Outline -...

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Ultra-cold Trapped Atomic Gases

Outline What are They? Why are they Interesting? How are they Produced? Experiments, Calculations, Results Some Applications

Zehra AkdenizPiri Reis Üniversitesi

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What – Why Quantum Mechanics

Quantum Mechanics on a Macroscopic Scale

Dilute gasses Carefully chosen atomic species

Lithium, Potassium, Rubidium,.. Contained Cooled

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Colder t han Out er Spac e

The cosmic microwave background (Left over from the ‘big bang’) has a temperature of about 2.7K. This is the temperature in the depths of outer space.

At about 1/30,000,000 of this temperature (100nK) certain atoms can start to exist in exactly the same place at the same time. They exhibit literally visible quantum mechanical effects. A condensate of Bosons.

Other atoms never occupy exactly the same state no matter how cold they get, the Fermions, but exhibit their own kind of ‘quantum degeneracy’.

Bose-Einstein

FermiDirac

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Why Worldwide Interest

"Advanced Research Projects" , European Network of research sponsored by the European Community : research groups in Western and Central Europe.

Besides being at the current frontier in fundamental physical research , these studies hold promise of wholly novel technical achievements in regard to the construction of matter-wave lasers and to the development of quantum computing methods.

More recently a strong interest has also arisen in ultracold gases of fermionic isotopes, the main aim being the realization of novel superfluid states of matter.

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What Basic Thermodynamics

BE Distribution is εi energy µ chemical potential T temperature k Boltzman’s constant Tc Critical temperature

At Tc λ=(2πmkT)-1/2

Implies conditions on density, ρ, and T

11/)( −

∝ − kTi ien µε

cTT ≥

cTT ≤ni

εi

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What Phase Space Diagram

BEC

Vapour

Liquid/Solid

Log(ρ)

Log(T)

Forbidden region

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How Cooling

Start at high T, low density Low density=>

• No 3 body collisions• No nucleation centres• Metastable homogeneous gas in BEC region of the

Temperature/density diagram Then cool, but

required T ≈ 100nK required ρ ≈ 1013 /cm3

Laser Cool and trap Switch to magnetic trap Cool evapouratively

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How Laser Cooling & Trapping

Use Doppler effect toSelectively absorbphotonsX

γ νν =′

σRandomRe-emission⇒ on averageSlowed in direction of motion

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How Laser Cooling and Trapping

X

ZY

By using six laserbeams organised tocool in all directionsan ‘optical molasses’is created

KTmhp 510−≈→= ν

ρ ≈ 1011 /cm3

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How Magnetic Trap

The lasers are turned off The atoms spin polarised An inhomogeneous B field applied

Axially symmetric, harmonic TOP,IP Dipole attracted to local minima

for moments parallel to B Repelled if anti-parallel

(& therefore lost from the trap

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How Evapourative Cooling

Like sweating Liquid -> gas =>

• <energy> in water molecule evapouratedis greater than <energy>, so the meandecreases as molecules are evapourated

Efficient, 2% molecule loss gives 20% decrease in temperature in remaining molecules

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How Evapourative Cooling

Energy of spin-fliptransition is positiondependent, so anRF field, tuned toflip the spin of onlyhigh energy atomsis applied. The RFis reduced in freqover a period of timeto effect the cooling

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How Fermion cooling

Evapourative cooling relies on thermalisation, ie elastic collisions between atoms.

Identical fermions cannot scatter in an s-wave and so cannot thermalise fast enough for the ‘simple’ form of this process to work.

Fermions can be cooled sympathetically by a second species, either of fermions or bosons, or by using a single species in a mixture of hyperfine sub-states.

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What Condensed States

The degenerate Fermion states are more spatially extended than the condensed Bosons.

Ef

Fermi temperature, Tf = Ef /kB

At about Tf/2, λ ≈ d

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How Trap Frequencies

The Fermi temperature depends on the details of the trap, and is characterised by the geometric mean of the trap frequencies.

( )( ) 3/16/ FBF NkhT ω=

( ) 3/12raxωωω =

( ) ( ) 3/12.1// BBC NkhT ϖ=

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What - Condensation

Achieving Bose-Einstein condensation in confined gases of the bosonic isotopes of Rb and Na in 1995Won a Nobel Prize in 2001 for

Cornel, Ketterle and Wieman

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Why Interest

Basic physics – there are few examples of quantum states with macroscopic dimensions – help explore the limits of quantum physics

Atom ‘lasers’ Precision metrology Superconductivity Cosmology Quantum Computing

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Applications – Optical Lattice

Multiple, phase-locked lasers can be used to set up an interference pattern with regions of high and low intensity.

In 2D or 3D this is called an optical lattice. Its like an artificial crystal that can be controlled.

Cooled atoms can now be transferred to such a lattice in large numbers.

Mott Insulator – ‘qbits’

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Applications Quantum Computing

Free to tunnel – single largecoherent matter wave. Whenreleased from trap and measuredinterference patterns are seen.

Isolated by higher potentialatoms become incoherent andshow no interference whenreleased from trap.

State dependentoptical potentialused to producephase gates.

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Applications – Super-fluidity/conductivity

High temperature superconductivity The study of superconductivity and

super-fluidity is crucial, but hard. Cooper pairs of fermionic atoms can

be Bose-Einstein condensed.

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Applications – Stellar Models

Degeneracy Pressure Stabilises stars against collapse

If they are not too massive!   ‘Explains’ neutron lifetime

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Observing Statistics

Fermi pressure due to Pauli principle

FermionsBosons

Truscott et al.,Science ‘01

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Applications – Cosmology in the Lab.

Big bang long gone Use analogy – equations very similar Cold gases accessible experimentally

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Applications - Clocks

New clocks could be designed using these ultra- cold atoms so that the atoms collide less frequently, which would lead to even greater accuracy.

More precise clocks would help digital communications systems and improve deep space navigation

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Fundamental physical research: Theory & Simulations

Stationary solutions (e.g. ground state):

Gross-Pitaevski Equation

Macroscopic condansate wave function

Coupling strength

It can be both positive and negative.

Positive (negative) scattering length corresponds to repulsive (attractive)interaction.

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THE MODEL Boson-Fermion Mixtures

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Validity of the Model

•For the condensate, Thomas-Fermi approximation: we neglect the kinetic energy•Hartree-Fock approximation for the spin-polarized Fermi cloud: we treat it as an ideal Fermi gas subjected to an effective potential•binary collisions: diluteness condition

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Phase Separation abf>0

For strong repulsive interactions the total energy is minimized if the bosons and the fermions occupy different spatial regions. In this regime it exist several structurally stable configurations corresponding to different energies. In Q2D and in Q1D the lowest energy configuration is always the “standard” one with a core of bosons surrounded by the fermions.

It is amazing that in Q1D the system undergoes phase separation for low number of fermions!!!!!!!!

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What - Phase Separation

Predicted 3-D configurations

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What Phase Separation – column densities

Normal Configuration

How can experimentalistsbe sure that full phaseseparation has been reached?

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Phase Separation – column densities

AsymmetricConfiguration

Boson RingConfiguration

SandwichConfiguration

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