DOCSLIB.ORG

Interaction of Quantum Vortex Beams with Matter

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Interaction of Quantum Vortex Beams with Matter Interaction of Quantum Vortex Beams with Matter by Maria Solyanik-Gorgone B.S. in Physics, May 2009, Karazin Kharkiv National University, Kharkiv, Ukraine M.S. in Theoretical Physics, May 2010, Karazin Kharkiv National University, Kharkiv, Ukraine A Dissertation submitted to The Faculty of The Columbian College of Arts and Sciences of The George Washington University in partial satisfaction of the requirements for the degree of Doctor of Philosophy August 31, 2019 Dissertation directed by Andrei Afanasev Associate Professor of Physics The Columbian College of Arts and Sciences of The George Washington University certifies that Maria Solyanik-Gorgone has passed the Final Examination for the degree of Doctor of Philosophy as of May 10, 2019. This is the final and approved form of the dissertation. Interaction of Quantum Vortex Beams with Matter Maria Solyanik-Gorgone Dissertation Research Committee: Andrei Afanasev, Associate Professor of Physics, Dissertation Director Helmut Haberzettl, Professor of Physics, Committee Member Alexander van der Horst, Assistant Professor of Physics, Committee Member ii c Copyright 2019 by Maria Solyanik-Gorgone All rights reserved iii Dedication To my beloved parents for believing in me unconditionally and loving me selflessly. iv Acknowledgments I would like to express my deepest appreciation and gratitude to my research advisor, Professor Andrei Afanasev, for sharing his diverse expertise, for his continuous support of my research, patience and encouragement. This work would not be possible without his guidance. I especially thank my collaborators: Professor C. E. Carlson, Professor C. T. Schmiegelow, Professor F. Schmidt-Kaler and Professor V. G. Serbo for a supportive and friendly environ- ment, productive work, stimulating discussions, insightful comments and hard questions throughout the whole time of us working together on projects. I would also like to ac- knowledge the contribution of Professor C. W. Clark on the early stages of my project. His discussions and lectures during my summer internship in 2016 provided the necessary foundation for future theoretical work in Atomic Physics and Spectroscopy. The experience and skills I obtained while working with this group of scientists is unique and irreplaceable in my future endeavors. My sincere thanks go to my readers, Professor H. Haberzettl and Professor A. van der Horst for the valuable comments, insightful questions and kind corrections. I would like to express my deepest gratitude to the department professors and staff for supporting friendly, nurturing but also stimulating and challenging environment for students to develop, mature as specialists and form their scientific identity. Also, I am grateful for financial support that has come from the department funds towards completion of my project. Special thanks go to my graduate student mentor, Professor E. J. Downie. Her great example as a scientist, teacher and leader helped me grow into who I am today and, I am sure, will continue inspiring me in the future. Very special words of thanks go to my dear husband, life mentor and friend, Nicholas M. Gorgone, for his kind support and advice. Thank you for sheltering me when it is tough and sharing happiness in the moments of delight. v Abstract Interaction of Quantum Vortex Beams with Matter The excitations in atomic, nuclear and semiconductor structures with orbital angular momentum carrying photons are analyzed. The violations of the conventional set of an- gular momentum selection rules are derived and discussed in detail for all three types of structures. In the case of atoms and ions, fine and hyperfine coupling are accounted for by means of the multipole expansion of partial transition amplitudes. The theory is devel- oped for arbitrary beam polarization, alignment of the beam’s optical axis with respect to the target’s quantization axis, and transition multipolarity. The approach is extrapolated to semiconductor structures using the Luttinger formalism. Spin polarization anomalies for electrons photo-excited by twisted light in G-point in zinc-blende GaAs are revealed. Unusual sensitivity to the twisted beam polarization content, and radial and axial positioning of the target in the beam profile, are identified and studied in detail. The phenomenon of circular dichroism due to twisted beam topology during propagation in isotropic matter is predicted and analyzed. Three families of modes are considered and analyzed: Bessel, Bessel-Gauss and Laguerre-Gauss. The results are applicable in a wide range of studies: spectroscopy, metrology, quantum computing and communications, cybersecurity and more. vi Statement of Originality Herein I certify that the content of this thesis is my own work with the exceptions, listed below. Any resemblance to the results elsewhere, that are not mentioned in this statement and/or throughout this thesis, is accidental. Chapter 1: The overview of the general trends and fundamental breakthroughs in Singular Optics and Photonics, that paved the foundation for modern study of twisted light and matter beams is provided. Chapter 2: The overview of the necessary concepts in Laser Optics and Photonics, and systematic description of the Quantum Mechanical formalism for twisted mode quantization, established in the field, is provided. Chapter 3: Professor C. E. Carlson made a substantial integrated contribution in developing the theoretical model for the data in Section 3.5. The data in Chapter 3 is the product of work done by Professor C. T. Schmiegelow, as a part of an experimental collaboration under the supervision of Professor F. Schmidt-Kaler. Chapter 4: The theoretical analysis and main predictions were done by Professor A. Afanasev and Professor C. E. Carlson for the spin-less case. Chapter 5: The formalism and analysis for mesoscopic proton targets for the np-capture discussed here was done by Professor A. Afanasev and Professor V. G. Serbo. Chapter 6: The atomic-like approximation in the eqn. (6.13) was done by Professor A. Afanasev. In the process of the completion of this work, many Mathematica code prototypes with key ideas and plots were shared with me by Professor A. Afanasev before the corresponding theoretical background was developed. vii Table of Contents Dedication ............................. iv Acknowledgments ..........................v Abstract .............................. vi Statement of Originality........................ vii List of Figures ............................ ix List of Tables ............................x List of Abbreviations ......................... xi List of Symbols ........................... xii Chapter 1: Introduction........................1 1.1 History.......................2 1.2 Thesis Outline....................6 Chapter 2: OAM Photon States.....................9 2.1 Review of Necessary Fundamentals in Optics........9 2.2 Vortex Beams.................... 13 2.2.1 Orbital Angular Momentum and Spin of Light....... 16 2.3 Orbital Angular Momentum Modes............ 17 2.3.1 Bessel Beams.................... 18 2.3.2 Bessel-Gauss Beams.................. 23 2.3.3 Laguerre-Gauss Beams................. 24 2.4 Orbital Angular Momentum Beams and Polarization States.. 26 viii Chapter 3: Quantum Mechanical Transition Matrix for Twisted Light - Atom Inter- actions.......................... 29 3.1 Plane-wave Transition Amplitude............. 30 3.2 Photo-Excitation by Twisted Beams in Total Angular Momen- tum Basis...................... 32 3.3 Twisted Photo-Excitation in Atoms: Hyperfine Structure... 35 3.4 Photo-Excitation with Twisted Light in Cooled Trapped Ions.. 37 3.4.1 40Ca Ion in Parallel Configuration Irradiated by Circularly Po- larized Light..................... 37 3.4.2 40Ca Ion in 45◦-Configuration and More.......... 46 3.4.3 Ion photo-excitations in Radially and Azimuthally Polarized Orbital Angular Momentum Beams............ 56 3.5 Recoil from Orbital Angular Momentum Photons in Trapped Ions........................ 58 Chapter 4: Chirality, Chirooptics and Circular Dichroism in Orbital Angular Mo- mentum Photon-Matter Interactions............... 62 4.1 Chirality in Light................... 62 4.2 Optical Activity and Twisted Photon Beams........ 66 Chapter 5: Electromagnetic Interactions and Neutron-Proton Systems...... 68 5.1 Deuteron Photodisintegration and np-Capture with Orbital An- gular Momentum Beam States.............. 69 Chapter 6: Photo-Induced Processes in Semiconductor Materials and Quantum Dots........................... 75 6.1 Twisted Photon Interaction with Bulk GaAs........ 76 6.2 Twisted Photon Interaction with Semiconductor Quantum Dots. 86 Chapter 7: Conclusions........................ 91 Bibliography............................. 94 ix Chapter A: List of Useful Formulas.................... 105 Chapter B: Spherical Wave Decomposition of Twisted Modes......... 108 x List of Figures Figure 2.1. The generic phase profile of the OAM-carrying beam with a screw-like dislocation at the beam center, propagating in the z-direction. ····· 14 Figure 2.2. LG (rows 1 and 2), Bessel (row 3) and BG (row 4) modes’ intensity profiles for different values of OAM `g , p nodal number, and TAM mg . All the axes are in arbitrary units and the columns correspond to topological charge `g for LG, and TAM quantum number mg for BB and BG. ·························· 19 Figure 2.3. Schematic picture of the twisted beam geometry from the prospective of the local observer P’ versus the coordinate system P attached to the beam axis. The red arrow specifies the overall direction of the
Load more

Recommended publications
  • Φ0-Magnetic Force Microscopy for Imaging and Control of Vortex
    Imaging and controlling vortex dynamics in mesoscopic superconductor-normal-metal-superconductor arrays Tyler R. Naibert1, Hryhoriy Polshyn1,2,*, Rita Garrido-Menacho1, Malcolm Durkin1, Brian Wolin1, Victor Chua1, Ian Mondragon-Shem1, Taylor Hughes1, Nadya Mason1,*, and Raffi Budakian1,3 1Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801-3080, USA 2Department of Physics, University of California, Santa Barbara, CA 93106, USA 3Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L3G1 Department of Physics, University of Waterloo, Waterloo, ON, Canada, N2L3G1 Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L2Y5 Canadian Institute for Advanced Research, Toronto, ON, Canada, M5G1Z8 *Corresponding authors. Email: [email protected]; [email protected] Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, we obtain a variety of striking spatial patterns that encode information about the energy landscape for vortices in the system. We interpret these patterns in terms of local vortex dynamics and extract the relative strengths of the characteristic energy scales in the system, such as the vortex-magnetic field and vortex-vortex interaction strengths, as well as the vortex chemical potential.
    [Show full text]
  • Scanning Hall Probe Microscopy of Vortex Matter in Single-And Two-Gap Superconductors
    ARENBERG DOCTORAL SCHOOL Faculty of Science Scanning Hall probe microscopy of vortex matter in single-and two-gap superconductors - Bart Raes Promotors: Dissertation presented in partial Prof.Dr. Victor V. Moshchalkov fulfillment of the requirements for the Prof.Dr. Jacques Tempère PhD degree July 2013 Scanning Hall probe microscopy of vortex matter in single-and two-gap superconductors Bart RAES Dissertation presented in partial fulfillment of the requirements for the PhD degree Members of the Examination committee: Prof. Dr. Victor V. Moshchalkov KU Leuven (Promotor) Prof. Dr. Jacques Tempère Universiteit Antwerpen (Co-promotor) Prof. Dr. J. Van de Vondel KU Leuven (Secretary) Prof. Dr. L. Chibotaru KU Leuven (President) Prof. Dr. J. Vanacken KU Leuven Dr. J. Gutierrez Royo KU Leuven Prof. Dr. A.V. Silhanek Université de Liège Prof. Dr. S. Bending University of Bath Prof. Dr. G. Borghs KU Leuven, IMEC July 2013 © 2013 KU Leuven, Groep Wetenschap & Technologie, Arenberg Doctoraatsschool, W. de Croylaan 6, 3001 Leuven, België Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm, elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without written permission from the publisher. ISBN 978-90-8649-638-9 D/2013/10.705/53 Dankwoord-Acknowledgements Doctoreren is niet alleen het resultaat van bijna vier jaar wetenschappelijk onderzoek, het is een lange weg met veel hindernissen maar zeker ook enkele hoogtepunten.
    [Show full text]
  • LESSONS from TOPOLOGICAL SUPERFLUIDS: SAFE and DANGEROUS ROUTES to ANTISPACETIME 1 1 1,2 Llv.B
    FEATURES LESSONS FROM TOPOLOGICAL SUPERFLUIDS: SAFE AND DANGEROUS ROUTES TO ANTISPACETIME 1 1 1,2 l V.B. Eltsov , J. Nissinen and G.E. Volovik – DOI: https://doi.org/10.1051/epn/2019504 l 1 Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland l 2 Landau Institute for Theoretical Physics, acad. Semyonov av., 1a, 142432, Chernogolovka, Russia All realistic second order phase transitions are undergone at finite transition rate and are therefore non-adiabatic. In symmetry-breaking phase transitions the non-adiabatic processes, as predicted by Kibble and Zurek [1, 2], lead to the formation of topological defects (the so-called Kibble-Zurek mechanism). The exact nature of the resulting defects depends on the detailed symmetry-breaking pattern. or example, our universe – the largest condensed topological and nontopological objects (skyrmions and matter system known to us – has undergone Q-balls), etc. several symmetry-breaking phase transitions The model predictions can be tested in particle accel- Fafter the Big Bang. As a consequence, a variety erators (now probing energy densities >10-12s after the of topological defects might have formed during the early Big Bang) and in cosmological observations (which have evolution of the Universe. Depending on the Grand Uni- not yet identified such defects to date). The same physics, fied Theory model, a number of diffierent cosmic -topo however, can be probed in symmetry breaking transitions logical defects have been predicted to exist. Among them in condensed matter systems — in fermionic superfluid are point defects, such as the 't Hooft-Polyakov magnetic 3He to an astonishing degree of similarity.
    [Show full text]
  • Twist Effects on Quantum Vortex Defects
    Journal of Physics: Conference Series PAPER • OPEN ACCESS Twist effects on quantum vortex defects To cite this article: M Foresti 2021 J. Phys.: Conf. Ser. 1730 012016 View the article online for updates and enhancements. This content was downloaded from IP address 170.106.40.40 on 26/09/2021 at 14:31 IC-MSQUARE 2020 IOP Publishing Journal of Physics: Conference Series 1730 (2021) 012016 doi:10.1088/1742-6596/1730/1/012016 Twist effects on quantum vortex defects M Foresti Department of Mathematics & Applications, University of Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy E-mail: [email protected] Abstract. We demonstrate that on a quantum vortex in Bose-Einstein condensates can form a new, central phase singularity. We define the twist phase for isophase surfaces and show that if the injection of a twist phase is global this phenomenon is given by an analog of the Aharonov- Bohm effect. We show analytically that the injection of a twist phase makes the filament unstable, that is the GP equation is modified by a new term that makes the Hamiltonian non-Hermitian. Using Kleinert's theory for multi-valued fields we show that this instability is compensated by the creation of the second vortex, possibly linked with the first one. 1. Introduction A Bose-Einstein condensate (BEC) is a diluted gas of bosons at very low temperature (see [1] and [2]) described by a unique scalar, complex-valued field = (x; t) called order parameter, that depends on position x and time t. The equation that describes the dynamics of a BEC is the Gross-Pitaevskii equation (GPE) written here in a non-dimensional [3]: i i @ = r2 + 1 − j j2 : (1) t 2 2 This is a type of non-linear Scrh¨odingerequation in three-dimensional space.
    [Show full text]
  • Generation and Detection of Continuous Variable Quantum Vortex States Via Compact Photonic Devices
    hv photonics Article Generation and Detection of Continuous Variable Quantum Vortex States via Compact Photonic Devices David Barral *, Daniel Balado and Jesús Liñares Optics Area, Department of Applied Physics, Faculty of Physics and Faculty of Optics and Optometry, University of Santiago de Compostela, Campus Vida s/n (Campus Universitario Sur), Santiago de Compostela, Galicia E-15782, Spain; [email protected] (D.B.); [email protected] (J.L.) * Correspondence: [email protected]; Tel.: +34-881-811-000 Received: 10 October 2016; Accepted: 29 December 2016; Published: 3 January 2017 Abstract: A quantum photonic circuit with the ability to produce continuous variable quantum vortex states is proposed. This device produces two single-mode squeezed states which go through a Mach-Zehnder interferometer where photons are subtracted by means of weakly coupled directional couplers towards ancillary waveguides. The detection of a number of photons in these modes heralds the production of a quantum vortex. Likewise, a measurement system of the order and handedness of quantum vortices is introduced and the performance of both devices is analyzed in a realistic scenario by means of the Wigner function. These devices open the possibility of using the quantum vortices as carriers of quantum information. Keywords: quantum information processing; continuous variables; integrated optics 1. Introduction In recent years, there has been an increasing interest in the processing of quantum information (QIP) with continuous variables (CV-QIP) [1]. CV-QIP protocols are based on Gaussian states as resources of entanglement. However, the use of non-Gaussian states has been shown to be essential in certain quantum protocols, like the entanglement distillation [2–5].
    [Show full text]
  • A Vortex Formulation of Quantum Physics Setting Discrete Quantum States Into Continuous Space-Time
    Fred Y. Ye, IJNSR, 2017; 1:4 Research Article IJNSR (2017) 1:4 International Journal of Natural Science and Reviews (ISSN:2576-5086) A Vortex Formulation of Quantum Physics Setting Discrete Quantum States into Continuous Space-time Fred Y. Ye 1, 2* 1 School of Information Management, Nanjing University, Nanjing 210023, CHINA 2International Joint Informatics Laboratory (IJIL), UI-NU, Champaign-Nanjing ABSTRACT Any quantum state can be described by a vortex, which is math- *Correspondence to Author: ematically a multi-vector and physically a united-measure. Fred Y. Ye When the vortex formulation of quantum physics is introduced, School of Information Management, Hamil-ton principle keeps its core position in physical analysis. Nanjing University, Nanjing 210023, While the global characteristics are described by Lagranrian CHINA; International Joint Informat- function for dynamics and double complex core function for ics Laboratory (IJIL), UI-NU, Cham- stable states, Schrödinger equation and gauge symmetries paign-Nanjing reveal local char-acteristics. The vortex-based physics provides a new unified understanding of wave-particle duality and uncertainty, quantum entanglement and teleportation, as How to cite this article: well as quantum information and computation, with setting Fred Y. Ye. A Vortex Formulation of discrete quantum states into con-tinuous space-time for Quantum Physics Setting Discrete keeping concordance of methodology in processing micro- Quantum States into Continuous particle and macro-galaxy. Two fundamental experiments are Space-time. International Journal suggested to correct and verify the physical for-mulation. of Natural Science and Reviews, 2017; 1:4. Keywords: Vortex; vortex formulation; quantum mechanism; quantum state; quantum physics; space-time eSciPub LLC, Houston, TX USA.
    [Show full text]
  • Physics of Superfluid Helium-4 Vortex Tangles in Normal-Fluid Strain Fields
    Physics of superfluid helium-4 vortex tangles in normal-fluid strain fields Demosthenes Kivotides1, Anthony Leonard2 1Strathclyde University, Glasgow, UK 2California Institute of Technology, Pasadena, CA, USA (Dated: March 5, 2021) Abstract By employing dimensional analysis, we scale the equations of the mesoscopic model of finite temperature superfluid hydrodynamics. Based on this scaling, we set up three problems, that depict the effects of kinematic, normal-fluid strain fields on superfluid vortex loops, and characterize small- scale processes in fully developed turbulence. We also develop a formula for the computation of energy spectra corresponding to superfluid vortex tangles in unbounded domains. Employing this formula, we compute energy spectra of superfluid vortex patterns induced by uniaxial, equibiaxial and simple-shear normal-fluid flows. By comparing the steady-state superfluid spectra and vortex structures, we conclude that normal-flow strain fields do not play important role in explaining the phenomenology of fully developed superfluid turbulence. This is in sharp contrast with the role of vortical normal-flow fields in offering plausible, structural explanations of superfluid vortex patterns and spectra entailed in numerical turbulent solutions of the mesoscopic model. 1 INTRODUCTION The advent of quantum theory posed the problem of quantizing fluid dynamics. The most obvious choice, i.e., quantizing the Navier-Stokes fluid, leads to unsurpassable mathematical difficulties with uncontrollable singularities [1]. This could be because Navier-Stokes is a statistical, dissipative field theory and, traditionally, quantum mechanics was successful operating on conservative classical field theories. Indeed, things become better with the quantization of (nonlinear) Schroedinger (NLS) type fluids, that can explain superfluidity via spontaneous breaking of the particle number symmetry which induces a ground state (superfluid) whose topological defects (superfluid vortices) interact with the fluctuations of the quantum field (normal fluid) [2–7].
    [Show full text]
  • Modeling Quantum Fluid Dynamics at Nonzero Temperatures
    Modeling quantum fluid dynamics at SPECIAL FEATURE nonzero temperatures Natalia G. Berloffa,b,1, Marc Brachetc, and Nick P. Proukakisd aDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom; bCambridge-Skoltech Quantum Fluids Laboratory, Skolkovo Institute of Science and Technology ul. Novaya, Skolkovo 143025, Russian Federation; cCentre National de la Recherche Scientifique, Laboratoire de Physique Statistique, Université Pierre-et-Marie-Curie Paris 06, Université Paris Diderot, Ecole Normale Supérieure, 75231 Paris Cedex 05, France; and dJoint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom Edited by Katepalli R. Sreenivasan, New York University, New York, NY, and approved December 13, 2013 (received for review July 15, 2013) The detailed understanding of the intricate dynamics of quantum similar [e.g., Kolmogorov spectrum (9–13)], features sensitive to fluids, in particular in the rapidly growing subfield of quantum the vortex core structure arising at lengthscales smaller than the turbulence which elucidates the evolution of a vortex tangle in average intervortex spacing [e.g., velocity statistics (20–22) and a superfluid, requires an in-depth understanding of the role of finite pressure (23)] show starkly different behavior––see, e.g., the temperature in such systems. The Landau two-fluid model is the most recent reviews (24, 25). In addition to liquid helium (2, 26), there successful hydrodynamical theory of superfluid helium, but by the has been some recent interest in the observation of turbulence in nature of the scale separations it cannot give an adequate descrip- smaller inhomogeneous confined weakly interacting gases (27, tion of the processes involving vortex dynamics and interactions.
    [Show full text]
  • A New Self-Consistent Approach of Quantum Turbulence in Superfluid
    A new self-consistent approach of quantum turbulence in superfluid helium Luca Galantucci, Andrew W. Baggaley, Carlo F. Barenghi Joint Quantum Centre Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK and Giorgio Krstulovic Universit´eC^oted'Azur, Observatoire de la C^oted'Azur, CNRS, Laboratoire Lagrange, Nice, France We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that de- scribes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is governed by a modified Navier-Stokes equa- tion. The superfluid vortex lines and normal fluid components are fully coupled in a self-consistent manner by the friction force, which induce local disturbances in the normal fluid in the vicinity of vortex lines. The main focus of this work is the numerical scheme for distributing the friction force to the mesh points where the normal fluid is defined and for evaluating the velocity of the normal fluid on the Lagrangian discretization points along the vortex lines. In particular, we show that if this numerical scheme is not careful enough, spurious results may occur. The new scheme which we propose to overcome these difficulties is based on physical principles. Finally, we apply the new method to the problem of the motion of a superfluid vortex ring in a stationary normal fluid and in a turbulent normal fluid. I. INTRODUCTION Quantum turbulence [1{3] is the disordered motion of quantum fluids - fluids which are governed by the laws of quantum mechanics rather than classical physics.
    [Show full text]
  • Half-Quantum Vortices in Superfluid Helium
    VIEWPOINT Half-Quantum Vortices in Superfluid Helium Researchers working with superfluid helium in a porous medium have generated vortices with half the quantum unit of fluid flow. by James A. Sauls∗ quantum vortex in a superfluid is a point-like hole around which the superfluid flows. This flow is quantized in the sense that the circulation—which is the sum of the velocity along a path around Athe vortex—takes on discrete values [1]. The quantum unit of circulation is h/m, where h is Planck’s constant and m is the mass of the superfluid particles. The first detection of quantized vortices with unit circulation were made in the 1960s with superfluid helium-4 and then later in su- perfluids of the lighter isotope helium-3 [2]. However, in the 1970s theorists predicted the existence of vortices with Figure 1: In superfluid helium-3, different types of quantum vortices can be observed. (Left) A ``normal'' vortex, or single half of a quantum unit of circulation in superfluid helium- quantum vortex, around which the circulation is equal to h/2m. 3 [3]. Since then, researchers have detected half-quantum This corresponds to a change of 2p in the quantum phase J. By vortices (HQVs) in diverse condensed-matter systems, from contrast, the phase a, related to the spin direction d~, remains fixed. Bose-Einstein condensates to spin-triplet superconductors (Right) A half quantum vortex has a circulation of h/4m. Both J thought to be electronic analogs of superfluid helium-3 [4]. and a change by p to give a total phase change of 2p.
    [Show full text]
  • Vortex Flux and Berry Phase in a Bose-Einstein Condensate Confined in a Toroidal Trap
    Vortex flux and Berry phase in a Bose-Einstein condensate confined in a toroidal trap Aranya B Bhattacherjee* INFM, Dipartimento di Fisica E.Fermi, Universita di Pisa, Via Buonarroti 2, I-56127, Pisa, Italy E-Mail: [email protected] Abstract: We study system of large number of singly quantized vortices in a BEC confined in a rotating toroidal geometry. Analogous to the Meissner effect in superconductors, we show that the external rotational field can be tuned to cancel the Magnus field, resulting in a zero vortex flux. We also show that the Berry’s phase for this system is directly related to the vortex flux. *Permanent Institute and address for correspondence: Department of Physics, Atma Ram Sanatan Dharma College, University of Delhi (South campus), Dhaula Kuan , New Delhi-110021, India. 1 Introduction Vortices in a superfluid formed due to rapid rotation tend to organize into a triangular lattice (also known as Abrikosov lattice) as a result of mutual repulsion. Such a lattice also has an associated rigidity. In the recent years, it has become possible to achieve such a vortex lattice state in a rapidly rotating Bose-Einstein condensate [1]. These new developments in experiments have opened a new direction for the theoretical study of quantum vortex matter, such as fractional quantum Hall like and melted vortex lattice states [2-7]. This new state of quantum vortex matter occurs only at very rapid rotations, where the system enters the “ mean field” quantum Hall regime, in which the condensation is only in lowest Landau level orbits. Eventually the vortex lattice melts, and the system enters a strongly correlated regime.
    [Show full text]
  • Phase Transition in a Chain of Quantum Vortices
    PHYSICAL REVIEW B VOLUME 59, NUMBER 2 1 JANUARY 1999-II Phase transition in a chain of quantum vortices C. Bruder* Institut fu¨r Theoretische Festko¨rperphysik, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany L. I. Glazman Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 and Delft University of Technology, 2600 GA Delft, The Netherlands A. I. Larkin Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 and L. D. Landau Institute for Theoretical Physics, Moscow 117940, Russia J. E. Mooij and A. van Oudenaarden Delft University of Technology, 2600 GA Delft, The Netherlands ~Received 8 September 1998! We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capaci- tance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array.
    [Show full text]