UltraCold Matter Technology Physics and Applications Seth A

Ultra-Cold Matter Technology Physics and Applications Seth A. M. Aubin University of Toronto, Canada June 15, 2006 NRC, Ottawa

Outline Ø Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Ø Physics Past: Past 40 K-87 Rb cross-section. Present: Present Matter-wave interferometry. Future: Future Constructing larger quantum systems.

What’s Ultra-Cold Matter ? m. K Ø Very Cold μK Typically nano. Kelvin – micro. Kelvin n. K Atoms/particles have velocity ~ mm/s – cm/s Ø 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 Dp x fundamental unit of phase space volume Dx Quantum physics is important when Equivalent: de. Broglie wavelength ~ inter-particle separation Quantum régime Boltzmann régime

Quantum Statistics Bosons Fermions Ø symmetric multi-particle wavefunction. Ø anti-symmetric multi-particle wavefunction. Ø Integer spin: photons, 87 Rb. Ø ½-integer spin: electrons, protons, neutrons, 40 K. Ø probability of occupying a state |i> with energy Ei. NBEC 1 Ni Ni Ei EF 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 v Atom’s frame Lab frame, after absorption v-vrecoil 2 87 Rb: = - m/s VØrecoil = 6 mm/s Absorb a photon atom gets momentum kick. I = Isat Ø Repeat process at 107 kicks/s large deceleration. Ø Emitted photons are radiated symmetrically Vdoppler ~ 10 docm/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 thermal atoms Laser cooling ~ 100 K 1 ? ? ? quantum behavior PSD

Magnetic Traps Interaction between external magnetic field and atomic magnetic moment: B For an atom in the hyperfine state Energy = minimum |B| = minimum

Micro-magnetic Traps Advantages of “atom” chips: Ø Very tight confinement. Ø Fast evaporation time. Ø photo-lithographic production. Ø Integration of complex trapping potentials. Ø Integration of RF, microwave and optical elements. Ø 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 B Ø RF frequency determines energy at which spin flip occurs. Ø Sweep RF between 1 MHz and 30 MHz. Ø Chip wire serves as RF B-field source.

Outline Ø Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Ø Physics Past: Past 40 K-87 Rb cross-section. Present: Present Matter-wave interferometry. Future: Future Constructing larger quantum systems.

Bose-Einstein Condensation of 87 Rb 10 -13 thermal atoms 10 -6 MOT magnetic trapping 1 evap. cooling 105 PSD BEC Evaporation Efficiency

87 Rb BEC RF@1. 740 MHz: RF@1. 725 MHz: RF@1. 660 MHz: N = 7. 3 x 105, T>Tc N = 6. 4 x 105, T~Tc N=1. 4 x 105, T<Tc

87 Rb BEC RF@1. 740 MHz: RF@1. 725 MHz: RF@1. 660 MHz: N = 7. 3 x 105, T>Tc N = 6. 4 x 105, T~Tc N=1. 4 x 105, T<Tc Surprise! Reach Tc with only a 30 x loss in number. (trap loaded with 2 x 107 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 40 K atoms sympathetically with an 87 Rb BEC. “Iceberg” BEC Fermi Sea

Sympathetic Cooling 104 102 100 10 2 104 106 108 105 106 107 Cooling Efficiency

Below TF 0. 9 TF Ø For Boltzmann statistics and a harmonic trap, Ø For ultra-cold fermions, even at T=0, 0. 35 TF

Pauli Pressure Fermi Boltzmann Gaussian Fit First time on a chip ! S. Aubin et al. Nature Physics 2, 384 (2006).

Outline Ø Intro to Ultra-cold Matter What is it ? How do you make it ? Bose-Einstein Condensates Degenerate Fermi Gases Ø Physics Past: Past 40 K-87 Rb cross-section. Present: Present Matter-wave interferometry. Future: Future Constructing larger quantum systems.

What’s Special about Ultra-cold Atoms ? Extreme Control: Ø Perfect knowledge (T=0). Ø Precision external and internal control with magnetic, electric, and electromagnetic fields. Interactions: Ø Tunable interactions between atoms with a Feshbach resonance. Ø Slow dynamics for imaging. Narrow internal energy levels: Ø Energy resolution of internal levels at the 1 part per 109 – 1014. Ø 100+ years of spectroscopy. Ø Frequency measurements at 103 -1014 Hz. Ø Ab initio calculable internal structure.

Past: Surprises with Rb-K cold collisions

Naïve Scattering Theory Collision Rates Rb-Rb Rb-K Sympathetic cooling should work really well !!! Sympathetic cooling 1 st try: Ø “Should just work !” -- Anonymous Ø Add 40 K to 87 Rb BEC No sympathetic cooling observed !

Experiment: Sympathetic cooling only works for slow evaporation Evaporation 3 times slower than for BEC

Cross-Section Measurement TK 40 ( K) Thermalization of 40 K with 87 Rb

What’s happening? Rb-K Effective range theory Rb-K Naïve theory Rb-Rb cross-section

Present: Atom Interferometry

Atom Interferometry IDEA: replace photon waves with atom waves. atom photon Example: 87 Rb atom @ v=1 m/s atom 5 nm. green photon 500 nm. 2 orders of magnitude increase in resolution at v=1 m/s !!! Mach-Zender atom Interferometer: Measure a phase difference ( ) between paths A and B. Path A Path B AB can be caused by a difference in length, force, energy, etc … D 1 D 2

Bosons and Fermions … again 1 st Idea: use a Bose-Einstein condensate Photons (bosons) 87 Rb (bosons) ü Laser has all photons in same “spatial mode”/state. ü BEC has all atoms in the same trap ground state. Identical bosonic atoms interact through collisions. PROBLEM Good for evaporative cooling. Bad for phase stability: interaction potential energy depends on density -- AB is unstable. Better Idea: Use a gas of degenerate fermions Ø Ultra-cold identical fermions don’t interact. AB is independent of density !!! Ø Small/minor reduction in energy resolution since E ~ EF. EF

RF beamsplitter How do you beamsplit ultra-cold atoms ? Energy h x

RF beamsplitter How do you beamsplit ultra-cold atoms ? Energy h x

RF beamsplitter How do you beamsplit ultra-cold atoms ? Energy h x

RF beamsplitter How do you beamsplit ultra-cold atoms ? Energy Position of well is determined by h rabi = Atom-RF coupling h x

Implementation figure from Schumm et al. , Nature Physics 1, 57 (2005).

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1. 6 MHz to a final value BRF ~ 1 Gauss

Interferometry Procedure: Ø Make ultra-cold atoms Ø Apply RF split Ø Turn off the trap Ø Probe atoms after a fixed time Time of Flight Ø Fringe spacing = (h TOF)/(mass splitting) Bosonic 87 Rb figures courtesy of T. Schumm

Future: Condensed Matter Simulations

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: Ø Atoms are more easily controlled and probed than electrons. Ø An optical lattice can simulate a defect-free crystal lattice. Ø All crystal and interaction parameters are easily tuned.

The Hubbard Model Ø Model of particles moving on a lattice. Ø Simulates electrons moving in a crystal. Hopping term, kinetic energy 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 3 D 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: Ø Very hard not yet solved analytically. Ø Numerical simulations are difficult due to Fermi Sign Problem. Computation is “NP hard”. d-wave superconductor ! Possible model for high-Tc materials Hofstetter, Cirac, Zoller, Demler, Lukin Phys. Rev. Lett. 89, 220407 (2002). n=filling fraction Figure from K. Madison, UBC.

Summary EF Ø Degenerate Bose-Fermi mixture on a chip. Ø Measured the 40 K-87 Rb cross-section. Ø Fermion Interferometry on a chip soon. Ø Condensed-matter simulations

Thywissen Group S. Aubin D. Mc. Kay B. Cieslak S. Myrskog M. H. T. Extavour A. Stummer T. Schumm Colors: Staff/Faculty Postdoc Grad Student Undergraduate L. J. Le. Blanc J. H. Thywissen

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