Creating entanglement using integrals of motion

Olshanii, Maxim; Scoquart, Thibault; Yampolsky, Dmitry; Dunjko, Vanja; Jackson, Steven Glenn

doi:10.1103/physreva.97.013630

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…In this article, we show that for hard-core interactions there exist families of unequal masses for which there are exact solutions for the ground state and all excited states. This extends results first derived for hardcore interactions in free space [33][34][35]. Exact solutions for hard-core interactions form the basis for approximation schemes for strongly-interacting systems, providing a valuable benchmark for testing numerical methods [36][37][38].…”

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confidence: 74%

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Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

et al. 2017

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We show that the dynamics of particles in a one-dimensional harmonic trap with hard-core interactions can be solvable for certain arrangements of unequal masses. For any number of particles, there exist two families of unequal mass particles that have integrable dynamics, and there are additional exceptional cases for three, four and five particles. The integrable mass families are classified by Coxeter reflection groups and the corresponding solutions are Bethe ansatz-like superpositions of hyperspherical harmonics in the relative hyperangular coordinates that are then restricted to sectors of fixed particle order. We also provide evidence for superintegrability of these Coxeter mass families and conjecture maximal superintegrability.

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confidence: 74%

“…In the third scheme, described in more detail in [35], the role of massive particles is played by bosonic solitons in an atom waveguides [78][79][80]. The solitons are made of atoms in two alternating internal states where the intraspecies interaction is attractive and the interspecies interaction is repulsive.…”

Section: Experimental Outlookmentioning

confidence: 99%

Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

et al. 2017

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“…Another motivation for considering the quantum version of this system is the daunting experimental challenge of realizing Galperin billiards with macroscopic objects. Quantum realizations of effectively one-dimensional mixed-mass systems like Galperin billiards can be experimentally realized with ultracold atoms in few-body systems [37] or as bi-solitons in ultracold atomic gases, via a scheme described in [31]. There, a bi-soliton of a desired mass ratio is created using a coupling constant quench [38]; one of the two solitons is subsequently transferred to a different internal atomic state that leads to a repulsion between the solitons.…”

Section: Discussionmentioning

confidence: 99%

“…Remark that the case v in = V in , where v out vanishes, may be regarded as a generalization of a notion of a Galilean Cannon [31]: a system of balls that arrives at the wall with the same speed and transfers all the energy to the far-most one in the end.…”

Section: Superintegrability and Maximal Superintegrabilitymentioning

confidence: 99%

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

et al. 2020

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In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases.

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“…Second, the Busch et al solution for two particles can be extended to cases of anisotropic harmonic traps [48]. Third, in the case of a four-body problem and contact forces, neat analytical solutions associated with the symmetries of the three-dimensional and four-dimensional icosahedra were discussed in [49] while a very specific system of N hard-sphere particles having special mass ratios was solved in [50]. Finally, different exact solutions of the two-body problem with other than contact interactions were also announced: an attractive 1/r 6 interaction in [51], a repulsive 1/r 3 interaction in [52,53], and a finite-range (repulsive and attractive) interaction modeled by a step function in [54][55][56].…”

Section: Two Particles In a Harmonic Trapmentioning

confidence: 99%

One-dimensional mixtures of several ultracold atoms: a review

Sowiński¹,

2019

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Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

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Creating entanglement using integrals of motion

Cited by 6 publications

References 20 publications

Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

One-dimensional mixtures of several ultracold atoms: a review

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