Ultra-Cold Matter TechnologyUltra-Cold Matter Technology

Physics and ApplicationsPhysics and Applications

Seth A. M. Aubin

University of Toronto, Canada

June 15, 2006

NRC, Ottawa

OutlineOutline

Intro to Ultra-cold Matter

What is it ?

How do you make it ?

Bose-Einstein Condensates Degenerate Fermi Gases

Physics

PastPast: 40K-87Rb cross-section.

PresentPresent: Matter-wave interferometry.

FutureFuture: Constructing larger quantum systems.

Path A

Path A

Path A

Path A

Path A

Path A

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

Ultra-cold Quantum MechanicsUltra-cold Quantum Mechanics

x

p

x

p

/2 px fundamental unit of phase space volume

Quantum mechanics requires

/2 px

Quantum physics is important when 1 ~ PSD

Equivalent:

deBroglie wavelength ~ inter-particle separation

1~deBroglien

Quantum régimeBoltzmann régime

Ei

Ni

1

EF

Quantum StatisticsQuantum Statistics

BosonsBosons FermionsFermions

symmetricsymmetric multi-particle wavefunction.

Integer spin: photons, 87Rb.

probability of occupying a state |i> with energy Ei.

1

1)( /)( kTEi ie

EP

anti-symmetricanti-symmetric multi-particle wavefunction.

½-integer spin: electrons, protons, neutrons, 40K.

probability of occupying a state |i> with energy Ei.

1

1)( /)( kTEi ie

EP

Ei

Ni

NBEC

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

Magnetic traps

Evaporation

2. Evaporative cooling

Magnetic traps

Evaporation

Doppler CoolingDoppler CoolingLab frame

vground

excited

Atom’s frame

' '

Absorb a photon atom gets momentum kick.

Repeat process at 107 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 107 kicks/s large deceleration.

Emitted photons are radiated symmetrically do not affect motion on average

k

Lab frame, after absorption

v-vrecoil

m/s

m/s2 87Rb: = - I = Isat

Vdoppler ~ 10 cm/s

Vrecoil = 6 mm/s

Magneto-Optical Trap (MOT)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.

zB,

~10 G/cm~14 MHz/cm

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

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

quantumbehavior

thermalatoms

Lasercooling

10-13 110-6PSD

???

~ 100 K

Magnetic TrapsMagnetic Traps

B

U

B

Interaction between external magnetic field and atomic magnetic moment:

For an atom in the hyperfine state

F,mF

BmgU BFF

cos mF / F

Energy = minimum |B| = minimum

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

Evaporative CoolingEvaporative Cooling

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.

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)

RF EvaporationRF 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:In a harmonic trap:

B

B

RF

RFE

OutlineOutline

Intro to Ultra-cold Matter

What is it ?

How do you make it ?

Bose-Einstein Condensates Degenerate Fermi Gases

Physics

PastPast: 40K-87Rb cross-section.

PresentPresent: Matter-wave interferometry.

FutureFuture: Constructing larger quantum systems.

Path A

Path A

Path A

Path A

Path A

Path A

Bose-Einstein Condensation of Bose-Einstein Condensation of 8787RbRb

1.095.3ln(N)

ln(PSD)

d

d

Evaporation Efficiency

BECthermalatoms

magnetictrapping

evap.coolingMOT

10-13 110-6 105

PSD

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

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 cool our fermionic 40K atoms sympathetically with an 87Rb BEC.We cool our fermionic 40K atoms sympathetically with an 87Rb BEC. Fermi

Sea

“Iceberg”BEC

Sympathetic CoolingSympathetic Cooling

8ln(N)

ln(PSD)

Cooling EfficiencyCooling Efficiency

108

106

104

102

100

102

104

105 106 107

108

106

104

102

100

102

104

105 106 107

108

106

104

102

100

102

104

105 106 107

Below TBelow TFF

0.9 TF0.9 TF0.35 TF0.35 TF

For Boltzmann statistics and a harmonic trap,

For ultra-cold fermions, even at T=0,

TvkTmv 212

21

m

EvEmv F

FF 2221

Fermi

Boltzmann

Gaussian Fit

Pauli PressurePauli Pressure

First time on a chip !S. Aubin et al.

Nature Physics 2, 384 (2006).

OutlineOutline

Intro to Ultra-cold Matter

What is it ?

How do you make it ?

Bose-Einstein Condensates Degenerate Fermi Gases

Physics

PastPast: 40K-87Rb cross-section.

PresentPresent: Matter-wave interferometry.

FutureFuture: Constructing larger quantum systems.

Path A

Path A

Path A

Path A

Path A

Path A

What’s Special aboutWhat’s Special aboutUltra-cold Atoms ?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 109 – 1014.

100+ years of spectroscopy.

Frequency measurements at 103-1014 Hz.

Ab initio calculable internal structure.

Past:Past:

Surprises with Rb-KSurprises with Rb-K

cold collisionscold collisions

Naïve Scattering TheoryNaïve Scattering Theory

Sympathetic cooling 1Sympathetic cooling 1stst try: try: “Should just work !” -- Anonymous

Add 40K to 87Rb BEC No sympathetic cooling observed !

Sympathetic cooling 1Sympathetic cooling 1stst try: try: “Should just work !” -- Anonymous

Add 40K to 87Rb BEC No sympathetic cooling observed !

RbRbRbRbRbRbRb vn

Rb-RbRb-Rb

Collision RatesCollision Rates

28 RbRba

nm 238.5RbRba

RbKRbKRbRbK vn

Rb-KRb-K

24 RbKa

nm 8.10RbKa

7.2RbRb

RbK

Sympathetic cooling Sympathetic cooling should work really well !!!should work really well !!!

Experiment: Experiment:

Sympathetic cooling only worksSympathetic cooling only works

for for slowslow evaporation evaporation

10-8

10-6

10-4

10-2

100

102

104

105 106 107

Atom Number

Pha

se S

pace

Den

sity

10-8

10-6

10-4

10-2

100

102

104

105 106 107

10-8

10-6

10-4

10-2

100

102

104

10-8

10-6

10-4

10-2

100

102

104

10-8

10-6

10-4

10-2

100

102

104

105 106 107105 106 107

Atom Number

Pha

se S

pace

Den

sity

Evaporation 33 times slower than for BEC

Evaporation 33 times slower than for BEC

Cross-Section MeasurementCross-Section Measurement

TK

40 (K

)

Thermalization of 40K with 87Rb

What’s happening?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:Present:Atom InterferometryAtom Interferometry

Atom InterferometryAtom 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 !!!

Path A

Path B

Mach-Zender atom Interferometer: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 … againBosons and Fermions … again1st Idea: use a Bose-Einstein condensate1st Idea: use a Bose-Einstein condensate

Photons (bosons) 87Rb (bosons)

Laser has all photons in same “spatial mode”/state.

BEC has all atoms in the same trap ground state.

PROBLEMPROBLEM

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 fermionsBetter Idea: Use a gas of degenerate fermionsBetter Idea: Use a gas of degenerate fermionsBetter 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 ~ EF .

EF

RF beamsplitterRF beamsplitter

How do you beamsplit ultra-cold atoms ?How do you beamsplit ultra-cold atoms ?

x

Energy

h

RF beamsplitterRF beamsplitter

x

Energy

How do you beamsplit ultra-cold atoms ?How do you beamsplit ultra-cold atoms ?

h

RF beamsplitterRF beamsplitter

x

Energy

How do you beamsplit ultra-cold atoms ?How do you beamsplit ultra-cold atoms ?

h

RF beamsplitterRF beamsplitter

x

Energy

How do you beamsplit ultra-cold atoms ?How do you beamsplit ultra-cold atoms ?

h

hrabi =Atom-RF couplinghrabi =Atom-RF coupling

Position of well is

determined by Position of well is

determined by

ImplementationImplementation

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

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

RF splitting of ultra-cold RF splitting of ultra-cold 8787RbRb

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

Scan the RF magnetic field from 1.6 MHz to a final value

BRF ~ 1 Gauss

InterferometryInterferometry

Procedure:Procedure: Make ultra-cold atoms

Apply RF split

Turn off the trap

Probe atoms after a fixed time Time of Flight

Fringe spacingFringe spacing = (h TOF)/(mass splitting)

Procedure:Procedure: Make ultra-cold atoms

Apply RF split

Turn off the trap

Probe atoms after a fixed time Time of Flight

Fringe spacingFringe spacing = (h TOF)/(mass splitting)

Bosonic 87Rb figures courtesy of T. Schumm

Future:Future:

Condensed Matter SimulationsCondensed Matter Simulations

Condensed Matter SimulationsCondensed 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 ModelThe Hubbard Model

i

iiiiji

jiji aaaaUaaaatH,,,,

},,{,,,,

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 energy Particle-particle interaction

Laser standing wave creates an optical lattice potential for atoms.

Laser standing wave creates an optical lattice potential for atoms.

Hopping term, t

control with laser intensity

Use a FeshbachFeshbach resonance to control atom-atom interaction, U.

tune with a magnetic field.

Optical LatticeOptical Lattice

Bose-Hubbard ModelBose-Hubbard Model

IDEA: Put a BEC in a 3D optical lattice.

Look for Mott-Insulator transitionMott-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~0 U/t < 36 U/t ~ 36 U/t > 36

Greiner et al., Nature 415, 39-44 (2002).

Excellent agreement with theory !!!

Fischer et al., Phys. Rev. B 40, 546 (1989).

Jaksch et al., Phys. Rev. Lett. 3108 (1998).

Fermi-Hubbard ModelFermi-Hubbard ModelIDEA: 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:Theory: Very hardVery 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 fractionHofstetter, Cirac, Zoller, Demler, LukinPhys. Rev. Lett. 89, 220407 (2002). Figure from K. Madison, UBC.

SummarySummary

Degenerate Bose-Fermi mixtureBose-Fermi mixture on a chip.

Measured the 40K-87Rb cross-section.

Fermion InterferometryFermion Interferometry on a chip soon.

Condensed-matter simulationsCondensed-matter simulations.

EF

Thywissen GroupThywissen Group

J. H. Thywissen

S. Aubin M. H. T. Extavour

A. StummerS. Myrskog

L. J. LeBlanc

D. McKay

B. Cieslak

Staff/FacultyPostdocGrad StudentUndergraduate

Colors:

T. Schumm

Thank You