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

Outline  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  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 ?  Very Cold  Very Dense … in Phase Space  Typically nanoKelvin – microKelvin  Atoms/particles have velocity ~ mm/s – cm/s x p x p x p Different temperatures Same phase space density Higher phase space density mK μKμK nK

Ultra-cold Quantum Mechanics x p xx pp  fundamental unit of phase space volume Quantum mechanics requires  Quantum physics is important when Equivalent: deBroglie wavelength ~ inter-particle separation Quantum régime Boltzmann régime

EiEi NiNi 1 EFEF Quantum Statistics Bosons Fermions symmetric  symmetric multi-particle wavefunction.  Integer spin: photons, 87 Rb.  probability of occupying a state |i> with energy E i. anti-symmetric  anti-symmetric multi-particle wavefunction.  ½-integer spin: electrons, protons, neutrons, 40 K.  probability of occupying a state |i> with energy E i. EiEi NiNi N BEC

How do you make ULTRA-COLD matter? 1. Laser cooling  Doppler cooling  Magneto-Optical Trap (MOT) 1. Laser cooling  Doppler cooling  Magneto-Optical Trap (MOT) Two step process: 2. Evaporative cooling  Magnetic traps  Evaporation 2. Evaporative cooling  Magnetic traps  Evaporation

Doppler Cooling Lab frame v  Atom’s frame  Absorb a photon  atom gets momentum kick.  Repeat process at 10 7 kicks/s  large deceleration.  Emitted photons are radiated symmetrically  do not affect motion on average  Absorb a photon  atom gets momentum kick.  Repeat process at 10 7 kicks/s  large deceleration.  Emitted photons are radiated symmetrically  do not affect motion on average Lab frame, after absorption v-v recoil m/s m/s 2 87 Rb:  = -  I = I sat V doppler ~ 10 cm/s V recoil = 6 mm/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. z B,  ~10 G/cm ~14 MHz/cm

Magneto-Optical Trap (MOT)

quantum behavior thermal atoms Laser cooling PSD ??? ~ 100  K

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

Evaporative Cooling Wait time is given by the elastic collision rate k elastic = n  v Macro-trap: low initial density, evaporation time ~ s. Micro-trap: high initial density, evaporation time ~ 1-2 s. Remove most energetic (hottest) atoms Wait for atoms to rethermalize among themselves

Evaporative Cooling Remove most energetic (hottest) atoms Wait for atoms to rethermalize among themselves Wait time is given by the elastic collision rate k elastic = n  v Macro-trap: low initial density, evaporation time ~ s. Micro-trap: high initial density, evaporation time ~ 1-2 s. v P(v)

RF Evaporation  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. In a harmonic trap: B  B  RF

Outline  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  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 Evaporation Efficiency BEC thermal atoms magnetic trapping evap. cooling MOT PSD

87 Rb BEC MHz: N = 7.3x10 5, T>T c MHz: N = 6.4x10 5, T~T c MHz: N=1.4x10 5, T<T c

87 Rb BEC Surprise! Reach T c with only a 30x loss in number. (trap loaded with 2x10 7 atoms)  Experimental cycle = seconds MHz: N = 7.3x10 5, T>T c MHz: N = 6.4x10 5, T~T c MHz: N=1.4x10 5, T<T c

Fermions: Sympathetic Cooling Problem: Cold identical fermions do not interact due to Pauli Exclusion Principle.  No rethermalization.  No evaporative 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. Solution: add non-identical particles  Pauli exclusion principle does not apply. We cool our fermionic 40 K atoms sympathetically with an 87 Rb BEC. Fermi Sea “Iceberg” BEC

Sympathetic Cooling Cooling Efficiency

Below T F 0.9 T F 0.35 T F  For Boltzmann statistics and a harmonic trap,  For ultra-cold fermions, even at T=0,

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

Outline  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  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:  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 10 9 –  100+ years of spectroscopy.  Frequency measurements at Hz.  Ab initio calculable internal structure.

Past: Surprises with Rb-K cold collisions

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

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

Cross-Section Measurement T K40 (  K) Thermalization of 40 K with 87 Rb

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

Present: Atom Interferometry

IDEA: replace photon waves with atom waves.  atom  photon Example: 87 Rb v=1 m/s  atom  5 nm. green photon  photon  500 nm. 2 orders of magnitude increase in resolution at v=1 m/s !!! 2 orders of magnitude increase in resolution at v=1 m/s !!! Path A Path B Mach-Zender atom Interferometer: Measure a phase difference (  ) between paths A and B. D1 D2  AB can be caused by a difference in length, force, energy, etc …

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

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

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

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

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

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 B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

RF splitting of ultra-cold 87 Rb Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss Scan the RF magnetic field from 1.6 MHz to a final value B RF ~ 1 Gauss

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

Future: 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. 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. 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.  Model of particles moving on a lattice.  Simulates electrons moving in a crystal. Hopping term, kinetic energyParticle-particle interaction

Laser standing wave creates an optical lattice potential for atoms. Hopping term, t  control with laser intensity Feshbach Use a Feshbach resonance to control atom-atom interaction, U.  tune with a magnetic field. Optical Lattice

Bose-Hubbard Model IDEA: Put a BEC in a 3D optical lattice. Mott-Insulator transition  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). U/t~0U/t < 36U/t ~ 36U/t > 36 Greiner et al., Nature 415, (2002). Excellent agreement with theory !!! Fischer et al., Phys. Rev. B 40, 546 (1989). Jaksch et al., Phys. Rev. Lett (1998).

Fermi-Hubbard Model IDEA: do the same thing with fermions !!!  Put a degenerate Fermi gas in an optical lattice.  See what happens. IDEA: do the same thing with fermions !!!  Put a degenerate Fermi gas in an optical lattice.  See what happens. Theory: Very hard  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-T c materials n=filling fraction Hofstetter, Cirac, Zoller, Demler, Lukin Phys. Rev. Lett. 89, (2002). Figure from K. Madison, UBC.

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

Thywissen Group J. H. Thywissen S. Aubin M. H. T. Extavour A. Stummer S. MyrskogL. J. LeBlanc D. McKay B. Cieslak Staff/Faculty Postdoc Grad Student Undergraduate Colors: T. Schumm

Thank You