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Trapped Ions Stronglystrongly Correlatedcorrelated Coulombcoulomb Systemssystems Nonideal complex Plasmas in the Universe and in the lab Michael Bonitz Institut für Theoretische Physik und Astrophysik Christian-Albrechts-Universität zu Kiel 2nd Summer Institute „Complex Plasmas“, Greifswald, 4 August 2010 PlasmaPlasma = System of many charged particles, dominated by Coulomb interaction Wikipedia: „More than 99 % of the visible matter in our universe is in the Plasma state“ I. Langmuir/L. Tonks (1929): ionized gas - „plasma“ „4th state of matter“: solid Æ fluid Æ gas Æ plasma ideal hot classical gas made of electrons and ions OccurencesOccurences ofof PlasmaPlasma Contemporary Physics Education Project (CPEP)http://www.cpepweb.org/ Nonideal Laboratory & astrophysical plasmas PlasmaPlasma = System of many charged particles, dominated by Coulomb interaction I. Langmuir/L. Tonks (1929): ionized gas - „plasma“ „4th state of matter“: solid Æ fluid Æ gas Æ plasma ideal hot classical gas made of electrons and ions BUT: there exist unusual („complex“) plasmas which -are„non-ideal“, - often contain non-classical electrons, [- may contain other particles, chemically reactive] ContentsContents 1. Introduction: Examples of nonideal plasmas - White dwarf and neutron stars - matter at extreme density 2. Plasma physics approach to dense matter 3. Computer simulations of quantum plasmas StarsStars inin thethe MilkyMilky wayway Milky Way Central Bulge, viewed from the inside. It is a vast collection of more than 200 billion stars, planets, nebulae, clusters, dust and gas. StarsStars inin thethe MilkyMilky wayway Milky Way, Southern part, red emission nebulae, bright star clouds Sagittarius and Scorpius, Red giant Antares StarsStars sortedsorted:: schematicschematic Hertzsprung- Russel- Diagram StarsStars sortedsorted:: observationsobservations 22000 stars from the Hipparcos Catalogue together with 1000 low-luminosity stars (red and white dwarfs) from the Gliese Catalogue of Nearby Stars. Source: Wikipedia WhyWhy therethere areare differentdifferent StarsStars • All Stars contain the same matter as we know on Earth • Origin of different Stars: - different mixture of elements (composition) - different physical state of matter (temperature, density) - different physical processes (nuclear fusion) • All Stars undergo similar evolution (only few options) CompactCompact Stars:Stars: dwarfsdwarfs • There is a close connection between size R and mass M: 3 Example water: MR~ ρ = const R, M 2 R, 8 M Stars: The smaller a star, the larger its mass! MR~ −3 ρ ~ R−6 R/2, 8 M R, M WhiteWhite dwarfsdwarfs • Balance of gravity and Fermi pressure of electrons Chandrasekhar Limiting mass −3 10000km M ~ R 5000km Relativistic electrons 0.5M_sun 1.0M_s M SUN 6 −3 ~ρ 3 ~g 10 cm R EARTH Source: Wikipedia PicturePicture ofof aa whitewhite dwarfdwarf White dwarf in the planetary nebula NGC 2440 (“cocoon”) In center of Milky Way. The hottest star? Surface T~200,000K Credit: H. Bond (STSci), R. Ciardullo (PSU), WFPC2, HST, NASA WhatWhat isis insideinside aa whitewhite dwarfdwarf?? • Spectroscopy: Core: carbon, oxygen, … • Seismology: core crystalline White Dwarf in NGC 2440. 250 time brighter than our Sun Image: Hubble Space Telescope. InIn thethe newsnews ((BBCBBC 1616 FebFeb 20042004)) „Diamond star thrills astronomers“ „Twinkling in the sky is a diamond star „A diamond that is almost forever“ of 10 billion trillion trillion carats, astronomers have discovered.“ The cosmic diamond is a chunk of crystallised carbon, 4,000 km across, some 50 light-years from the Earth in the constellation Centaurus. It's the compressed heart of an old star that was once bright like our Sun but has since faded and shrunk. „The diamond star completely outclasses White Dwarf BPM 37093, the largest diamond on Earth, T. Metcalfe, Harvard-Smithsonian the 546-carat Golden Jubilee (South Africa).“ Astronomers have decided to call the star "Lucy" after the Beatles song Lucy in the Sky with Diamonds. DensityDensity ofof compactcompact starsstars M White Dwarfs: SUN 6 −3 ρ~WD 3 ~g 10 cm (M<1.4 M_sun) R EARTH M Neutron stars: SUN 15 −3 ρ NS ~ ~3 10g cm (M~1.4…2.1 M_sun) ( 10km ) M~2.1…3 M_sun: quark tars (?) • owH does matter behave at such extreme densities?? Æ The answer is given by plasma physics! OccurencesOccurences ofof PlasmaPlasma Contemporary Physics Education Project (CPEP)http://www.cpepweb.org/ White dwarfs Plasma theory of white dwarfs • Starting in the 1960s: Van Horn, DeWitt, Ichimaru, Chabrier… • At extreme densities matter is expected to be fully ionized… (?) • Energy of electron-ion plasma (neutral) in thermodynamic equilibrium: K – kinetic energy, G – gravitation, U – Coulomb interaction HKKGUUUi= e+ + e i+ + ee+ + ii ei Plasma theory of white warfsd K – kinetic G –energy, ravitation, U –g oulombC interaction HKKGUUUi= e+ + e i+ + ee+ + ii ei H n[0 M ( )]≈ const U (small) • Electrons exptected to be spatially homogeneous, quantum degenerate, weakly interacting • One-component plasma odelm OCP, jellium), TD equilibrium:( H T n−(,) H −0 Ue , back =i K + i U =1 i[ (K i + ,] Γ ) T n Æ Plasma state defined by single „coupling“ parameter Thermodynamics of OCP Classical „one-component plasma“ (OCP) |U | e2 Γ = = EKIN kB T r Liquid-solid transition below critical temperature (above critical coupling strength). 175Γcr ≈ ( 2D : 137 ) 2D MD simulation of OCP cooling/heating, Periodic b.c., Torben Ott Predicted by Wigner 1934 for the electron gas in metals. See lectures by P. Hartmann and T. Ott Wigner crystals in the laboratory Need: Ways to achieve: Γ ≥ Γ 1. cooling cr Γ = = ∝ |U | E KIN e 2 k T r e2 n 1 / 3 Ideal gas behavior B T Physically equivalent systems Strongly coupled plasma Wigner (Coulomb) crystal) White dwarfs Ion crystals in traps 1987 first realization in Paul trap and laser cooling (Ca, Mg,…) Bollinger et al. (NIST), Walther et al. (true 1-component plasma) Today many active groups in Innsbruck (Blatt), Aarhus (Drewsen)… Drewsen Ions in storage rings, U. Schramm, LMU München Ion crystals in traps (2) Applications: atomic physics, quantum optics, collective excitations, quantum computing… R. Blatt, Uni Innsbruck Measured oscillation of bi-crystal, Drewsen, Aarhus Wigner crystals – solution 2 Need: Ways to achieve: Γ ≥ Γ 1. cooling cr Γ = = ∝ 2. Charge |U | increase E KIN e 2 k T r e2 n 1 / 3 Ideal gas behavior B T Physically equivalent systems Strongly coupled plasma Wigner (Coulomb) crystal) dTrappe ions White dwarfs StronglyStrongly correlatedcorrelated CoulombCoulomb SystemsSystems |U | e2 e2 1 n / 3 Need: Γ ≥ Γcr Γ = = ∝ EKIN kB T r T Ways to achieve: 1. cooling 2. Charge increase „Dusty plasma“ Lectures on Monday, Tuesday dTrappe ions WignerWigner crystallizationcrystallization byby compressioncompression |U | e2 e2 1 n / 3 Need: Γ ≥ Γcr Γ = = ∝ EKIN kB T r T Ways to achieve: 1. cooling 2. Charge increase Dusty plasmas 3. compression semiconductors dTrappe ions MesoscopicMesoscopic quantumquantum CoulombCoulomb clustersclusters inin quantumquantum dotsdots Prediction of electron crystallization: A.Filinov, MB, Yu. Lozovik, PRL 86, 3851 (2001) quasi-2-dimensional system, First-principle path integral Monte Carlo results compression Density increase Æ quantum („cold“) melting of „crystal“ Phys. Rev. Focus (April 2001), Sciences et Avenir, Scientific American, FAZ 1.8. 2001… QuantumQuantum couplingcoupling parameterparameter Q r cr 2 2 1 / 3 Q |U | e e n 1− / 3 Need:Γ =rs ∝rs ≥ Γ = ~ ∝ ∝n a 2 / 3 B EKIN EF r n Quantum degeneracy χ= n 3 λ r DeBroglie wave length λ λh= / 2 mk π B T cr iFerm gas Wigner crystal Fermi iquidl 34rs ≈ ... 37D ( 2 ) Ceperley et al., A. Filinov, MB Universality of one-component plasmas OCP with same coupling parameter(s) show same behavior M. Bonitz, Physik Journal 7/8 (2002) „Artificial atoms“ (electrons in quantum dots) Noneq.-Green functions-Simulation: Lasse Rosenthal (length 0.001mm, T=1K) Classical 2D finite Coulomb Clusters „Mendeleyev table“ Length: 10mm, T~300K Dusty plasma experiments by A. Melzer et al. Summary: Universal behavior of OCP • classical plasma described by single parameter Γ • quantum OCP described by two parameters Application: Mapping of white dwarf properties on entirely different laboratory plasmas But: does the OCP model apply to real plasmas in stars?? Phase diagram of 2-comp. plasmas 157,000K Atoms, molecules ~1 Ryd weakly correlated! White Neutron dwarfs stars Plasma theory of white dwarfs (2) K – kinetic energy, G – gravitation, U – Coulomb interaction HKKGUUUi= e+ + e i+ + ee+ + ii ei Include: • Dynamics of electrons (no rigid background) • Formation of atoms, molecules; partial ionization • quantum and spin effects of electrons • quantum and spin effects of ions Need: Selfconsistent first-principle approach to equilibrium properties Æ quantum Monte Carlo Ultradense neutral plasmas 157,000K Atoms, molecules ~1 Ryd classical ion crystal + quantum electron gas Pressure ionization of atoms (Mott effect) Filinov, Bonitz, Fortov, JETP Letters 72, 245 (2000) ConditionsConditions forfor TCPTCP CoulombCoulomb crystalscrystals Additional parameters in TCP: mass, charge and temperature asymmetry m q T =M h,,Z =h Θe = me qe Th cr cr I. strong ion ouplingc (OCP)Γ: ≥h Γ175 ≅rsh , r s ≥100 ≅ (D 3 ) II. no Coulomb bound states: 3 Mott kT2 e≥ r B Ese, = r e/ a B ≤ r s 1 ≅ . 2 Analytical Results: Bonitz et al. PRL 95, 235006 (2005) 1. Classical system: 2 kT 2ΘZ2 / 3 Æ finite temperature anger orf crystal ro ≤e ≤ Æ minimum charge Z cr 3 EB Γ rse QuantumQuantum TCPTCP CoulombCoulomb crystalscrystals m q T mass, charge and temperature symmetrya =M h,,Z =h Θe = me qe Th AnalyticalAnalytical ResultsResults (2):(2): QuantumQuantum systemsystem M +1 3 • inite densityF range: Mott ⎛ ⎞ Mott n≤e n ≤⎜ ⎟ n ⎝ M cr +1⎠ r cr MMT≥cr() = s −1 • Critical mass ratio: e 4 / 3 Mott Z rs ()e T k T ZMΘ2 ( 1 + ) B e = 4 • Maximum temperature: cr cr EB Γ rs Applies o White dwarft tarss WhiteWhite dwarfdwarf starstar classical fluid and crystal in „quantum sea“ of electrons Size ~ our Earth Mass ~ our Sun Ædensity: 6 ≅ 10 ρρ ERDE D. Schneider, LLNL Diamond???Diamond??? „Diamond star thrills astronomers“ „A diamond that is almost forever“ Diamond: ρ ≈ 5.3 gcm−3 Melting point: 3820K White dwarf: ρ ≈106gcm− 3 TK≈106 Æ Crystal of bare C6+ nuclei! White Dwarf BPM 37093, T.
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