9 research outputs found
Quantum Knots and Monopoles
No full textBose–Einstein condensation is a quantum statistical phase transition that occurs in a system consisting of bosons when a single-particle quantum state becomes macroscopically occupied. This peculiar state of matter was first predicted in 1925 and finally realized seventy years later in vapours of weakly-interacting alkali-metal atoms. Since then, Bose–Einstein condensates have been one of the most fascinating research fields in modern physics.
The gaseous condensates offer a robust platform to accurately study interacting many-particle systems from the first principles. Experimentally, the possibility to precisely control a condensate with external fields and directly image its order parameter provides unforeseen opportunities to obtain deep insight into phenomena across different subfields of physics. In particular, gaseous condensates can emulate complicated models that arise in atomic, condensed-matter, and even particle physics, allowing realizations of exotic phenomena that are elusive in their original contexts. An outstanding example is the existence of various topological defects in ultacold quantum gases with internal degrees of freedom.
In this thesis, we investigate the creation, stability, and dynamical properties of various topological defects in spinor Bose–Einstein condensates. The majority of the theoretical results is obtained by numerically solving the dynamics using Gross–Pitaevskii equations for spin-1 condensates. Many theoretical predictions are confirmed by the very good agreement with experiments.
The first experimental observations of a topological point defect in an order parameter describing the quantum gas are presented. Such a point defect is reminiscent to the magnetic monopole particle appearing in grand unified theories. Therefore, the discovery of monopoles in quantum gases further encourages the quest for finding magnetic monopoles in natural electromagnetic fields, a search largely initiated by Paul Dirac almost a century ago.
Subsequently, the fine structure and decay dynamics of the point defect are studied numerically and verified in experiments. The created monopole is gradually destroyed during the polar-to-ferromagnetic quantum phase transition, which results in the spontaneous emergence of a Dirac monopole in synthetic magnetic field. In addition to the singular point defect, the first experimental realization of a knot soliton in the context of quantum field is reported. This thesis lays the foundation for studies of the dynamics and stability of three-dimensional topological structures in quantum systems
Correcting non independent and non identically distributed errors with surface codes
No full textA common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single qubit errors. However, the available experimental data shows that realistic errors in modern multi qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non uniform single qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface code error correctio
Experimental Realization of a Dirac Monopole through the Decay of an Isolated Monopole
No full textWe experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.peerReviewe
Decay of an isolated monopole into a Dirac monopole configuration
No full textWe study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field. We observe quantitatively matching decay dynamics for both ferromagnetic and antiferromagnetic spin-spin interactions.Peer reviewe
Towards Spin-Multiphoton Entanglement using Quantum Dots with Asymmetric Waveguide Coupling
No full textWe demonstrate selectively enhanced dipoles of an InAs quantum dot embedded in a nanophotonic waveguide, thereby forming optical cycling transitions, a basic tool for scalable spin-multiphoton entanglement generation. (C) 2020 The Author(s)</p
Domain Wall Color Code
No full textWe introduce the domain wall color code, a new variant of the quantum error correcting color code that exhibits exceptionally high code capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a two dimensional color code decouples into a series of repetition codes, resulting in an error correcting threshold of 50 . Interestingly, at finite bias, our color code demonstrates thresholds identical to those of the noise tailored XZZX surface code for all single qubit Pauli noise channels. The design principle of the code is that it introduces domain walls which permute the code s excitations upon domain crossing. For practical implementation, we supplement the domain wall code with a scalable restriction decoder based on a matching algorithm. The proposed code is identified as a comparably resource efficient quantum error correcting code highly suitable for realistic nois
Magneettisen monopolin analogiat ja topologiset rakenteet kaasumaisissa Bosen–Einsteinin kondensaateissa
No full textSince their experimental discovery in 1995, dilute Bose–Einstein condensates have proven to be excellent platforms for studying interacting many-body quantum systems. The gaseous condensates can be conveniently controlled in space and time with lasers and magnetic fields. Theoretically, these low-temperature systems can be described starting from first principles, and their dynamics is accurately captured by the mean-field approach. Dilute condensates with internal spin degrees of freedom may host various topological defects including vortices, monopoles, and skyrmions. Precise external control fields can be used to engineer and study these topological states.
In this thesis, we investigate the creation, stability, and dynamics of various topological defects in spinor Bose–Einstein condensates. A combination of numerical and analytical methods is used and a part of the research is carried out in collaboration with an experimental research group. The majority of the research involves numerically solving the mean-field Gross–Pitaevskii equation for a spin-1 condensate. The computations are accelerated with graphics processing units.
We find that the ground state of a ferromagnetic spin-1 condensate supports a Dirac monopole in its synthetic magnetic field in the presence of a quadrupole magnetic field. The energetics of various stationary states of spin-orbit coupled condensates are analyzed and a robust method to observe these exotic states in experiments is proposed. The creation of topological skyrmions is simulated and a very good quantitative agreement with a recent experiment is obtained. Importantly, the first experimental observations of both, Dirac monopoles and topological point defects in a system governed by a quantum field are presented. Subsequently, the decay dynamics of the point defect is studied, revealing the decay into a ferromagnetic state supporting the Dirac monopole.
The impact of the research conducted in this thesis is not limited to gaseous Bose–Einstein condensates, but due to the universality of quantum mechanics and topological defects, our work provides knowledge, ideas, and inspiration across research fields.Bosen–Einsteinin kondensaatit, jotka muodostuvat heikosti vuorovaikuttavista alkalimetalliatomeista, ovat osoittautuneet erinomaisiksi työkaluiksi monen hiukkasen kvanttisysteemien tutkimuksessa. Näiden kylmien kvanttikaasujen mallintaminen on mahdollista perusteorioihin nojaten ja yksinkertainen keskeiskenttäteoria kuvaa tarkasti niiden dynamiikkaa. Lisäksi kondensaattien paikka- ja aikariippuvuutta voidaan säädellä ulkoisten laser- ja magneettikenttien avulla. Kondensaatit tarjoavatkin mahdollisuuden mallintaa ilmiöitä, joiden tutkiminen niiden alkuperäisessä kontekstissa on osoittautunut hankalaksi. Niinkutsutuissa spinorikondensaateissa sisäiset spinvapausasteet mahdollistavat monien topologisten eksitaatioiden kuten vorteksien, skyrmionien ja monopolien olemassaolon sekä niiden kontrolloidun luomisen ja tutkimisen.
Tässä väitöskirjassa tutkitaan erilaisten topologisten defektien luomista, stabiillisuutta ja dynamiikkaa laskennallisin ja analyyttisin menetelmin. Osa tutkimuksesta on toteutettu yhteisyössä kokeellisen tutkimusryhmän kanssa. Tutkimus perustuu suurelta osin Grossin–Pitaevskiin yhtälön numeeriseen ratkaisemiseen spin-1 kondensaatin tapauksessa. Laskentaa on nopeutettu näytönohjaimilla.
Työssä tutkitaan numeerisesti ferromagneettista spin-1 kondensaattia kvadrupolimagneettikentässä. Perustilassa kondensaatin havaitaan sisältävän Diracin monopolin spinvapausasteen aikaansaamassa synteettisessä magneettikentässä. Lisäksi analysoidaan Spin–orbit-kytkettyjen kondensaattien eksoottisten stationaaritilojen energetiikkaa ja ehdotetaan menetelmää näiden tilojen kokeelliseksi havaitsemiseksi. Työn numeeriset simulaatiot skyrmionieksitaatioiden luomisesta tuottavat erittäin hyvän kvantitatiivisen vastaavuuden koehavaintojen kanssa. Erityisesti tässä väitöskirjassa esitetään ensimmäiset kokeelliset havainnot sekä Diracin monopolista että pistemäisestä topologisesta defektistä systeemissä, jota kuvaa kvanttikenttä. Lopuksi tutkitaan luodun pistedefektin dynamiikkaa ja polaarisen faasin pistedefektin havaitaan hajoavan ferromagneettisen faasin Diracin monopoliksi.
Tässä väitöskirjassa esitetyt tulokset ja niiden vaikutukset eivät rajoitu vain harvoihin Bose-kaasuihin, vaan kvanttimekaniikan ja topologisten defektien universaalisuuden johdosta tutkimuksemme tuottaa tietoa, ideoita ja inspiraatioita useille fysiikan aloille
Topologisten rakenteiden luonti ja dynamiikka Bosen–Einsteinin kondensaateissa
No full textTopology provides deep conceptual links between the various branches of physics. Bose–Einstein condensates with spin degrees of freedom are among the most accessible quantum systems available for studying topological structures. A wide range of topological defects and textures available in condensates, such as vortices, monopoles, knots, and skyrmions, are analogous to those predicted in electromagnetism, high-energy physics, and cosmology.
In this dissertation, we numerically and experimentally investigate novel creation methods for topological structures and study their dynamical properties. Specifically, we experimentally observe the evolution of an isolated monopole into a Dirac monopole in the presence of a quadrupole magnetic field. The Dirac monopole appears in the synthetic magnetic field of the condensate and is accompanied by spontaneously emerging nodal lines. We observe the decay of a quantum knot into a polar-core spin vortex in the presence of a uniform magnetic field. Furthermore, we observe that a decaying coreless-vortex state gives rise to a pair of singular SO(3) vortices.
Many of the studied creation methods for topological structures in the condensate rely on adiabatic control of the external magnetic field. The counterdiabatic protocol offers a way to speed up the otherwise slow magnetic field driving required for adiabatic dynamics with a correcting magnetic field. Using this method, we numerically implement a scheme for fast vortex pumping which leads to the vortex with highest angular momentum reported to date in Bose–Einstein condensates with experimentally feasible methods. We further use the counterdiabatic protocol in a novel way to create quantum knots in the condensate.
Another focal point of this dissertation is the study on different types of skyrmions in spinor condensates. Our simulations of two-dimensional skyrmions are in a quantitative agreement with an experiment carried out elsewhere, explaining the experimentally observed instabilities. We numerically analyze the exotic spin-2 skyrmions available in the cyclic and biaxial nematic phases. Importantly, we present the first experimental observations of Shankar skyrmions in spin-1 condensates and analyze their synthetic electromagnetic properties.
This dissertation addresses an extensive amount of topological structures available in the condensate, but many different structures await future studies. In addition, the precise computational characterization of the elementary excitations of monopoles, knots, and skyrmions is of great interest. The results of this dissertation form a sturdy basis for future experimental studies on the dynamics of topological structures in spinor condensates.Topologia tarjoaa syvällisiä käsitteellisiä yhteyksiä fysiikan eri haarojen välillä. Bosen–Einsteinin kondensaatit spin-vapausasteilla ovat yksiä monipuolisimmista systeemeistä topologisten rakenteiden tutkimukseen. Laaja kirjo kondensaatissa esiintyviä topologisia rakenteita, kuten kvanttipyörteet, monopolit, solmut ja skyrmionit, ovat analogisia sähkömagnetismissa, korkean energian fysiikassa ja kosmologiassa ennustettujen rakenteiden kanssa.
Tässä väitöskirjassa tutkitaan uudenlaisia topologisten rakenteiden luomismenetelmiä sekä näiden rakenteiden dynamiikkaa laskennallisin ja kokeellisin työkaluin. Työssä näytetään kokeellisesti, kuinka eristetty monopoli kehittyy Diracin monopoliksi kvadrupolimagneettikentän läsnäollessa. Diracin monopoli ilmenee kondensaatin synteettisessä magneettikentässä ja siihen on linkittynyt spontaanisti syntyneitä nodaalilinjoja. Kvanttisolmun havaitaan hajoavan polaariytimiseksi spinpyörteeksi vakiomagneettikentässä. Lisäksi työssä havaitaan kuinka ytimettömän pyörretilan hajoaminen aiheuttaa kahden singulaarisen SO(3)-pyörteen syntymisen.
Monet tutkituista topologisten rakenteiden luomismenetelmistä nojautuvat ulkoisen magneettikentän adiabaattiseen hallintaan. Vasta-adiabaattinen menetelmä tarjoaa keinon nopeuttaa tätä muutoin hidasta magneettikentän hallintaa korjaavan magneettikentän avulla. Menetelmää sovelletaan kvanttipyörteiden nopeaan pumppaukseen, johtaen korkeimman pyörimismäärän kvanttipyörteeseen, joka kondensaattiin on onnistuttu luomaan käyttämällä kokeellisesti käyttökelpoisia menetelmiä. Lisäksi näytämme kuinka kondensaattiin voidaan luoda vasta-adiabaattisella menetelmällä kvanttisolmuja.
Työn eräänä päätutkimuskohteena on erilaisten skyrmionien ominaisuuksien tutkimus. Kaksiulotteisten skyrmionien simulaatiot vastaavat kvantitatiivisesti toisaalla suoritettuja kokeita ja ne selittävät kokeellisesti havaitun skyrmionin epästabiilisuuden. Eksoottisia spin-2 skyrmioneja analysoidaan laskennallisesti syklisessä ja biaksiaalisessa nemaattisessa faasissa. Erityisesti työssä esitellään Shankarin skyrmionin ensimmäinen kokeellinen havainto spin-1 kondensaateissa ja analysoidaan sen synteettisiä sähkömagneettisia ominaisuuksia.
Tämän väitöskirjan tutkimus kattaa mittavan määrän topologisia rakenteita, mutta kondensaatit tarjoavat edelleen monia muita rakenteita jatkotutkimuksille. Monopoleihin, solmuihin ja skyrmioneihin liittyvien eksitaatioiden tarkka laskennallinen karakterisointi on myös kiinnostava jatkotutkimuksen kohde. Tämän väitöskirjan tulokset luovat vankan perustan topologisten rakenteiden dynamiikan kokeelliselle tutkimukselle spinorikondensaateissa
