Quantum PhysicsQuantum Physics&&

Ultra-Cold MatterUltra-Cold Matter

Seth A. M. Aubin

Dept. of Physics

College of William and Mary

December 16, 2009

Washington, DC

OutlineOutline

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: ge = 2.002 319 304 362

12-digits

Theory and experiment agree to 9 digits.

[Wikipedia, 2009]

LASER source

Screen

Light as a waveLight as a wave

LASER source

Screen

Light as a waveLight as a wave

LASER source

Screen

Light as a waveLight as a wave

Path B

Path A

LASER source

Light as a waveLight as a wave

an

gle

Intensity

ang

le

ang

le

Intensity

screen

LASERsource

Light as a waveLight as a wave

Also works for single photons !!!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

Photons follow 2 paths simultaneously

an

gle

Intensity

ang

le

ang

le

Intensity

screen

LASERsource

path A

path B

… but, Matter is a

OutlineOutline

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 ?What’s Ultra-Cold Matter ?

Very Cold Very Cold

Very Dense … in Phase SpaceVery Dense … in Phase Space

Typically nanoKelvin – microKelvin

Atoms/particles have velocity ~ mm/s – cm/s

x

p

x

p

x

p

Different temperaturesSame phase space density Higher

phase space density

mK

μK

nK

How cold is Ultra-Cold?How cold is Ultra-Cold?

mK

μK

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 MechanicsUltra-cold Quantum Mechanics

Quantum régimeRoom 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 StatisticsQuantum Statistics

BosonsBosons FermionsFermions

Integer spin: photons, 87Rb. ½-integer spin: electrons, protons, neutrons, 40K.

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?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

Magneto-Optical Trap (MOT)Magneto-Optical Trap (MOT)

~ 100 K

Micro-magnetic TrapsMicro-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

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

Evaporative CoolingEvaporative Cooling

Macro-trap: low initial density, evaporation time ~ 10-30 s.

Micro-trap: high initial density, evaporation time ~ 1-2 s.

Remove most energetic (hottest) atoms

Wait for atoms to rethermalize among

themselves

Evaporative CoolingEvaporative 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.

v

P(v)

8787Rb BECRb BECRF@1.740 MHz:

N = 7.3x105, T>Tc

RF@1.725 MHz:

N = 6.4x105, T~Tc

RF@1.660 MHz:

N=1.4x105, T<Tc

8787Rb BECRb BEC

Surprise! Reach Tc with only a 30x loss in number.

(trap loaded with 2x107 atoms)

Experimental cycle = 5 - 15 seconds

RF@1.740 MHz:

N = 7.3x105, T>Tc

RF@1.725 MHz:

N = 6.4x105, T~Tc

RF@1.660 MHz:

N=1.4x105, T<Tc

~ 500 nK~ 500 nK

BEC HistoryBEC History

1995:E. Cornell, C. Wieman, and W. Ketterle observe Bose-Einstein condensation in 87Rb and 23Na.

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 CoolingFermions: 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 40K atoms sympathetically with an 87Rb BEC.We can cool fermionic 40K atoms sympathetically with an 87Rb BEC. Fermi

Sea

“Iceberg”BEC

Sympathetic CoolingSympathetic Cooling

“High” temperature

Low temperature

Quantum Behavior

OutlineOutline

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 InterferometryAtom Interferometry

Time-domain interferometryTime-domain interferometry

atomic clock.

Time-domain interferometryTime-domain interferometry

atomic clock.

Spatial interferometrySpatial interferometry

Precision measurements of forces.

Spatial interferometrySpatial interferometry

Precision measurements of forces.

BEC InterferometryBEC Interferometry

Spatial Atom InterferometrySpatial Atom Interferometry

IDEA: replace photon waves with atom waves.

atom photon

Example: 87Rb atom @ v=1 m/s atom 5 nm.

green photon photon 500 nm.

2 orders of magnitude increase in resolutionat v=1 m/s !!!

2 orders of magnitude increase in resolutionat v=1 m/s !!!

Mach-Zender atom Interferometer:Mach-Zender atom Interferometer:

Path A

Path B

D1

D2

Atomic ClocksAtomic 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 1016 … 16 digits !!!

Applications: Keeping time.

GPS Navigation.

Deep space navigation.

SummarySummary

Quantum PhysicsQuantum Physics.

Ultra-cold atom technologyUltra-cold atom technology.

Matter-wave interferometryMatter-wave interferometry.

Ultra-cold atoms groupUltra-cold atoms group

Prof. Seth Aubin

Lab: room 15Office: room 333saaubi@wm.edu

Megan Ivory Austin Ziltz Jim Field

Francesca Fornasini

Yudistira Virgus

Brian Richards

Thywissen GroupThywissen Group

J. H. Thywissen

M. H. T. Extavour

A. StummerS. Myrskog

L. J. LeBlancD. McKay B. Cieslak

Staff/FacultyPostdocGrad StudentUndergraduate

Colors:

T. Schumm