Impurity dynamics and nearest-neighbor interactions in one-dimensional lattices

Anne-Maria Visuri

Impurity dynamics and nearest-neighbor interactions in one-dimensional lattices

Julkaisun otsikon käännös: Epäpuhtaushiukkasten liike ja lähinaapurivuorovaikutukset yksiulotteisissa hiloissa

Anne-Maria Visuri

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Hiukkaskylvyn kanssa vuorovaikuttavat epäpuhtaushiukkaset esiintyvät usein monen kappaleen fysiikassa. Tässä työssä epäpuhtaushiukkasten teoriaa tutkitaan yksidimensioisissa hiloissa käyttäen sekä numeerista time-evolving block decimation -menetelmää (hajotelma kvanttimekaanisen aikakehityksen laskemiseen) että analyyttisiä menetelmiä. Hilassa hiukkasten liike-energiaa rajoittaa energiavyön leveys. Löydämme uudenlaisia ajasta riippuvia ilmiöitä, kun hiukkaskylpyä häiritään vyönleveyttä suuremmalla energia-alueella. Julkaisu I käsittelee singlettisupranestetilassa olevia fermioneja. Supranestekorrelaatioiden huomataan säilyvän, kun fermioneja häiritään liikkuvalla potentiaalihäiriöllä, jonka nopeus on suurempi kuin äänennopeus hiukkassysteemissä. Julkaisussa III tutkimme epäpuhtaushiukkasen kvanttitilan koherenssin häviämistä sen tiheysmatriisin puhtauden avulla. Näytämme, että koherenssi katoaa nopeimmin, kun kevyt epäpuhtaushiukkanen vuorovaikuttaa raskaiden kylpyhiukkasten kanssa. Epäpuhtaushiukkasen energiahukka taas on nopeinta, kun massat ovat yhtä suuret. Julkaisuissa II ja IV tutkimme hiukkaskylpyä, jossa äärellisen kantaman vuorovaikutus saa aikaan jaksollisen rakenteen. Aikaisempi tutkimus on keskittynyt tasajakautuneisiin hiukkaskylpyihin, joissa hiukkaset vuorovaikuttavat vain kontaktissa. Kun hiukkaset hylkivät toisiaan vierekkäisillä hilapaikoilla ollessaan, ja hiukkasten määrä on puolet hilapaikkojen määrästä, ne järjestäytyvät joka toiselle paikalle. Tätä tilaa kutsutaan Mottin eristeeksi. Kun hiukkasia on hieman enemmän, muodostuu eri tavoin järjestäytyneitä alueita, joiden rajapintoja kutsutaan solitoneiksi. Osoitamme, että kun hiukkasten väliset vuorovaikutukset ovat resonanssialueella, epäpuhtaushiukkanen luo kylvyssä solitoni-antisolitoniparin. Nämä kaksi viritystilaa käyttäytyvät hyvin eri tavoin: Solitoni etenee hilassa, kun taas antisolitoni voi muodostaa sidotun tilan epäpuhtaushiukkasen kanssa. Kun hiukkaskylvyssä on solitoneja jo alkutilassa, antisoliton liike on rajoitettu, sillä se johtaisi prosesseihin joissa energia ei säily. Tämän työn teoreettiset ennusteet on mahdollista testata kokeissa, joissa ultrakylmiä kaasuja vangitaan optisiin hiloihin. Kokeissa voidaan toteuttaa hilasysteemejä, joissa vierekkäisillä hilapaikoilla olevat hiukkaset vuorovaikuttavat dipoli-dipolivuorovaikutuksella. Lisäksi on mahdollista luoda epäpuhtauksia ja häiriöitä sekä mitata hiukkasten liike yhden hilapaikan tarkkuudella. Myös monen hiukkasen kvanttitilan puhtaus voidaan mitata.

Julkaisun otsikon käännös	Epäpuhtaushiukkasten liike ja lähinaapurivuorovaikutukset yksiulotteisissa hiloissa
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Ohjaaja	Törmä, Päivi, Vastuuprofessori Törmä, Päivi, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-7369-9
Sähköinen ISBN	978-952-60-7368-2
Tila	Julkaistu - 2017
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

monen kappaleen kvanttifysiikka
laajennettu Hubbardin malli
dekoherenssi
supranestekorrelaatiot

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-7368-2Lisenssi: Määrittelemätön

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@phdthesis{b279d05073c74f43a3e8cdc23e536606,

title = "Impurity dynamics and nearest-neighbor interactions in one-dimensional lattices",

abstract = "An impurity coupled to a bath is a paradigmatic problem of many-body physics and relevant for various systems. In this work, we study the dynamics due to impurities in one-dimensional lattice systems using the numerical time-evolving block decimation method and analytic calculations. We consider both noninteracting and interacting fermions as the bath, in particular fermions in a singlet superfluid state due to attractive on-site interactions, and baths with a periodic or nearly periodic structure due to nearest-neighbor repulsion. Previous theoretical and experimental research mainly considers homogeneous baths with contact interactions. We find novel phenomena when the bath is probed with energies above its characteristic energyscale. In publication I, a driven perturbation with velocity above the speed of sound of the interacting fermions retains the ground-state power-law decay of singlet superfluid correlations. In publication III, we study the decoherence of an impurity in terms of the purity of its density matrix. The impurity and the bath fermions have different masses, and we find the fastest decoherence for a light impurity in a heavy bath, whereas the fastest dissipation of energy occurs for equal masses. In publications II and IV, we consider a bath of fermions with repulsive nearest-neighbor interactions. In a half-filled lattice, the bath is in the Mott insulator state with a particle every two sites. A filling above one half leads to solitons seen as domain walls in the arrangement of the particles. We find that within a resonance region of interactions, the impurity can create an additional soliton-antisoliton pair in the bath. These two excitations have very different dynamics: The antisoliton can form a bound state with the impurity while the soliton excitation propagates. When the ground state of the bath contains solitons, the antisoliton excitation is confined close to its origin. These phenomena are explained by energy conservation, since processes with an energy change larger than the bandwidth are suppressed. Recent developments in experiments with ultracold gases in optical lattices offer possibilities for testing the theoretical predictions of this work. Long-range interactions in lattice models have been observed in experiments with magnetic atoms and dipolar molecules. Furthermore, single-site addressing techniques allow to create localized impurities and track their motion, and to measure the purity of many-body states.",

keywords = "impurity dynamics, domain walls, time-evolving block decimation, extended Hubbard model, decoherence, superfluid correlations, monen kappaleen kvanttifysiikka, laajennettu Hubbardin malli, dekoherenssi, supranestekorrelaatiot, impurity dynamics, domain walls, time-evolving block decimation, extended Hubbard model, decoherence, superfluid correlations",

author = "Anne-Maria Visuri",

year = "2017",

language = "English",

isbn = "978-952-60-7369-9",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "62",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Impurity dynamics and nearest-neighbor interactions in one-dimensional lattices

AU - Visuri, Anne-Maria

PY - 2017

Y1 - 2017

N2 - An impurity coupled to a bath is a paradigmatic problem of many-body physics and relevant for various systems. In this work, we study the dynamics due to impurities in one-dimensional lattice systems using the numerical time-evolving block decimation method and analytic calculations. We consider both noninteracting and interacting fermions as the bath, in particular fermions in a singlet superfluid state due to attractive on-site interactions, and baths with a periodic or nearly periodic structure due to nearest-neighbor repulsion. Previous theoretical and experimental research mainly considers homogeneous baths with contact interactions. We find novel phenomena when the bath is probed with energies above its characteristic energyscale. In publication I, a driven perturbation with velocity above the speed of sound of the interacting fermions retains the ground-state power-law decay of singlet superfluid correlations. In publication III, we study the decoherence of an impurity in terms of the purity of its density matrix. The impurity and the bath fermions have different masses, and we find the fastest decoherence for a light impurity in a heavy bath, whereas the fastest dissipation of energy occurs for equal masses. In publications II and IV, we consider a bath of fermions with repulsive nearest-neighbor interactions. In a half-filled lattice, the bath is in the Mott insulator state with a particle every two sites. A filling above one half leads to solitons seen as domain walls in the arrangement of the particles. We find that within a resonance region of interactions, the impurity can create an additional soliton-antisoliton pair in the bath. These two excitations have very different dynamics: The antisoliton can form a bound state with the impurity while the soliton excitation propagates. When the ground state of the bath contains solitons, the antisoliton excitation is confined close to its origin. These phenomena are explained by energy conservation, since processes with an energy change larger than the bandwidth are suppressed. Recent developments in experiments with ultracold gases in optical lattices offer possibilities for testing the theoretical predictions of this work. Long-range interactions in lattice models have been observed in experiments with magnetic atoms and dipolar molecules. Furthermore, single-site addressing techniques allow to create localized impurities and track their motion, and to measure the purity of many-body states.

AB - An impurity coupled to a bath is a paradigmatic problem of many-body physics and relevant for various systems. In this work, we study the dynamics due to impurities in one-dimensional lattice systems using the numerical time-evolving block decimation method and analytic calculations. We consider both noninteracting and interacting fermions as the bath, in particular fermions in a singlet superfluid state due to attractive on-site interactions, and baths with a periodic or nearly periodic structure due to nearest-neighbor repulsion. Previous theoretical and experimental research mainly considers homogeneous baths with contact interactions. We find novel phenomena when the bath is probed with energies above its characteristic energyscale. In publication I, a driven perturbation with velocity above the speed of sound of the interacting fermions retains the ground-state power-law decay of singlet superfluid correlations. In publication III, we study the decoherence of an impurity in terms of the purity of its density matrix. The impurity and the bath fermions have different masses, and we find the fastest decoherence for a light impurity in a heavy bath, whereas the fastest dissipation of energy occurs for equal masses. In publications II and IV, we consider a bath of fermions with repulsive nearest-neighbor interactions. In a half-filled lattice, the bath is in the Mott insulator state with a particle every two sites. A filling above one half leads to solitons seen as domain walls in the arrangement of the particles. We find that within a resonance region of interactions, the impurity can create an additional soliton-antisoliton pair in the bath. These two excitations have very different dynamics: The antisoliton can form a bound state with the impurity while the soliton excitation propagates. When the ground state of the bath contains solitons, the antisoliton excitation is confined close to its origin. These phenomena are explained by energy conservation, since processes with an energy change larger than the bandwidth are suppressed. Recent developments in experiments with ultracold gases in optical lattices offer possibilities for testing the theoretical predictions of this work. Long-range interactions in lattice models have been observed in experiments with magnetic atoms and dipolar molecules. Furthermore, single-site addressing techniques allow to create localized impurities and track their motion, and to measure the purity of many-body states.

KW - impurity dynamics

KW - domain walls

KW - time-evolving block decimation

KW - extended Hubbard model

KW - decoherence

KW - superfluid correlations

KW - monen kappaleen kvanttifysiikka

KW - laajennettu Hubbardin malli

KW - dekoherenssi

KW - supranestekorrelaatiot

KW - impurity dynamics

KW - domain walls

KW - time-evolving block decimation

KW - extended Hubbard model

KW - decoherence

KW - superfluid correlations

M3 - Doctoral Thesis

SN - 978-952-60-7369-9

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Impurity dynamics and nearest-neighbor interactions in one-dimensional lattices

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Tutkimusalat

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