VORTICES in SUPERFLUIDS & SUPERCONDUCTORS. CIFAR Q MATERIALS SUMMER SCHOOL (May 14-16, 2012) LECTURE 2 VORTICES

Size: px
Start display at page:

Download "VORTICES in SUPERFLUIDS & SUPERCONDUCTORS. CIFAR Q MATERIALS SUMMER SCHOOL (May 14-16, 2012) LECTURE 2 VORTICES"

Transcription

1 VORTICES in SUPERFLUIDS & SUPERCONDUCTORS CIFAR Q MATERIALS SUMMER SCHOOL (May 14-16, 2012) LECTURE 2 VORTICES

2 Quantum Vortices in Superfluids Suppose we look at a vortex in a superfluid- ie., fluid circulating around a core. From what we know about atoms (ie., from de Broglie) this tells us we have probability waves circulating round the core with wavelength λ = h/p = h/mv where v is the velocity of the particles circulating around the core. But then, as noted by Onsager in 1950, as in atoms, only certain velocities are allowed, if we are to fit the waves around the core. Hence we find that the total circulation is quantized- we have quantized vortices. In this simple picture the core is like a string, in which the superfluid density goes to zero at the origin - the core has a finite diameter, because the singularity in the phase cannot persist in bulk superfluid. In He-4 this diameter is very small (only about 1 Angstrom!), but in other superfluids like He-3 it is much larger (~150 Angstroms), & so the core is itself very complex. The vortices themselves are quantum excitations- so they also have a probability density! They have fascinating properties, many of which were first discussed by Feynman in the early 1950 s, as fully quantum-mechanical objects. We now know that most of the flow properties of He superfluid are governed by the vortices in them, which can form very complex patterns. They can form closed vortex rings, which are also quantum objects, and which can tunnel and form state superpositions. The macroscopic properties of the A quantized vortex ring superfluid are typically determined by vast vortex tangles of intertwined vortex loops. L Onsager ( ) RP Feynman ( )

3 VORTICES: The EXPERIMENTAL PROBLEM In recent years experiments have been done on a variety of rotating systems, where the number of vortices can be controlled (in superconductors, the same is done using an external flux) SUPERFLUIDS: ions, or H atoms (the tools used to see the vortices) completely change their dynamics. SUPERCONDUCTORS: Vortices interact with each other (to form lattices), and also very strongly with defects (which pin them). This also completely changes their dynamics PROBLEM: how to do experiments on individual vortices without changing their dynamics COLD BEC GASES: No problem with defects or ions. But so far very hard to actually manipulate individual vortices.

4 OBSERVING SUPERFLUID VORTICES The first indirect observation of a quantum vortex was in 1956, in a famous experiment by Vinen a vortex attached to a vibrating wire altered its dynamics (see RIGHT). Later experiments imaged vortices in rotating cylinders by allowing electrons to attach to them (a hydrodynamic effect) and then sucking them off with an electric field. However the electrons form a large bubble around themselves in the superfluid, which has a very large hydrodynamic effective mass, and this radically alters the vortex dynamics. More recent imaging experiments attach H 2 molecules to the vortices, and the H trackers are then observed by tuning a laser to one of the H spectral lines

5 PROBING VORTEX DYNAMICS Vortex nucleation (He-4 & He-3) The tunneling rate & dynamics of vortex rings & other vortex configurations are influenced by the quasiparticles in interesting ways. PC Hendry et al., PRL 60, 604 (1988) Turbulence This is a much more complicated problem, since it can in principle involve very fast motions of the vortex lines, and it is intrinsically 3-dimensional and multi-vortex in nature. P Walmsley et al., PRL 99, (2007) P Walmsley, A Golov, PRL 100, (2008)

6 VORTICES IN ROTATING COLD GASES It is actually much easier to image vortices in cold gases without disturbing the vortex dynamics. Some remarkable experiments have looked not only at the dynamics and different phases of vortex lattices in these systems, but also at the nucleation and dynamics of single vortices in both 3d and even 2d BECs. Z Hadzibabic et al., Nature 441, 1118 (2006)

7 DESCRIPTION of a BOSE SUPERFLUID VORTEX For a stationary vortex we assume: Then, since we get quantized circulation: Velocity field falls off like classical vortex. Density profile depends on form of energy functional The vortex inertial mass is given in terms of the energy by: The vortex energy, obtained by integrating energy functional over entire volume, depends on sample shape (cf. method of images at right) Eg., for cylinder

8 VORTEX in the GRAVITATIONAL ANALOGY If we describe a vortex in the GR language, we get an interesting cosmic string situation: spacetime has to be cut, then repasted together, with a time jump across the cut. Time jump: where for string with angular momentum J Outside the vortex core, the metric is then flat: constant phase eikonal plot M Stone, Phys Rev B61, (2000) There is actually a lot more interesting physics to be gained from this analogy.the usual gravitational bending of light (ie., of phonons) doesn t happen here. Instead, phonons are deflected in the same sense, no matter which side of the vortex core they pass. One can also ask about the precession of a gyroscope attached to a phonon. We expect 2 contributions a de Sitter geodetic contribution, and a Lense-Thirring frame dragging contribution. Both should be present here; the AdS term comes from the acceleration of the phonon, and the ALT term from the interaction with the vortex angular momentum

9 2-FLUID PHENOMENOLOGY INCLUDING VORTICES STANDARD HVI PHENOMENOLOGY: add the Magnus force: + quasiparticle force: let This gives MUTUAL FRICTION: where These equations are phenomenological as we shall see they have been very controversial. If one accepts the general form they can be applied equally to both superfluids and superconductors (one simply has to find the coefficients in each case). REFS: GENERALIZED 2-FLUID EQUATIONS By balancing forces between the normal fluid quasiparticles, the superfluid, and the vortices (taken to have some coarse-grained distribution) we then get the following force equations:

10 VORTICES in SUPERFLUID 3 He The diversity of vortices in the various phases is so large that whole books have been written about them. Experiments use rotating cryostats, and the vortices can be observed in various ways (notably NMR). The core size is ~ 15 nm at T=0. A 2-fluid phenomenology can also be developed.

11 Some Examples (of a very complicated topic)

12 Quantum Vortices in Superconductors Superconductivity is a condensation of pairs of electrons, all into a single state. If we try to disturb this quantum state by applying an external magnetic field, the supercurrents in the system, flowing without resistance, simply adjust to block the field from entering the superconductor (the Meissner effect ). However, as shown by Abrikosov in1957, in some materials the field can get in via vortices, like those in superfluids- again, the circulating current is quantised. If we have a loop of superconducting material we can trap magnetic flux inside it- this is kept out of the superconductor by currents in it, as before. Again, the circulating current is quantised, and Magnetic Field through superconducting ring AA Abrikosov (1928- ) thus so is the flux- in units of a flux quantum h/e PCES 5.55 TOP: magnetic field lines around a superconductor MIDDLE: vortices penetrate BOTTOM: close-up of vortex in superconductor

13 OBSERVING SUPERCONDUCTING VORTICES The analogue of the Hess-Fairbank in a superconductor is the Meissner effect an equilibrium effect. One can also of course have metastable supercurrents set up this is the basis of superconducting technology which also relies on the pinning of vortices in a finite supercurrent. Meissner effect in type-i superconductor Meissner effect in type-ii superconductor Vortex Imaging using Aharonov-Bohm effect with electrons

14 SUPERCONDUCTING VORTEX DYNAMICS We can set up a set of equations analogous to the HVI equations for a neutral superfluid, by looking at the forces on the vortices in a classical analysis. These forces are then as follows: Force from superfluid Force from normal fluid (Lorentz force) (quasiparticle drag) Now we can always write the current in the form The two are related by: Longitudinal Ohmic current Transverse Hall current But this is exactly the same as the HVI mutual friction equations. To see this just rewrite the above in the form: in which

15 NEUTRON STAR DYNAMICS This is observed in the famous glitches that exist in the rotation rate. These are caused by vortex depinning. Vortices are pinned in the solid crust but the slow spin-down of the star causes the vortex rotation to go out of equilibrium with the internal superfluid rotation.

16 Q. VORTICES in MAGNETS A vortex-like topological excitation can exist in a 2-d ordered spin system, or in a thin film. These vortices can be imaged in a variety of ways (magneto-optical, or using MFM techniques. In this way one can also watch the dynamics of individual magnetic vortices under external influences.

17 TYPICAL EXPERIMENTAL SYSTEM: PERMALLOY A well-controlled system where many experiments on vortices have been done is permalloy, Ni 80 Fe 20, which has very small (quartic) magnetoelastic coupling. The vortex dynamics is very important for hard drive technology, and is described using the phenomenological eqtn: We will be interested in a disc geometry (see above for others). Key parameters: Magnon velocity: Exchange length: where: so that:

18 Quantum Vortex in 2D Easy-plane Ferromagnet Hamiltonia Continuum + The action is: where (Berry The vortex is a skyrmion, with profile: Vortex core radius MAGNON with Spin Wave velocity: with

DYNAMICS of a QUANTUM VORTEX

DYNAMICS of a QUANTUM VORTEX PCE STAMP DYNAMICS of a QUANTUM VORTEX (ORLANDO, Dec 21st, 2010) Physics & Astronomy UBC Vancouver Pacific Institute for Theoretical Physics DYNAMICS of a QUANTUM VORTEX L THOMPSON & PCE STAMP I WILL TALK

More information

CONDENSED MATTER: towards Absolute Zero

CONDENSED MATTER: towards Absolute Zero CONDENSED MATTER: towards Absolute Zero The lowest temperatures reached for bulk matter between 1970-2000 AD. We have seen the voyages to inner & outer space in physics. There is also a voyage to the ultra-cold,

More information

1 Superfluidity and Bose Einstein Condensate

1 Superfluidity and Bose Einstein Condensate Physics 223b Lecture 4 Caltech, 04/11/18 1 Superfluidity and Bose Einstein Condensate 1.6 Superfluid phase: topological defect Besides such smooth gapless excitations, superfluid can also support a very

More information

Lecture 4: Superfluidity

Lecture 4: Superfluidity Lecture 4: Superfluidity Previous lecture: Elementary excitations above condensate are phonons in the low energy limit. This lecture Rotation of superfluid helium. Hess-Fairbank effect and persistent currents

More information

Collective Effects. Equilibrium and Nonequilibrium Physics

Collective Effects. Equilibrium and Nonequilibrium Physics Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 4, April 7, 2006 1 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech

More information

Superfluids, Superconductors and Supersolids: Macroscopic Manifestations of the Microworld Laws

Superfluids, Superconductors and Supersolids: Macroscopic Manifestations of the Microworld Laws University of Massachusetts Amherst From the SelectedWorks of Egor Babaev 2008 Superfluids, Superconductors and Supersolids: Macroscopic Manifestations of the Microworld Laws Egor Babaev, University of

More information

The Superfluid Phase s of Helium 3

The Superfluid Phase s of Helium 3 The Superfluid Phase s of Helium 3 DIETER VOLLHARD T Rheinisch-Westfälische Technische Hochschule Aachen, Federal Republic of German y PETER WÖLFL E Universität Karlsruhe Federal Republic of Germany PREFACE

More information

Vortices and other topological defects in ultracold atomic gases

Vortices and other topological defects in ultracold atomic gases Vortices and other topological defects in ultracold atomic gases Michikazu Kobayashi (Kyoto Univ.) 1. Introduction of topological defects in ultracold atoms 2. Kosterlitz-Thouless transition in spinor

More information

Quantum Theory of Matter

Quantum Theory of Matter Quantum Theory of Matter Overview Lecture Derek Lee Imperial College London January 2007 Outline 1 Course content Introduction Superfluids Superconductors 2 Course Plan Resources Outline 1 Course content

More information

The Ginzburg-Landau Theory

The Ginzburg-Landau Theory The Ginzburg-Landau Theory A normal metal s electrical conductivity can be pictured with an electron gas with some scattering off phonons, the quanta of lattice vibrations Thermal energy is also carried

More information

Study of superfluidity in magnetars by van Hoven and Levin

Study of superfluidity in magnetars by van Hoven and Levin Study of superfluidity in magnetars by van Hoven and Levin Overview What is a superfluid and how does it look like in neutron stars? What can happen when both a superfluid and a strong magnetic field are

More information

Spinor Bose gases lecture outline

Spinor Bose gases lecture outline Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor Bose-Einstein condensates 3. Imaging spin textures 4. Spin-mixing dynamics 5. Magnetic excitations We re here Coupling

More information

First, we need a rapid look at the fundamental structure of superfluid 3 He. and then see how similar it is to the structure of the Universe.

First, we need a rapid look at the fundamental structure of superfluid 3 He. and then see how similar it is to the structure of the Universe. Outline of my talk: First, we need a rapid look at the fundamental structure of superfluid 3 He and then see how similar it is to the structure of the Universe. Then we will look at our latest ideas on

More information

From Last Time. Partially full bands = metal Bands completely full or empty = insulator / seminconductor

From Last Time. Partially full bands = metal Bands completely full or empty = insulator / seminconductor From Last Time Solids are large numbers of atoms arranged in a regular crystal structure. Each atom has electron quantum states, but interactions shift the energies. End result is each type atomic electron

More information

Dynamics and Statistics of Quantum Turbulence in Quantum Fluid

Dynamics and Statistics of Quantum Turbulence in Quantum Fluid Dynamics and Statistics of Quantum Turbulence in Quantum Fluid Faculty of Science, Osaka City University Michikazu Kobayashi May 25, 2006, Kansai Seminar House Contents 1. 2. 3. 4. 5. Introduction - history

More information

Baruch Rosenstein Nat. Chiao Tung University

Baruch Rosenstein Nat. Chiao Tung University Dissipationless current carrying states in type II superconductors in magnetic field Baruch Rosenstein Nat. Chiao Tung University D. P. Li Peking University, Beijing, China B. Shapiro Bar Ilan University,

More information

QUANTUM MECHANICS Intro to Basic Features

QUANTUM MECHANICS Intro to Basic Features PCES 4.21 QUANTUM MECHANICS Intro to Basic Features 1. QUANTUM INTERFERENCE & QUANTUM PATHS Rather than explain the rules of quantum mechanics as they were devised, we first look at a more modern formulation

More information

On the Higgs mechanism in the theory of

On the Higgs mechanism in the theory of On the Higgs mechanism in the theory of superconductivity* ty Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften D-85748 Garching Outline Phenomenological

More information

Lecture 2. Phenomenology of (classic) superconductivity Phys. 598SC Fall 2015 Prof. A. J. Leggett

Lecture 2. Phenomenology of (classic) superconductivity Phys. 598SC Fall 2015 Prof. A. J. Leggett Lecture 2. Phenomenology of (classic) superconductivity Phys. 598SC Fall 2015 Prof. A. J. Leggett (References: de Gannes chapters 1-3, Tinkham chapter 1) Statements refer to classic (pre-1970) superconductors

More information

DYNAMICS OF QUANTISED VORTICES IN SUPERFLUIDS

DYNAMICS OF QUANTISED VORTICES IN SUPERFLUIDS DYNAMICS OF QUANTISED VORTICES IN SUPERFLUIDS A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids

More information

10 Supercondcutor Experimental phenomena zero resistivity Meissner effect. Phys463.nb 101

10 Supercondcutor Experimental phenomena zero resistivity Meissner effect. Phys463.nb 101 Phys463.nb 101 10 Supercondcutor 10.1. Experimental phenomena 10.1.1. zero resistivity The resistivity of some metals drops down to zero when the temperature is reduced below some critical value T C. Such

More information

Quantised Vortices in an Exciton- Polariton Condensate

Quantised Vortices in an Exciton- Polariton Condensate 4 th International Conference on Spontaneous Coherence in Excitonic Systems Quantised Vortices in an Exciton- Polariton Condensate Konstantinos G. Lagoudakis 1, Michiel Wouters 2, Maxime Richard 1, Augustin

More information

Fundamentals and New Frontiers of Bose Einstein Condensation

Fundamentals and New Frontiers of Bose Einstein Condensation Contents Preface v 1. Fundamentals of Bose Einstein Condensation 1 1.1 Indistinguishability of Identical Particles.......... 1 1.2 Ideal Bose Gas in a Uniform System............ 3 1.3 Off-Diagonal Long-Range

More information

Schematic for resistivity measurement

Schematic for resistivity measurement Module 9 : Experimental probes of Superconductivity Lecture 1 : Experimental probes of Superconductivity - I Among the various experimental methods used to probe the properties of superconductors, there

More information

Temperature Effects and Oscillations on Vortices in Superfluid Helium

Temperature Effects and Oscillations on Vortices in Superfluid Helium Temperature Effects and Oscillations on Vortices in Superfluid Helium May Palace and Dr. Rena Zieve UC Davis 2015 Physics REU A new measurement technique for studying kelvin wave oscillations along vortices

More information

Quantum Theory of Matter

Quantum Theory of Matter Quantum Theory of Matter Revision Lecture Derek Lee Imperial College London May 2006 Outline 1 Exam and Revision 2 Quantum Theory of Matter Microscopic theory 3 Summary Outline 1 Exam and Revision 2 Quantum

More information

A Superfluid Universe

A Superfluid Universe A Superfluid Universe Lecture 2 Quantum field theory & superfluidity Kerson Huang MIT & IAS, NTU Lecture 2. Quantum fields The dynamical vacuum Vacuumscalar field Superfluidity Ginsburg Landau theory BEC

More information

1 Quantum Theory of Matter

1 Quantum Theory of Matter Quantum Theory of Matter: Superfluids & Superconductors Lecturer: Derek Lee Condensed Matter Theory Blackett 809 Tel: 020 7594 7602 dkk.lee@imperial.ac.uk Level 4 course: PT4.5 (Theory Option) http://www.cmth.ph.ic.ac.uk/people/dkk.lee/teach/qtm

More information

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields

More information

Introduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance

Introduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Introduction to Superconductivity Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Meissner Effect Magnetic field expelled. Superconducting surface current ensures

More information

TDGL Simulation on Dynamics of Helical Vortices in Thin Superconducting Wires in the Force-Free Configuration

TDGL Simulation on Dynamics of Helical Vortices in Thin Superconducting Wires in the Force-Free Configuration 5th International Workshop on Numerical Modelling of High-Temperature Superconductors, 6/15-17/2016, Bologna, Italy TDGL Simulation on Dynamics of Helical Vortices in Thin Superconducting Wires in the

More information

Lecture 10: Supercurrent Equation

Lecture 10: Supercurrent Equation Lecture 10: Supercurrent Equation Outline 1. Macroscopic Quantum Model 2. Supercurrent Equation and the London Equations 3. Fluxoid Quantization 4. The Normal State 5. Quantized Vortices October 13, 2005

More information

SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES

SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES Congresso Nazionale della Società Italiana di Fisica Università della Calabria 17/21 Settembre 2018 SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES Sandro Stringari Università di Trento CNR-INO - Bose-Einstein

More information

Superfluidity and Superconductivity

Superfluidity and Superconductivity Superfluidity and Superconductivity These are related phenomena of flow without resistance, but in very different systems Superfluidity: flow of helium IV atoms in a liquid Superconductivity: flow of electron

More information

Superinsulator: a new topological state of matter

Superinsulator: a new topological state of matter Superinsulator: a new topological state of matter M. Cristina Diamantini Nips laboratory, INFN and Department of Physics and Geology University of Perugia Coll: Igor Lukyanchuk, University of Picardie

More information

Superfluidity and Condensation

Superfluidity and Condensation Christian Veit 4th of June, 2013 2 / 29 The discovery of superfluidity Early 1930 s: Peculiar things happen in 4 He below the λ-temperature T λ = 2.17 K 1938: Kapitza, Allen & Misener measure resistance

More information

Vortices in superconductors& low temperature STM

Vortices in superconductors& low temperature STM Vortices in superconductors& low temperature STM José Gabriel Rodrigo Low Temperature Laboratory Universidad Autónoma de Madrid, Spain (LBT-UAM) Cryocourse, 2011 Outline -Vortices in superconductors -Vortices

More information

Superfluidity of a 2D Bose gas (arxiv: v1)

Superfluidity of a 2D Bose gas (arxiv: v1) Superfluidity of a 2D Bose gas (arxiv:1205.4536v1) Christof Weitenberg, Rémi Desbuquois, Lauriane Chomaz, Tarik Yefsah, Julian Leonard, Jérôme Beugnon, Jean Dalibard Trieste 18.07.2012 Phase transitions

More information

Unexpected Connections in Physics: From Superconductors to Black Holes. Talk online: sachdev.physics.harvard.edu

Unexpected Connections in Physics: From Superconductors to Black Holes. Talk online: sachdev.physics.harvard.edu Unexpected Connections in Physics: From Superconductors to Black Holes Talk online: sachdev.physics.harvard.edu The main unsolved problem in theoretical physics today: Unification of The main unsolved

More information

SUPERFLUID TURBULENCE

SUPERFLUID TURBULENCE SUPERFLUID TURBULENCE Carlo F. Barenghi School of Mathematics, University of Newcastle Acknowledgments: Demos Kivotides, Daniel Poole, Anthony Youd and Yuri Sergeev (Newcastle), Joe Vinen (Birmingham),

More information

Superfluidity and Supersolidity in 4 He

Superfluidity and Supersolidity in 4 He Superfluidity and Supersolidity in 4 He Author: Lars Bonnes Supervisor: Lode Pollet Proseminar Theoretische Physik: Phase Transitions SS 07 18.06.2007 Superfluid Liquid Helium Motivation Two-fluid Model

More information

Techniques for inferring M at small scales

Techniques for inferring M at small scales Magnetism and small scales We ve seen that ferromagnetic materials can be very complicated even in bulk specimens (e.g. crystallographic anisotropies, shape anisotropies, local field effects, domains).

More information

Vortex lattice pinning in high-temperature superconductors.

Vortex lattice pinning in high-temperature superconductors. Vortex lattice ning in high-temperature superconductors. Victor Vakaryuk. Abstract. Vortex matter in high temperature superconductors has many peculiar properties such as melting of the vortex lattice,

More information

Superconductivity. Alexey Ustinov Universität Karlsruhe WS Alexey Ustinov WS2008/2009 Superconductivity: Lecture 3 1

Superconductivity. Alexey Ustinov Universität Karlsruhe WS Alexey Ustinov WS2008/2009 Superconductivity: Lecture 3 1 Superconductivity Alexey Ustinov Universität Karlsruhe WS 2008-2009 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 3 1 Electrodynamics of superconductors Two-fluid model The First London Equation

More information

The Aharanov Bohm Effect

The Aharanov Bohm Effect Supplement 6-A The Aharanov Bohm Effect Let us return to the description of an electron of charge e and mass m e, in a timeindependent magnetic field. The system is described by the Hamiltonian and the

More information

Abrikosov vortex lattice solution

Abrikosov vortex lattice solution Abrikosov vortex lattice solution A brief exploration O. Ogunnaike Final Presentation Ogunnaike Abrikosov vortex lattice solution Physics 295b 1 / 31 Table of Contents 1 Background 2 Quantization 3 Abrikosov

More information

Correlated 2D Electron Aspects of the Quantum Hall Effect

Correlated 2D Electron Aspects of the Quantum Hall Effect Correlated 2D Electron Aspects of the Quantum Hall Effect Outline: I. Introduction: materials, transport, Hall effects II. III. IV. Composite particles FQHE, statistical transformations Quasiparticle charge

More information

From laser cooling to BEC First experiments of superfluid hydrodynamics

From laser cooling to BEC First experiments of superfluid hydrodynamics From laser cooling to BEC First experiments of superfluid hydrodynamics Alice Sinatra Quantum Fluids course - Complement 1 2013-2014 Plan 1 COOLING AND TRAPPING 2 CONDENSATION 3 NON-LINEAR PHYSICS AND

More information

Physics Nov Bose-Einstein Gases

Physics Nov Bose-Einstein Gases Physics 3 3-Nov-24 8- Bose-Einstein Gases An amazing thing happens if we consider a gas of non-interacting bosons. For sufficiently low temperatures, essentially all the particles are in the same state

More information

BEC Vortex Matter. Aaron Sup October 6, Advisor: Dr. Charles Hanna, Department of Physics, Boise State University

BEC Vortex Matter. Aaron Sup October 6, Advisor: Dr. Charles Hanna, Department of Physics, Boise State University BEC Vortex Matter Aaron Sup October 6, 006 Advisor: Dr. Charles Hanna, Department of Physics, Boise State University 1 Outline 1. Bosons: what are they?. Bose-Einstein Condensation (BEC) 3. Vortex Formation:

More information

14.4. the Ginzburg Landau theory. Phys520.nb Experimental evidence of the BCS theory III: isotope effect

14.4. the Ginzburg Landau theory. Phys520.nb Experimental evidence of the BCS theory III: isotope effect Phys520.nb 119 This is indeed what one observes experimentally for convectional superconductors. 14.3.7. Experimental evidence of the BCS theory III: isotope effect Because the attraction is mediated by

More information

LARGE-SCALE QUANTUM PHENOMENA COURSE. UNIVERSITY of INNSBRUCK. (June 2010)

LARGE-SCALE QUANTUM PHENOMENA COURSE. UNIVERSITY of INNSBRUCK. (June 2010) LARGE-SCALE QUANTUM PHENOMENA COURSE to be given at the UNIVERSITY of INNSBRUCK (June 2010) INTRODUCTION 1.BASIC PHENOMENA 2.EXPERIMENTAL OBSERVATIONS 3.THEORETICAL FRAMEWORK LARGE-SCALE QUANTUM PHENOMENA:

More information

Measuring the Whirling of Spacetime

Measuring the Whirling of Spacetime Measuring the Whirling of Spacetime Lecture series on Experimental Gravity (revised version) Kostas Glampedakis Prologue: does spin gravitate? M 1 M 2 System I: F = GM 1M 2 r 2 J 1 J 2 System II: M 1?

More information

David Snoke Department of Physics and Astronomy, University of Pittsburgh

David Snoke Department of Physics and Astronomy, University of Pittsburgh The 6 th International Conference on Spontaneous Coherence in Excitonic Systems Closing Remarks David Snoke Department of Physics and Astronomy, University of Pittsburgh ICSCE6, Stanford University, USA

More information

Loop current order in optical lattices

Loop current order in optical lattices JQI Summer School June 13, 2014 Loop current order in optical lattices Xiaopeng Li JQI/CMTC Outline Ultracold atoms confined in optical lattices 1. Why we care about lattice? 2. Band structures and Berry

More information

Vortex States in a Non-Abelian Magnetic Field

Vortex States in a Non-Abelian Magnetic Field Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM

More information

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I)

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) B.V. COSTA UFMG BRAZIL LABORATORY FOR SIMULATION IN PHYSICS A Guide to Monte Carlo Simulations in Statistical Physics by Landau

More information

Magnetic measurements (Pt. IV) advanced probes

Magnetic measurements (Pt. IV) advanced probes Magnetic measurements (Pt. IV) advanced probes Ruslan Prozorov October 2018 Physics 590B types of local probes microscopic (site-specific) NMR neutrons Mossbauer stationary Bitter decoration magneto-optics

More information

Confining ultracold atoms on a ring in reduced dimensions

Confining ultracold atoms on a ring in reduced dimensions Confining ultracold atoms on a ring in reduced dimensions Hélène Perrin Laboratoire de physique des lasers, CNRS-Université Paris Nord Charge and heat dynamics in nano-systems Orsay, October 11, 2011 What

More information

Theory of Nonequilibrium Superconductivity *

Theory of Nonequilibrium Superconductivity * Theory of Nonequilibrium Superconductivity * NIKOLAI B.KOPNIN Low Temperature Laboratory, Helsinki University of Technology, Finland and L.D. Landau Institute for Theoretical Physics, Moscow, Russia CLARENDON

More information

Heterogeneous vortex dynamics in high temperature superconductors

Heterogeneous vortex dynamics in high temperature superconductors Heterogeneous vortex dynamics in high temperature superconductors Feng YANG Laboratoire des Solides Irradiés, Ecole Polytechnique, 91128 Palaiseau, France. June 18, 2009/PhD thesis defense Outline 1 Introduction

More information

(1) BEC (2) BEC (1) (BEC) BEC BEC (5) BEC (LT) (QFS) BEC (3) BEC. 3 He. 4 He. 4 He 3 He

(1) BEC (2) BEC (1) (BEC) BEC BEC (5) BEC (LT) (QFS) BEC (3) BEC. 3 He. 4 He. 4 He 3 He 22 (BEC) 4 He BEC We study theoretically and experimentally quantum hydrodynamics in quantum condensed phases at low temperature, namely superfluid helium and atomic Bose-Einstein condensates (BECs). Quantum

More information

Strongly correlated Cooper pair insulators and superfluids

Strongly correlated Cooper pair insulators and superfluids Strongly correlated Cooper pair insulators and superfluids Predrag Nikolić George Mason University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Affiliations and

More information

Superfluid instability in precessing neutron stars

Superfluid instability in precessing neutron stars Superfluid instability in precessing neutron stars Kostas Glampedakis SISSA, Trieste, Italy in collaboration with Nils Andersson & Ian Jones Soton October 2007 p.1/15 This talk Precessing neutron stars

More information

Magnetic measurements (Pt. IV) advanced probes

Magnetic measurements (Pt. IV) advanced probes Magnetic measurements (Pt. IV) advanced probes Ruslan Prozorov 26 February 2014 Physics 590B types of local probes microscopic (site-specific) NMR neutrons Mossbauer stationary Bitter decoration magneto-optics

More information

Superfluidity. v s. E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN University of Oulu, Finland (Dated: June 8, 2012)

Superfluidity. v s. E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN University of Oulu, Finland (Dated: June 8, 2012) Superfluidity E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN-90014 University of Oulu, Finland (Dated: June 8, 01) PACS numbers: 67.40.-w, 67.57.-z, 74., 03.75.-b I. INTRODUCTION Fluids

More information

(Color-)magnetic flux tubes in dense matter

(Color-)magnetic flux tubes in dense matter Seattle, Apr 17, 2018 1 Andreas Schmitt Mathematical Sciences and STAG Research Centre University of Southampton Southampton SO17 1BJ, United Kingdom (Color-)magnetic flux tubes in dense matter A. Haber,

More information

Classical and quantum regimes of the superfluid turbulence.

Classical and quantum regimes of the superfluid turbulence. arxiv:cond-mat/0310021v4 20 Oct 2003 Classical and quantum regimes of the superfluid turbulence. G.E. Volovik Low Temperature Laboratory, Helsinki University of Technology P.O.Box 2200, FIN-02015 HUT,

More information

Fundamentals and New Frontiers of Bose Einstein Condensation

Fundamentals and New Frontiers of Bose Einstein Condensation Experimental realization of Bose Einstein condensation (BEC) of dilute atomic gases [Anderson, et al. (1995); Davis, et al. (1995); Bradley, et al. (1995, 1997)] has ignited a virtual explosion of research.

More information

Neutron and x-ray spectroscopy

Neutron and x-ray spectroscopy Neutron and x-ray spectroscopy B. Keimer Max-Planck-Institute for Solid State Research outline 1. self-contained introduction neutron scattering and spectroscopy x-ray scattering and spectroscopy 2. application

More information

Low dimensional quantum gases, rotation and vortices

Low dimensional quantum gases, rotation and vortices Goal of these lectures Low dimensional quantum gases, rotation and vortices Discuss some aspect of the physics of quantum low dimensional systems Planar fluids Quantum wells and MOS structures High T c

More information

Contents Preface Physical Constants, Units, Mathematical Signs and Symbols Introduction Kinetic Theory and the Boltzmann Equation

Contents Preface Physical Constants, Units, Mathematical Signs and Symbols Introduction Kinetic Theory and the Boltzmann Equation V Contents Preface XI Physical Constants, Units, Mathematical Signs and Symbols 1 Introduction 1 1.1 Carbon Nanotubes 1 1.2 Theoretical Background 4 1.2.1 Metals and Conduction Electrons 4 1.2.2 Quantum

More information

Physics 598 ESM Term Paper Giant vortices in rapidly rotating Bose-Einstein condensates

Physics 598 ESM Term Paper Giant vortices in rapidly rotating Bose-Einstein condensates Physics 598 ESM Term Paper Giant vortices in rapidly rotating Bose-Einstein condensates Kuei Sun May 4, 2006 kueisun2@uiuc.edu Department of Physics, University of Illinois at Urbana- Champaign, 1110 W.

More information

Chapter 1. Introduction

Chapter 1. Introduction Chapter 1 Introduction The book Introduction to Modern Physics: Theoretical Foundations starts with the following two paragraphs [Walecka (2008)]: At the end of the 19th century, one could take pride in

More information

Reference for most of this talk:

Reference for most of this talk: Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding ultracold Fermi gases. in Ultracold Fermi Gases, Proceedings of the International School

More information

Steven W. Van Sciver. Helium Cryogenics. Second Edition. 4) Springer

Steven W. Van Sciver. Helium Cryogenics. Second Edition. 4) Springer Steven W. Van Sciver Helium Cryogenics Second Edition 4) Springer Contents 1 Cryogenic Principles and Applications 1 1.1 Temperature Scale 2 1.2 Historical Background 4 1.3 Applications for Cryogenics

More information

Collective Effects. Equilibrium and Nonequilibrium Physics

Collective Effects. Equilibrium and Nonequilibrium Physics Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 3, 3 March 2006 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech

More information

Superconductivity and Superfluidity

Superconductivity and Superfluidity Superconductivity and Superfluidity Contemporary physics, Spring 2015 Partially from: Kazimierz Conder Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland Resistivity

More information

Superconductivity and the BCS theory

Superconductivity and the BCS theory Superconductivity and the BCS theory PHY 313 - Statistical Mechanics Syed Ali Raza Roll no: 2012-10-0124 LUMS School of Science and Engineering Monday, December, 15, 2010 1 Introduction In this report

More information

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles October, 011 PROGRESS IN PHYSICS olume 4 Ultracold Fermi Bose Gases Spinless Bose Charged Sound Particles ahan N. Minasyan alentin N. Samoylov Scientific Center of Applied Research, JINR, Dubna, 141980,

More information

Physics 127a: Class Notes

Physics 127a: Class Notes Physics 127a: Class Notes Lecture 15: Statistical Mechanics of Superfluidity Elementary excitations/quasiparticles In general, it is hard to list the energy eigenstates, needed to calculate the statistical

More information

Your student ID 1 page notes, written double sided Calculator Pencil for marking answer sheet

Your student ID 1 page notes, written double sided Calculator Pencil for marking answer sheet Hour Exam 2: Wednesday, Oct. 27 In-class (1300 Sterling Hall) Twenty multiple-choice questions Will cover: 8.1-8.6 (Light and E&M) 9.1-9.5 (E&M waves and color) 10, 11 (Relativity) You should bring Your

More information

Superconductivity at nanoscale

Superconductivity at nanoscale Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and

More information

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9 Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................

More information

Physics (PHYS) Courses. Physics (PHYS) 1

Physics (PHYS) Courses. Physics (PHYS) 1 Physics (PHYS) 1 Physics (PHYS) Courses PHYS 5001. Introduction to Quantum Computing. 3 Credit Hours. This course will give an elementary introduction to some basics of quantum information and quantum

More information

Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007

Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007 1859-5 Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases 27 August - 7 September, 2007 Dipolar BECs with spin degrees of freedom Yuki Kawaguchi Tokyo Institute of

More information

Ref: Bikash Padhi, and SG, Phys. Rev. Lett, 111, (2013) HRI, Allahabad,Cold Atom Workshop, February, 2014

Ref: Bikash Padhi, and SG, Phys. Rev. Lett, 111, (2013) HRI, Allahabad,Cold Atom Workshop, February, 2014 Cavity Optomechanics with synthetic Landau Levels of ultra cold atoms: Sankalpa Ghosh, Physics Department, IIT Delhi Ref: Bikash Padhi, and SG, Phys. Rev. Lett, 111, 043603 (2013)! HRI, Allahabad,Cold

More information

Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION. Wolfgang Rindler. Professor of Physics The University of Texas at Dallas

Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION. Wolfgang Rindler. Professor of Physics The University of Texas at Dallas Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION Wolfgang Rindler Professor of Physics The University of Texas at Dallas OXPORD UNIVERSITY PRESS Contents Introduction l 1 From absolute space

More information

Dark Energy Stars and AdS/CFT

Dark Energy Stars and AdS/CFT Dark Energy Stars and AdS/CFT G. Chapline Lawrence Livermore National Laboratory, Livermore, CA 94551 Abstract The theory of dark energy stars illustrates how the behavior of matter near to certain kinds

More information

Cold atoms. 1: Bose-Einstein Condensation. Emil Lundh. April 13, Department of Physics Umeå University

Cold atoms. 1: Bose-Einstein Condensation. Emil Lundh. April 13, Department of Physics Umeå University 1: Bose-Einstein Condensation Department of Physics Umeå University lundh@tp.umu.se April 13, 2011 Umeå 114 000 inhabitants Average age 37.9 years Cultural capital of Europe 2014 400 km ski tracks 180

More information

There are two main theories in superconductivity: Ginzburg-Landau Theory. Outline of the Lecture. Ginzburg-Landau theory

There are two main theories in superconductivity: Ginzburg-Landau Theory. Outline of the Lecture. Ginzburg-Landau theory Ginzburg-Landau Theory There are two main theories in superconductivity: i Microscopic theory describes why materials are superconducting Prof. Damian Hampshire Durham University ii Ginzburg-Landau Theory

More information

Atoms, Molecules and Solids. From Last Time Superposition of quantum states Philosophy of quantum mechanics Interpretation of the wave function:

Atoms, Molecules and Solids. From Last Time Superposition of quantum states Philosophy of quantum mechanics Interpretation of the wave function: Essay outline and Ref to main article due next Wed. HW 9: M Chap 5: Exercise 4 M Chap 7: Question A M Chap 8: Question A From Last Time Superposition of quantum states Philosophy of quantum mechanics Interpretation

More information

Using SQUID VSM Superconducting Magnets at Low Fields

Using SQUID VSM Superconducting Magnets at Low Fields Application Note 1500-011 Using SQUID VSM Superconducting Magnets at Low Fields Abstract The superconducting magnet used in SQUID VSM is capable of generating fields up to 7 tesla (7x10 4 gauss) with the

More information

Interaction between atoms

Interaction between atoms Interaction between atoms MICHA SCHILLING HAUPTSEMINAR: PHYSIK DER KALTEN GASE INSTITUT FÜR THEORETISCHE PHYSIK III UNIVERSITÄT STUTTGART 23.04.2013 Outline 2 Scattering theory slow particles / s-wave

More information

Weak Link Probes and Space-Time Translation Symmetry Breaking

Weak Link Probes and Space-Time Translation Symmetry Breaking Weak Link Probes and Space-Time Translation Symmetry Breaking Frank Wilczek Center for Theoretical Physics, MIT, Cambridge MA 02139 USA August 10, 2013 Abstract Intermittent weak link (Josephson type)

More information

Design and realization of exotic quantum phases in atomic gases

Design and realization of exotic quantum phases in atomic gases Design and realization of exotic quantum phases in atomic gases H.P. Büchler and P. Zoller Theoretische Physik, Universität Innsbruck, Austria Institut für Quantenoptik und Quanteninformation der Österreichischen

More information

Missing pieces in the r-mode puzzle

Missing pieces in the r-mode puzzle Missing pieces in the r-mode puzzle Southampton Theory Astronomy Gravity Centre for Fundamental Physics Nils Andersson accreting systems Accreting neutron stars in LMXBs may be relevant gravitational-wave

More information

Critical fields and intermediate state

Critical fields and intermediate state 621 Lecture 6.3 Critical fields and intermediate state Magnetic fields exert pressure on a superconductor: expelling the flux from the sample makes it denser in the space outside, which costs magnetic

More information

University of Antwerp Condensed Matter Theory Group Vortices in superconductors IV. Hybrid systems

University of Antwerp Condensed Matter Theory Group Vortices in superconductors IV. Hybrid systems Vortices in superconductors IV. Hybrid systems François Peeters Magnetic impurities T c decreases with increasing impurity density Origin: exchange interaction between electron and impurity: Γ(r i -r e

More information

Cooperative Phenomena

Cooperative Phenomena Cooperative Phenomena Frankfurt am Main Kaiserslautern Mainz B1, B2, B4, B6, B13N A7, A9, A12 A10, B5, B8 Materials Design - Synthesis & Modelling A3, A8, B1, B2, B4, B6, B9, B11, B13N A5, A7, A9, A12,

More information