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Fundamental Physics with Ultra-Cold Matter From particle physics to condensed matter Seth A. M. Aubin University of Toronto, Canada March 27, 2006 University of Manitoba Outline Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Fundamental Physics Constructing larger quantum systems. Exploring interactions inside atoms. What’s Ultra-Cold Matter ? mK Very Cold μK Typically nanoKelvin – microKelvin nK Atoms/particles have velocity ~ mm/s – cm/s Very Dense … in Phase Space p p x Different temperatures Same phase space density p x x Higher phase space density Ultra-cold Quantum Mechanics Quantum mechanics requires p Dx Dp /2 Dp fundamental unit of phase space volume x Dx Dp /2 Dx Quantum physics is important when PSD ~ 1 Equivalent: deBroglie wavelength ~ inter-particle separation ndeBroglie ~ 1 Boltzmann Quantum régime régime Quantum Statistics Bosons Fermions symmetric multi-particle wavefunction. anti-symmetric multi-particle wavefunction. Integer spin: photons, 87Rb. ½-integer spin: electrons, protons, neutrons, 40K. probability of occupying a state |i> with energy Ei. P( Ei ) probability of occupying a state |i> with energy Ei. 1 e ( Ei ) / kT P( Ei ) 1 NBEC 1 Ni Ni Ei EF 1 e ( Ei ) / kT 1 Ei How do you make ULTRA-COLD matter? Two step process: 1. Laser cooling Doppler cooling Magneto-Optical Trap (MOT) 2. Evaporative cooling Magnetic traps Evaporation Doppler Cooling Lab frame excited v ground Atom’s frame ' ' Lab frame, after absorption v-vrecoil 2 87Rb: = - m/s Vrecoil = 6 mm/s Absorb a photon atom gets k momentum kick. I = Isat Repeat process at 107 kicks/s large deceleration. Emitted photons are radiated symmetrically Vdoppler ~10docm/s not affect motion on average m/s Magneto-Optical Trap (MOT) Problem: Doppler cooling reduces momentum spread of atoms only. Similar to a damping or friction force. Does not reduce spatial spread. Does not confine the atoms. Solution: Spatially tune the laser-atom detuning with the Zeeman shift from a spatially varying magnetic field. B, z ~10 G/cm ~14 MHz/cm Magneto-Optical Trap (MOT) Magneto-Optical Trap (MOT) 10-13 10-6 1 thermal atoms Laser cooling quantum behavior ~ 100 K ??? PSD Magnetic Traps Interaction between external magnetic field and atomic magnetic moment: U B B For an atom in the hyperfine state F, mF cos mF / F Energy = minimum U g F mF B B |B| = minimum Micro-magnetic Traps Advantages of “atom” chips: Very tight confinement. Fast evaporation time. photo-lithographic production. Integration of complex trapping potentials. Integration of RF, microwave and optical elements. Single vacuum chamber apparatus. Iz Evaporative Cooling Remove most energetic (hottest) atoms Wait for atoms to rethermalize among themselves Wait time is given by the elastic collision rate kelastic = n v Macro-trap: low initial density, evaporation time ~ 10-30 s. Micro-trap: high initial density, evaporation time ~ 1-2 s. Evaporative Cooling Remove most energetic (hottest) atoms P(v) Wait for atoms to rethermalize among themselves Wait time is given by the elastic collision rate kelastic = n v Macro-trap: low initial density, evaporation time ~ 10-30 s. Micro-trap: high initial density, evaporation time ~ 1-2 s. v RF Evaporation In a harmonic trap: B RF ERF B RF frequency determines energy at which spin flip occurs. Sweep RF between 1 MHz and 30 MHz. Chip wire serves as RF B-field source. Outline Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Fundamental Physics Constructing larger quantum systems. Exploring interactions inside atoms. Bose-Einstein Condensation of 87Rb 10-13 thermal atoms 10-6 MOT magnetic trapping 105 1 evap. cooling PSD BEC Evaporation Efficiency d ln(PSD) 3.95 0.1 d ln(N) 87Rb BEC [email protected] MHz: [email protected] MHz: [email protected] MHz: N = 7.3x105, T>Tc N = 6.4x105, T~Tc N=1.4x105, T<Tc 87Rb BEC [email protected] MHz: [email protected] MHz: [email protected] MHz: N = 7.3x105, T>Tc N = 6.4x105, T~Tc N=1.4x105, T<Tc Surprise! Reach Tc with only a 30x loss in number. (trap loaded with 2x107 atoms) Experimental cycle = 5 - 15 seconds Fermions: Sympathetic Cooling Problem: Cold identical fermions do not interact due to Pauli Exclusion Principle. No rethermalization. No evaporative cooling. Solution: add non-identical particles Pauli exclusion principle does not apply. We cool our fermionic 40K atoms sympathetically with an 87Rb BEC. “Iceberg” BEC Fermi Sea Sympathetic Cooling of fermionic 40K with bosonic 87Rb 104 Phase Space Density 102 100 105 106 107 Cooling Efficiency 10-2 10-4 10-6 10-8 Atom Number D ln(PSD) 8 D ln(N) Below TF 0.9 TF 0.35 TF For Boltzmann statistics and a harmonic trap, For ultra-cold fermions, even at T=0, 1 2 1 2 mv2 12 kT v T mv EF 2 EF vF 2 m Pauli Pressure Fermi Boltzmann Gaussian Fit First time on a chip ! arXiv: cond-mat/0512518 Outline Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Fundamental Physics Constructing larger quantum systems. Exploring interactions inside atoms. So What ? What can you do with ultra-cold atoms ? Larger ultra-cold quantum systems: Condensed matter physics Ultra-cold chemistry Probe fundamental forces inside the atom: Parity violation in atoms and molecules Electron-dipole moment measurements Applied Physics: Atomic clocks Matter-wave interferometry What’s Special about Ultra-cold Atom ? Extreme Control: Perfect knowledge (T=0). Precision external and internal control with magnetic, electric, and electromagnetic fields. Interactions: Tunable interactions between atoms with a Feshbach resonance. Slow dynamics for imaging. Narrow internal energy levels: Energy resolution of internal levels at the 1 part per 109 – 1014. 100+ years of spectroscopy. Frequency measurements at 103-1014 Hz. Ab initio calculable internal structure. Condensed Matter Simulations IDEA: use ultra-cold atoms to simulate electrons in a crystal. useful if condensed matter experiment is difficult or theory is intractable. Advantages: Atoms are more easily controlled and probed than electrons. An optical lattice can simulate a defect-free crystal lattice. All crystal and interaction parameters are easily tuned. The Hubbard Model Model of particles moving on a lattice. Simulates electrons moving in a crystal. H t a {i , j }, i , a j , ai , a j , U ai, ai , ai, ai , Hopping term, kinetic energy i Particle-particle interaction Optical Lattice Laser standing wave creates an optical lattice potential for atoms. Hopping term, t control with laser intensity Use a Feshbach resonance to control atom-atom interaction, U. tune with a magnetic field. Bose-Hubbard Model IDEA: Put a BEC in a 3D optical lattice. Look for Mott-Insulator transition by varying ratio U/t. Gas undergoes a quantum phase transition from a superfluid to an insulating state at U/t ~ 36 (cubic lattice). Excellent agreement with theory !!! Fischer et al., Phys. Rev. B 40, 546 (1989). U/t~0 U/t < 36 U/t ~ 36 U/t > 36 Greiner et al., Nature 415, 39-44 (2002). Jaksch et al., Phys. Rev. Lett. 3108 (1998). Fermi-Hubbard Model IDEA: do the same thing with fermions !!! Put a degenerate Fermi gas in an optical lattice. See what happens. Theory: Very hard not yet solved analytically. Numerical simulations are difficult due to Fermi Sign Problem. Computation is “NP hard”. d-wave superconductor ! Possible model for high-Tc materials n=filling fraction Hofstetter, Cirac, Zoller, Demler, Lukin Phys. Rev. Lett. 89, 220407 (2002). Figure from K. Madison, UBC. Fundamental Interactions in atoms and molecules Fundamental Interactions: Weak Interaction Parity Violation. Nuclear anapole moment. ? Electron-neutrino correlations in -decay. Time-reversal symmetry breaking Searching for Super-symmetric extensions of the Standard Model. Use a big accelerator … or Exotic atoms and molecular states: Rare or artificial isotopes (Francium, Potassium isomer, etc…). Polar molecules … larger molecules. Cold and ultra-cold atoms are very useful. What’s Parity Violation ? d2r d 2 ( r) F ma m 2 m F 2 dt dt Parity transformation: x x Force is parity odd y y z z 2 P e H 2m R 2 ( P) e H 2m R Energy or Hamiltonian is parity even. z x x y Right-handed coordinate system y z Left-handed coordinate system Physics does not change, except for sign “I'll bet you only fifty to one you don't find anything.” -- Richard Feynman to Norman Ramsey, on a proposed experiment to search for Parity Violation (1956). A Brief History of Parity Violation Early 1956: Feynman bets against Parity Violation. October 1956: T.-D. Lee and C. N. Yang propose that Parity may be violated. January 1957: C.-S. Wu, E. Ambler, R. Hudson, R. Hayward, and D. Hoppes observe parity violation in the -decay of spin polarized Cobalt-60. 1957: T.-D. Lee and C. N. Yang win the Nobel Prize in Physics for the discovery of Parity Violation. -decay through W-- charged electroweak current Weak Neutral Currents in Atoms 1974: M.-A. Bouchiat and C. Bouchiat note that in heavy atoms: 3 S S P , with Z PV Spin independent effect! Z = # of protons Nuclear Anapole Moment: Z2.7 H anapole I P parity odd Spin dependent effect! ~ 10-10 in Francium (really small !) Use a parity-forbidden transition! “If it were really impossible, they wouldn’t have bothered to forbid it.” -- Eric Cornell, paraphrasing Joseph Heller. nS nS E1 transitio n Parity forbidden transition Parity Violation Slightly allowed transition Atomic Physics Contribution P.L. Anthony et al. (SLAC E158 collaboration), Phys. Rev. Lett. 95, 081601 (2005). Intro to Francium Properties: Z = 87, heaviest alkali. Least stable of first 103 elements. Fr Half-life ~ 1-20 minutes. Artificially produced by nuclear fusion reaction 18 O + @ 100 MeV Au Fr 215 neutrons Francium MOT PROBLEM: Accelerator produces only 106 Fr atoms/s. Very difficult to work with. SOLUTION: Attach a Francium Magneto-Optical Trap to the accelerator. Cold Francium is concentrated in ~1 mm3 volume. With T < 100 K, Doppler broadening is negligible. Long integration times. Minimally perturbative environment (substrate free). Francium MOT PROBLEM: Accelerator produces only 106 Fr atoms/s. Very difficult to work with. SOLUTION: Attach a Francium Magneto-Optical Trap to the accelerator. Cold Francium is concentrated in ~1 mm3 volume. With T < 100 K, Doppler broadening is negligible. Long integration times. Minimally perturbative environment (substrate free). MOT collection efficiency ~ 1 % MOT with ~105 210Fr atoms S. A. et al., Rev. Sci. Instrum. 74, 4342 (2003). Nuclear Anapole Moment Nuclear anapole moment via parity violation Unique probe of neutral current electroweak interactions inside nucleus. Anapole was first measured in Cesium by the Wieman group Wood et al. Science 275, 1759 (1997). Meson-nucleon couplings [Figure from G. Gwinner, U. of Manitoba.] Parity Violation Atoms vs. Molecules Atoms Molecules Measure a “forbidden” parityviolating transition rate. Can also measure parity violating energy splitting. 114 (?) elements available. Chiral molecules are common. Easy to cool to ultra-cold temperatures. Possible to cool to ultra-cold temperatures. Easy to interpret parity violating signals. Larger signals parity violating signals. Ultra-cold Chiral Molecules Chiral Molecules: need at least 4 atoms (example: H2O2). Parity violating energy splitting DE ~ 0.001–10,000 Hz. Favorable scaling: DE Z5. Extremely high energy resolution required ultra-cold molecules. Right-handed H2O2 Left-handed H2O2 Summary Ultra-cold Matter BEC, Degenerate Fermions. Cooling and Trapping MOT, B-trap, evaporative cooling. Fermi-Hubbard model Parity violation and anapole moment TRIUMF FrPNC collaboration TRIUMF – Vancouver, Canada Professor G. Gwinner, Spokesperson, University of Manitoba Professor G. D. Sprouse, SUNY Stony Brook Dr. J. A. Behr, Research Scientist, TRIUMF Dr. K. P. Jackson, Research Scientist, TRIUMF Dr. M. R. Pearson, Research Scientist, TRIUMF Professor L. A. Orozco, University of Maryland Professor V. V. Flambaum, University of New South Wales Dr. S. Aubin, Post-Doctoral Fellow, University of Toronto Thywissen Group S. Aubin D. McKay B. Cieslak M. H. T. Extavour S. Myrskog A. Stummer Colors: Staff/Faculty Postdoc Grad Student Undergraduate L. J. LeBlanc J. H. Thywissen Thank You