Quantum Physics & Ultra-Cold Matter Seth A. M. Aubin Dept. of Physics College of William and Mary December 16, 2009 Washington, DC

Outline  Quantum Physics: Particles and Waves  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  What can you do with ultra-cold matter

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense.

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense. 2. LIGHT behaves as both a PARTICLE and a WAVE.

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense. 2. LIGHT behaves as both a PARTICLE and a WAVE. 3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE.

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense. 2. LIGHT behaves as both a PARTICLE and a WAVE. 3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE. 4. If something is in 2 PLACES AT ONCE, then it will INTERFERE.

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense. 2. LIGHT behaves as both a PARTICLE and a WAVE. 3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE. 4. If something is in 2 PLACES AT ONCE, then it will INTERFERE. 5. Quantum physics is science’s most accurate theory.

Quantum Physics Summary or “take home message”: 1. It’s weird  defies everyday common sense. 2. LIGHT behaves as both a PARTICLE and a WAVE. 3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE. 4. If something is in 2 PLACES AT ONCE, then it will INTERFERE. 5. Quantum physics is science’s most accurate theory.

Quantum Accuracy Electron’s g-factor: g e = digits Theory and experiment agree to 9 digits. [Wikipedia, 2009]

LASER source Screen Light as a wave

LASER source Screen Light as a wave

LASER source Screen Light as a wave

Path B Path A  LASER source Light as a wave

screen LASER source Light as a wave

Also works for single photons !!! [A. L. Weiss and T. L. Dimitrova, Swiss Physics Society, 2009.] Experiment uses a CCD camera (i.e. sensor in your digital camera).

Photons follow 2 paths simultaneously screen LASER source path A path B

… but, Matter is a

Outline  Quantum Physics: Particles and Waves  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  What can you do with ultra-cold matter

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

How cold is Ultra-Cold? mK μKμK nK K 1000 K room temperature, 293 K Antarctica, ~ 200 K [priceofoil.org, 2008] Dilution refrigerator, ~ 2 mK Ultra-cold quantum temperatures

Ultra-cold Quantum Mechanics Quantum régime Room temperature Room temperature:  Matter waves have very short wavelengths.  Matter behaves as a particle. Ultra-Cold Quantum temperatures:  Matter waves have long wavelengths.  Matter behaves as a wave.

Quantum Statistics Bosons Fermions Integer spin: photons, 87 Rb. ½-integer spin: electrons, protons, neutrons, 40 K. Bose-Einstein Condensate (BEC) All the atoms go to the absolute bottom of trap. Degenerate Fermi Gas (DFG) Atoms fill up energy “ladder”.

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  Micro-magnetic traps  Evaporation 2. Evaporative cooling  Micro-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)

~ 100  K

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 [Figure by M. Extavour, U. of Toronto]

Evaporative Cooling 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)

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 ~ 500 nK

BEC History 1995: E. Cornell, C. Wieman, and W. Ketterle observe Bose- Einstein condensation in 87 Rb and 23 Na. 1924: S. N. Bose describes the statistics of identical boson particles. 1925: A. Einstein predicts a low temperature phase transition, in which particles condense into a single quantum state.

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 can cool fermionic 40 K atoms sympathetically with an 87 Rb BEC. Fermi Sea “Iceberg” BEC

Sympathetic Cooling “High” temperature Low temperature Quantum Behavior

Outline  Quantum Physics: Particles and Waves  Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases  What can you do with ultra-cold matter

Atom Interferometry Time-domain interferometry  atomic clock. Time-domain interferometry  atomic clock. Spatial interferometry  Precision measurements of forces. Spatial interferometry  Precision measurements of forces.

BEC Interferometry

Spatial 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 !!! Mach-Zender atom Interferometer: Path A Path B D1 D2

Atomic Clocks  Special type of atom interferometer.  Temporal interference, instead of spatial.  Most accurate time keeping devices that exist.  State-of-the-art: accuracy of 1 part in … 16 digits !!! Applications:  Keeping time.  GPS Navigation.  Deep space navigation.

Summary Quantum Physics  Quantum Physics. Ultra-cold atom technology  Ultra-cold atom technology. Matter-wave interferometry  Matter-wave interferometry.

Ultra-cold atoms group Prof. Seth Aubin Lab: room 15 Office: room 333 Megan Ivory Austin ZiltzJim Field Francesca Fornasini Yudistira Virgus Brian Richards

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