

References 957 publications

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“…It is well-known that this impenetrable boson model can be mapped to a free fermionic one [46][47][48]. In turn, this leads to an exact solution in the particular case above.…”

Section: Models and Main Resultsmentioning

confidence: 90%

“…Indeed, in this note we explain (full mathematical details will be provided elsewhere) that the magnetic-gauge picture Hamiltonian for 2D anyons of statistical parameter α ∈]0, 2[ converges, in the limit of a tight confinement along one spatial dimension, to the impenetrable boson model of the Tonks-Girardeau gas, soluble by Bose-Fermi mapping [46][47][48]. Thus, at leading order, the physics does not depend on α and is given by an extreme case of the Lieb-Liniger [49,50] model.…”

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confidence: 99%

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Anyons in a tight wave-guide and the Tonks-Girardeau gas

Rougerie,

Yang

2023

SciPost Phys. Core

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We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha ∈ ]0,2[α∈]0,2[. In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2\pi \alpha2πα, generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of \alphaα.

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“…It is well-known that this impenetrable boson model can be mapped to a free fermionic one [46][47][48]. In turn, this leads to an exact solution in the particular case above.…”

Section: Models and Main Resultsmentioning

confidence: 90%

mentioning

confidence: 99%

Anyons in a tight wave-guide and the Tonks-Girardeau gas

Rougerie,

Yang

2023

SciPost Phys. Core

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“…This ideal could help reduce the difficult integrals for the system energy. Recently, the theoretical and experimental progress in our understanding of quasi-one-dimensional cold-atom systems has served as a motivation to study these models [22][23][24][25][26]. The total Hamiltonian of the Moshinsky atom with two electrons is…”

Section: Three-body Problem and Many Interactions Of One-dimensional ...mentioning

confidence: 99%

A Mini-Review of the Kinetic Energy Partition Method in Quantum Mechanics

Chen,

Wu,

Chao

2024

Symmetry

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Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, we gradually increase the complexity in the number of particles and the interaction patterns. Our goal in the mini-review is to advocate for the utility of the KEP method in front-line research, in particular for research beginners in quantum many-body problems.

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“…Theoretically fundamental properties of these type of quasiparticles including effective mass [29][30][31], residue [1,2], and bound state formation [1,2,32] emerging in two-component systems have been discussed. Interestingly, by immersing at least two impurities into a quantum gas the latter mediates interactions between the former [33][34][35][36], a phenomenon that has been interpreted in terms of a Casimir-type interaction describing the induced interaction between two objects in a fluctuating medium [37][38][39]. In particular, induced interactions between two impurities are solely attractive as long as they couple in the same way (i.e.…”

Section: Introductionmentioning

confidence: 99%

Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

Theel,

Mistakidis,

Schmelcher

2024

SciPost Phys.

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We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and a trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

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Few-body Bose gases in low dimensions—A laboratory for quantum dynamics

Cited by 27 publications

References 957 publications

Anyons in a tight wave-guide and the Tonks-Girardeau gas

Anyons in a tight wave-guide and the Tonks-Girardeau gas

A Mini-Review of the Kinetic Energy Partition Method in Quantum Mechanics

Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

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