Bose-Einstein-Condensation - Max Planck Society · I S.N. Bose (1924) quantum statistical treatment...

Bose-Einstein-Condensation

Stefan KienzleTechnische Universitat Munchen

22. Mai 2013

Outline

1 About Bose-Einstein Condensation (BEC)

2 BEC Production

3 Evaporative Cooling

4 Absorption Imaging

5 Interference Between Two Bose Condensates

6 Summary

Outline

2 BEC Production

6 Summary

History of BEC

I BEC: state of matter in which all atoms occupy lowestquantum state (ground state)

I S.N. Bose (1924)quantum statistical treatment of photons

I A. Einstein (1924/25)extended Bose’s idea to material particlespredicted BEC in an ideal quantum gas

I W. Ketterle, E. Cornell & C. Wieman (1995)produced the first gaseous condensateNobel Price of Physics (2001)

About Bose-Einstein Condensation (BEC) History of BEC 4 / 28 c© Stefan Kienzle

History of BEC

What is a BEC

I High temperature T : weak interacting gasDescribe with thermal velocity v , number density n,distance between atoms d

I Low temperature T : quantum mechanical description

λDB =

2πmkBTDe-Broglie Wavelength

with Planck constant h, Boltzmann constant kB andmass of atoms m

I T = TC : wavepackets start to overlap and form aBEC

I T = 0 K: pure BEC, described by one singlewavefunction

About Bose-Einstein Condensation (BEC) What is a BEC 5 / 28 c© Stefan Kienzle

What is a BEC

λDB =

What is a BEC

λDB =

What is a BEC

λDB =

Prerequisites

I Ultracold bosonic gases, Ultra-high vacuum

I Bosons: integer spinFermions: half integer spin and governed byPauli-Principle

I Ultralow temperatures

λDB ≈ d = n−1/3 ⇒ TC (n) =h2

2πmkB· n2/3

with critical temperature Tc(n)I.e. TC (n) ≈ 100 nK for dilute gases at densities of1014 cm−3

I Phase-space density D crucial for BEC

D = n · λ3DB D > 2.612

About Bose-Einstein Condensation (BEC) Prerequisites 6 / 28 c© Stefan Kienzle

Prerequisites

λDB ≈ d = n−1/3 ⇒ TC (n) =h2

2πmkB· n2/3

D = n · λ3DB D > 2.612

Prerequisites

λDB ≈ d = n−1/3 ⇒ TC (n) =h2

2πmkB· n2/3

D = n · λ3DB D > 2.612

Prerequisites

λDB ≈ d = n−1/3 ⇒ TC (n) =h2

2πmkB· n2/3

D = n · λ3DB D > 2.612

BEC Dynamics

I Many-body ground stateψ(~r , t) = ψ(~r)e−iµt

with ground state energy / chemical potential µ

I Dynamic: Gross-Pitaevski equation

i h∂

∂tψ(~r , t) =

2m· ∇2 + U(~r) +U |ψ(~r , t)|2

]ψ(~r , t)

with harmonic potential U(~r) = 12m(ω2

xx2 +ω2

yy2 +ω2

zz2) and U = 4π h2a/m

describing two body collisions

I Thomas-Fermi limit (nU � hωx ,y ,z): neglect term for kinetic energy ⇒ density ofcondensate

nc(~r) = |ψ(~r , t)|2 = max

{µ− U(~r)

About Bose-Einstein Condensation (BEC) BEC Dynamics 7 / 28 c© Stefan Kienzle

BEC Dynamics

i h∂

∂tψ(~r , t) =

2m· ∇2 + U(~r) +U |ψ(~r , t)|2

]ψ(~r , t)

xx2 +ω2

yy2 +ω2

nc(~r) = |ψ(~r , t)|2 = max

{µ− U(~r)

BEC Dynamics

i h∂

∂tψ(~r , t) =

2m· ∇2 + U(~r) +U |ψ(~r , t)|2

]ψ(~r , t)

xx2 +ω2

yy2 +ω2

nc(~r) = |ψ(~r , t)|2 = max

{µ− U(~r)

Outline

2 BEC Production

6 Summary

Zeeman-Slowing

I reduces velocity & temperature by Laser-cooling

I provides high flux (1012 slow atoms per second) which enables more than 1010 atomsto be loaded into the MOT in one or two seconds

I Zeeman-slowed Sodium beam has velocity of 30 m/s corresponding to kinetic energyof 1 K

BEC Production Zeeman-Slowing 9 / 28 c© Stefan Kienzle

Zeeman-Slowing

Magneto-Optical-Trap (MOT)

I S. Chu, C. Cohen-Tannoudji & W. D. Phillipsreceived the Nobel Prize of Physics for development of methods tocool and trap atoms with laser light in 1997

I Cooling in optical molasses

I Reduces temperature to 1 mK or below

I Zeeman slowed atoms are confined and compressed to higherdensities (1010 - 1012 cm−3)

I Provides phase-space density D ≈ 10−7: still too low for phasetransitions

BEC Production Magneto-Optical-Trap (MOT) 10 / 28 c© Stefan Kienzle

Polarization-Gradient Cooling (Sisyphus-cooling)

I Technique already present in the center of the MOT

I Colder temperatures reached by switching off the MOT’s magnetic coils and addingshort cycle (few ms) of optimized Polarization-Gradient Cooling

I I.e. for sodium temperatures between 50 µK and 100 µK

I Provides phase-space density D ≈ 10−6: still too low for phase transitions

BEC Production Polarization-Gradient Cooling (Sisyphus-cooling) 11 / 28 c© Stefan Kienzle

Magnetic Trapping

I Magnetic Trapping of neutral atoms first observed in 1985

I Major role: Accomodate pre-cooled atoms and compress them ⇒ high collision ratesand evaporative cooling

I Atoms trapped by interactions of magnetic dipole with external magnetic fieldEnergy levels in a magnetic field E (mF ) = gµBmFB

I Maxwell ⇒ only confines weak-field seeker

I Excellent tool for evaporative cooling

BEC Production Magnetic Trapping 12 / 28 c© Stefan Kienzle

Magnetic Trapping

Outline

2 BEC Production

6 Summary

Concepts and History

I Continously removing trapped high-energy atoms toreach TC

I Evaporated atoms carry away more than averageenergy ⇒ temperature decreases

I Suggested by H. Hess in 1985 with trapped atomichydrogen

I Technique was extended to alkali atoms in 1994 bycombining Evaporative Cooling with Laser Cooling

Evaporative Cooling Concepts and History 14 / 28 c© Stefan Kienzle

RF Induced Evaporation

RF-Field

Distance to trap center

I Radio frequented (RF) radiation flips atomic spin ⇒ attractive trapping force turnsinto repulsive force and expels atoms from trap

I Energy selective ⇒ only atoms with E > h|mF |(ωRF −ω0)with rf frequenzy ω0 which induces spinflips at the bottom of the trap

I Other atoms rethermalyze

I Advantage: No need to weaken trapping potential in order to lower depth.Atoms evaporate from whole surface where RF resonance condition is fullfilled ⇒ 3Din velocity space

Evaporative Cooling RF Induced Evaporation 15 / 28 c© Stefan Kienzle

RF-Field

I Rethermalization: Scattering processes lead to new distribution

I Favorable ratio between elastic collision rate (provides Evaporative Cooling) andinelastic collision rate (leads to trap loss and heating) required

I Provides phase-space density D > 2.612

I Horizontal sections taken through center of velocitydistribution

I Lower values show appearance of condensate fraction

I Above 4.23 MHz: single Gaussian-like distribution

I At 4.23 MHz: sharp central peak appears

I Below 4.23 MHz: broad curve & narrow central peak; thenoncondensate & condensate fraction

I At 4.1 MHz: just little remains of noncondensate fraction

Outline

2 BEC Production

6 Summary

Absorption Imaging

I Switching off trap ⇒ condensate falling down (gravity) and ballistically expands

I Illuminating atoms with nearly resonant laser beam and imaging shadow cast oncharge-coupled device camera (CCD-camera)

I Cloud heats up by absorbing photons (about one recoil energy per photon)

I Single destructive image

I Provides reliable density distributions of which properties of condensates andthermal clouds can be inferred

Absorption Imaging

I 2D probe absorption images after 6 ms time of flightWidth of images is 870 µm

I Velocity distribution of cloud just above transition point

I Shows difference between isotropic thermal distribution and elliptical core attributedto expansion of dense condensate

I Almost pure condensate (after further evaporative cooling)

Absorption Imaging

I Produced in vapor of 87Rb atoms

I Fraction of condensed atoms first appear near T =170 nK & n = 2.5 · 1012 cm−3

Could be preserved for more than 15 seconds

I BEC on top of broad thermal velocity

I Fraction of atoms that were in this low-velocity peak increases abruptly

I Nonthermal, anisotropic velocity distribution expected of minimum-energy quantumstate of magnetic trap

Absorption Imaging

Outline

2 BEC Production

6 Summary

Interference

I Evidence for coherence of BEC’s

I Cut atom trap in half (double-well potential) byfocusing far-off-resonant laser light into center ofmagnetic trap

I Cool atoms in these two halves to form twoindependent condensates

I Quickly turn off laser and magnetic fields, allowingatoms to fall and expand freely

I Both condensates start to overlap and interfere witheach other

Interference

I Interference pattern of two expanding condensates after 40 ms time of flight for 2different powers of Argon-ion laser light (3 & 5 mW)

I Fringe periods 20 & 15 µm

I Fields of view: horizontally: 1.1 mmvertically: 0.5 mm

Interference

Interference Drop Tower

I Recent experiment: drop tower (Center of Applied SpaceTechnology and Microgravity ’ZARM’ Bremen)

I Height: 146 m (outside); 120 m (inside)Delivers 4.74 s of near weightlessness

I Capturing cold atoms in magneto-optical trap (MOT)

I Loading Ioffe-Pritchard trap, creating BEC consisting of104 87Rb atoms

I Evolution of BEC and asymmetric Mach-Zehnder interferometer (AMZI) visualizedby series of absorption images of atomic densities separated by 1 ms

I Interferometer starts at time t0 after release of BEC

I Two counter-propagating light beams of frequencies ω and ω+ δ creates coherentsuperposition of two wave packets that drift apart, redirects and partially recombinesthem

Summary

I BEC is a state of matter in which all atoms occupy the ground state

I Phase transistions for D > 2.612

I Condensate has anisotropic density distribution

I Interference between two condensates is evidence for coherence of BEC’s

Summary

References

M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W.Ketterle: Science 275, 637-641 (1997)http://www.sciencemag.org/content/275/5300/637.abstract

M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell: Science269, 198-201 (1995)http://www.sciencemag.org/content/269/5221/198.abstract

K.B. Davis, M.-O. Mewes, M.R. Andrews, N.j. van Druten, D.S. Durfee, D.M. Kurn,W. Ketterle: American Physical Society 75, 3969-3973 (1995)http://prl.aps.org/abstract/PRL/v75/i22/p3969_1

H. Muntinga et al. American Physical Society 110, 093602.1-093602.5 (2013)http://prl.aps.org/abstract/PRL/v110/i9/e093602

W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn: Making, probing and understandingBose-Einstein caondesates http://arxiv.org/abs/cond-mat/9904034

Bose-Einstein-Condensation - Max Planck Society · I S.N. Bose (1924) quantum statistical treatment...

Documents

Transcript of Bose-Einstein-Condensation - Max Planck Society · I S.N. Bose (1924) quantum statistical treatment...