Bose–Einstein Condensation in Dilute Gases in 1925 Einstein Predicted
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Lecture 3: Fermi-Liquid Theory 1 General Considerations Concerning Condensed Matter
Phys 769 Selected Topics in Condensed Matter Physics Summer 2010 Lecture 3: Fermi-liquid theory Lecturer: Anthony J. Leggett TA: Bill Coish 1 General considerations concerning condensed matter (NB: Ultracold atomic gasses need separate discussion) Assume for simplicity a single atomic species. Then we have a collection of N (typically 1023) nuclei (denoted α,β,...) and (usually) ZN electrons (denoted i,j,...) interacting ∼ via a Hamiltonian Hˆ . To a first approximation, Hˆ is the nonrelativistic limit of the full Dirac Hamiltonian, namely1 ~2 ~2 1 e2 1 Hˆ = 2 2 + NR −2m ∇i − 2M ∇α 2 4πǫ r r α 0 i j Xi X Xij | − | 1 (Ze)2 1 1 Ze2 1 + . (1) 2 4πǫ0 Rα Rβ − 2 4πǫ0 ri Rα Xαβ | − | Xiα | − | For an isolated atom, the relevant energy scale is the Rydberg (R) – Z2R. In addition, there are some relativistic effects which may need to be considered. Most important is the spin-orbit interaction: µ Hˆ = B σ (v V (r )) (2) SO − c2 i · i × ∇ i Xi (µB is the Bohr magneton, vi is the velocity, and V (ri) is the electrostatic potential at 2 3 2 ri as obtained from HˆNR). In an isolated atom this term is o(α R) for H and o(Z α R) for a heavy atom (inner-shell electrons) (produces fine structure). The (electron-electron) magnetic dipole interaction is of the same order as HˆSO. The (electron-nucleus) hyperfine interaction is down relative to Hˆ by a factor µ /µ 10−3, and the nuclear dipole-dipole SO n B ∼ interaction by a factor (µ /µ )2 10−6. -
Demonstration of a Persistent Current in Superfluid Atomic Gas
Demonstration of a persistent current in superfluid atomic gas One of the most remarkable properties of macroscopic quantum systems is the phenomenon of persistent flow. Current in a loop of superconducting wire will flow essentially forever. In a neutral superfluid, like liquid helium below the lambda point, persistent flow is observed as frictionless circulation in a hollow toroidal container. A Bose-Einstein condensate (BEC) of an atomic gas also exhibits superfluid behavior. While a number of experiments have confirmed superfluidity in an atomic gas BEC, persistent flow, which is regarded as the “gold standard” of superfluidity, had not been observed. The main reason for this is that persistent flow is most easily observed in a topology such as a ring or toroid, while past BEC experiments were primarily performed in spheroidal traps. Using a combination of magnetic and optical fields, we were able to create an atomic BEC in a toriodal trap, with the condensate filling the entire ring. Once the BEC was formed in the toroidal trap, we coherently transferred orbital angular momentum of light to the atoms (using a technique we had previously demonstrated) to get them to circulate in the trap. We observed the flow of atoms to persist for a time more than twenty times what was observed for the atoms confined in a spheroidal trap. The flow was observed to persist even when there was a large (80%) thermal fraction present in the toroidal trap. These experiments open the possibility of investigations of the fundamental role of flow in superfluidity and of realizing the atomic equivalent of superconducting circuits and devices such as SQUIDs. -
Unconventional Hund Metal in a Weak Itinerant Ferromagnet
ARTICLE https://doi.org/10.1038/s41467-020-16868-4 OPEN Unconventional Hund metal in a weak itinerant ferromagnet Xiang Chen1, Igor Krivenko 2, Matthew B. Stone 3, Alexander I. Kolesnikov 3, Thomas Wolf4, ✉ ✉ Dmitry Reznik 5, Kevin S. Bedell6, Frank Lechermann7 & Stephen D. Wilson 1 The physics of weak itinerant ferromagnets is challenging due to their small magnetic moments and the ambiguous role of local interactions governing their electronic properties, 1234567890():,; many of which violate Fermi-liquid theory. While magnetic fluctuations play an important role in the materials’ unusual electronic states, the nature of these fluctuations and the paradigms through which they arise remain debated. Here we use inelastic neutron scattering to study magnetic fluctuations in the canonical weak itinerant ferromagnet MnSi. Data reveal that short-wavelength magnons continue to propagate until a mode crossing predicted for strongly interacting quasiparticles is reached, and the local susceptibility peaks at a coher- ence energy predicted for a correlated Hund metal by first-principles many-body theory. Scattering between electrons and orbital and spin fluctuations in MnSi can be understood at the local level to generate its non-Fermi liquid character. These results provide crucial insight into the role of interorbital Hund’s exchange within the broader class of enigmatic multiband itinerant, weak ferromagnets. 1 Materials Department, University of California, Santa Barbara, CA 93106, USA. 2 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA. 3 Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 4 Institute for Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany. -
Contents 1 Classification of Phase Transitions
PHY304 - Statistical Mechanics Spring Semester 2021 Dr. Anosh Joseph, IISER Mohali LECTURE 35 Monday, April 5, 2021 (Note: This is an online lecture due to COVID-19 interruption.) Contents 1 Classification of Phase Transitions 1 1.1 Order Parameter . .2 2 Critical Exponents 5 1 Classification of Phase Transitions The physics of phase transitions is a young research field of statistical physics. Let us summarize the knowledge we gained from thermodynamics regarding phases. The Gibbs’ phase rule is F = K + 2 − P; (1) with F denoting the number of intensive variables, K the number of particle species (chemical components), and P the number of phases. Consider a closed pot containing a vapor. With K = 1 we need 3 (= K + 2) extensive variables say, S; V; N for a complete description of the system. One of these say, V determines only size of the system. The intensive properties are completely described by F = 1 + 2 − 1 = 2 (2) intensive variables. For instance, by pressure and temperature. (We could also choose temperature and chemical potential.) The third intensive variable is given by the Gibbs’-Duhem relation X S dT − V dp + Ni dµi = 0: (3) i This relation tells us that the intensive variables PHY304 - Statistical Mechanics Spring Semester 2021 T; p; µ1; ··· ; µK , which are conjugate to the extensive variables S; V; N1; ··· ;NK are not at all independent of each other. In the above relation S; V; N1; ··· ;NK are now functions of the variables T; p; µ1; ··· ; µK , and the Gibbs’-Duhem relation provides the possibility to eliminate one of these variables. -
Landau Effective Interaction Between Quasiparticles in a Bose-Einstein Condensate
PHYSICAL REVIEW X 8, 031042 (2018) Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate A. Camacho-Guardian* and Georg M. Bruun Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark (Received 19 December 2017; revised manuscript received 28 February 2018; published 15 August 2018) Landau’s description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentum- energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results. Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. -
Attractive Fermi Polarons at Nonzero Temperatures with a Finite Impurity
PHYSICAL REVIEW A 98, 013626 (2018) Attractive Fermi polarons at nonzero temperatures with a finite impurity concentration Hui Hu, Brendan C. Mulkerin, Jia Wang, and Xia-Ji Liu Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia (Received 29 June 2018; published 25 July 2018) We theoretically investigate how quasiparticle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration in three dimensions and in free space. By applying both non- self-consistent and self-consistent many-body T -matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependencies are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependencies. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At temperature T ∼ 0.1TF ,whereTF is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment [Schirotzek et al., Phys.Rev.Lett.102, 230402 (2009)] could be better theoretically explained. DOI: 10.1103/PhysRevA.98.013626 I. INTRODUCTION Experimentally, the first experiment on attractive Fermi polarons was carried out by the Zwierlein group at Mas- Over the past two decades, ultracold atomic gases have pro- sachusetts Institute of Technology (MIT) in 2009 using 6Li vided an ideal platform to understand the intriguing quantum many-body systems [1]. -
Electron-Electron Interactions(Pdf)
Contents 2 Electron-electron interactions 1 2.1 Mean field theory (Hartree-Fock) ................ 3 2.1.1 Validity of Hartree-Fock theory .................. 6 2.1.2 Problem with Hartree-Fock theory ................ 9 2.2 Screening ..................................... 10 2.2.1 Elementary treatment ......................... 10 2.2.2 Kubo formula ............................... 15 2.2.3 Correlation functions .......................... 18 2.2.4 Dielectric constant ............................ 19 2.2.5 Lindhard function ............................ 21 2.2.6 Thomas-Fermi theory ......................... 24 2.2.7 Friedel oscillations ............................ 25 2.2.8 Plasmons ................................... 27 2.3 Fermi liquid theory ............................ 30 2.3.1 Particles and holes ............................ 31 2.3.2 Energy of quasiparticles. ....................... 36 2.3.3 Residual quasiparticle interactions ................ 38 2.3.4 Local energy of a quasiparticle ................... 42 2.3.5 Thermodynamic properties ..................... 44 2.3.6 Quasiparticle relaxation time and transport properties. 46 2.3.7 Effective mass m∗ of quasiparticles ................ 50 0 Reading: 1. Ch. 17, Ashcroft & Mermin 2. Chs. 5& 6, Kittel 3. For a more detailed discussion of Fermi liquid theory, see G. Baym and C. Pethick, Landau Fermi-Liquid Theory : Concepts and Ap- plications, Wiley 1991 2 Electron-electron interactions The electronic structure theory of metals, developed in the 1930’s by Bloch, Bethe, Wilson and others, assumes that electron-electron interac- tions can be neglected, and that solid-state physics consists of computing and filling the electronic bands based on knowldege of crystal symmetry and atomic valence. To a remarkably large extent, this works. In simple compounds, whether a system is an insulator or a metal can be deter- mined reliably by determining the band filling in a noninteracting cal- culation. -
Non-Fermi Liquids in Oxide Heterostructures
UC Santa Barbara UC Santa Barbara Previously Published Works Title Non-Fermi liquids in oxide heterostructures Permalink https://escholarship.org/uc/item/1cn238xw Journal Reports on Progress in Physics, 81(6) ISSN 0034-4885 1361-6633 Authors Stemmer, Susanne Allen, S James Publication Date 2018-06-01 DOI 10.1088/1361-6633/aabdfa Peer reviewed eScholarship.org Powered by the California Digital Library University of California Reports on Progress in Physics KEY ISSUES REVIEW Non-Fermi liquids in oxide heterostructures To cite this article: Susanne Stemmer and S James Allen 2018 Rep. Prog. Phys. 81 062502 View the article online for updates and enhancements. This content was downloaded from IP address 128.111.119.159 on 08/05/2018 at 17:09 IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 81 (2018) 062502 (12pp) https://doi.org/10.1088/1361-6633/aabdfa 81 Key Issues Review 2018 Non-Fermi liquids in oxide heterostructures © 2018 IOP Publishing Ltd Susanne Stemmer1 and S James Allen2 RPPHAG 1 Materials Department, University of California, Santa Barbara, CA 93106-5050, United States of America 062502 2 Department of Physics, University of California, Santa Barbara, CA 93106-9530, United States of America S Stemmer and S J Allen E-mail: [email protected] Received 18 July 2017, revised 25 January 2018 Accepted for publication 13 April 2018 Published 8 May 2018 Printed in the UK Corresponding Editor Professor Piers Coleman ROP Abstract Understanding the anomalous transport properties of strongly correlated materials is one of the most formidable challenges in condensed matter physics. -
Phase Transition a Phase Transition Is the Alteration in State of Matter Among the Four Basic Recognized Aggregative States:Solid, Liquid, Gaseous and Plasma
Phase transition A phase transition is the alteration in state of matter among the four basic recognized aggregative states:solid, liquid, gaseous and plasma. In some cases two or more states of matter can co-exist in equilibrium under a given set of temperature and pressure conditions, as well as external force fields (electromagnetic, gravitational, acoustic). Introduction Matter is known four aggregative states: solid, liquid, and gaseous and plasma, which are sharply different in their properties and characteristics. Physicists have agreed to refer to a both physically and chemically homogeneous finite body as a phase. Or, using Gybbs’s definition, one can call a homogeneous part of heterogeneous system: a phase. The reason behind the existence of different phases lies in the balance between the kinetic (heat) energy of the molecules and their energy of interaction. Simplified, the mechanism of phase transitions can be described as follows. When heating a solid body, the kinetic energy of the molecules grows, distance between them increases, and in accordance with the Coulomb law the interaction between them weakens. When the temperature reaches a certain point for the given substance (mineral, mixture, or system) critical value, melting takes place. A new phase, liquid, is formed, and a phase transition takes place. When further heating the liquid thus formed to the next critical temperature the liquid (melt) changes to gas; and so on. All said phase transitions are reversible; that is, with the temperature being lowered, the system would repeat the complete transition from one state to another in reverse order. The important thing is the possibility of co- existence of phases and their reciprocal transition at any temperature. -
ABSTRACT for CWS 2002, Chemogolovka, Russia Ulf Israelsson
ABSTRACT for CWS 2002, Chemogolovka, Russia Ulf Israelsson Use of the International Space Station for Fundamental Physics Research Ulf E. Israelsson"-and Mark C. Leeb "Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 9 1 109, USA bNational Aeronautics and Space Administration, Code UG, Washington D.C., USA NASA's research plans aboard the International Space Station (ISS) are discussed. Experiments in low temperature physics and atomic physics are planned to commence in late 2005. Experiments in gravitational physics are planned to begin in 2007. A low temperature microgravity physics facility is under development for the low temperature and gravitation experiments. The facility provides a 2 K environment for two instruments and an operational lifetime of 4.5 months. Each instrument will be capable of accomplishing a primary investigation and one or more guest investigations. Experiments on the first flight will study non-equilibrium phenomena near the superfluid 4He transition and measure scaling parameters near the 3He critical point. Experiments on the second flight will investigate boundary effects near the superfluid 4He transition and perform a red-shift test of Einstein's theory of general relativity. Follow-on flights of the facility will occur at 16 to 22-month intervals. The first couple of atomic physics experiments will take advantage of the free-fall environment to operate laser cooled atomic fountain clocks with 10 to 100 times better performance than any Earth based clock. These clocks will be used for experimental studies in General and Special Relativity. Flight defiiiiiiori experirneni siudies are underway by investigators studying Bose Einstein Condensates and use of atom interferometers as potential future flight candidates. -
Thermophysical Properties of Helium-4 from 2 to 1500 K with Pressures to 1000 Atmospheres
DATE DUE llbriZl<L. - ' :_ Demco, Inc. 38-293 National Bureau of Standards A UNITED STATES H1 DEPARTMENT OF v+ *^r COMMERCE NBS TECHNICAL NOTE 631 National Bureau of Standards PUBLICATION APR 2 1973 Library, E-Ol Admin. Bldg. OCT 6 1981 191103 Thermophysical Properties of Helium-4 from 2 to 1500 K with Pressures qc to 1000 Atmospheres joo U57Q lV-O/ U.S. >EPARTMENT OF COMMERCE National Bureau of Standards NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scien- tific community, industry, and commerce. The Institute consists of a Center for Radia- tion Research, an Office of Measurement Services and the following divisions: Applied Mathematics—Electricity—Heat—Mechanics—Optical Physics—Linac Radiation 2—Nuclear Radiation 2—Applied Radiation 2 —Quantum Electronics3— Electromagnetics 3—Time and Frequency 3 —Laboratory Astrophysics 3—Cryo- 3 genics . -
Boiling a Unitary Fermi Liquid
PHYSICAL REVIEW LETTERS 122, 093401 (2019) Editors' Suggestion Featured in Physics Boiling a Unitary Fermi Liquid Zhenjie Yan,1 Parth B. Patel,1 Biswaroop Mukherjee,1 Richard J. Fletcher,1 Julian Struck,1,2 and Martin W. Zwierlein1 1MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2D´epartement de Physique, Ecole Normale Sup´erieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France (Received 1 November 2018; published 6 March 2019) We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T2 dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝ T−1=2. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons. DOI: 10.1103/PhysRevLett.122.093401 Landau’s Fermi liquid theory provides a quasiparticle the quantum critical region.