Bose-Einstein-Condensation
Stefan Kienzle
Technische Universität München
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
1 About Bose-Einstein Condensation (BEC)
2 BEC Production
3 Evaporative Cooling
4 Absorption Imaging
5 Interference Between Two Bose Condensates
6 Summary
History of BEC
I
BEC: state of matter in which all atoms occupy lowest
quantum state (ground state)
About Bose-Einstein Condensation (BEC)
History of BEC
4 / 28
c Stefan Kienzle
History of BEC
I
BEC: state of matter in which all atoms occupy lowest
quantum state (ground state)
I
S.N. Bose (1924)
quantum statistical treatment of photons
About Bose-Einstein Condensation (BEC)
History of BEC
4 / 28
c Stefan Kienzle
History of BEC
I
BEC: state of matter in which all atoms occupy lowest
quantum state (ground state)
I
S.N. Bose (1924)
quantum statistical treatment of photons
I
A. Einstein (1924/25)
extended Bose’s idea to material particles
predicted BEC in an ideal quantum gas
About Bose-Einstein Condensation (BEC)
History of BEC
4 / 28
c Stefan Kienzle
History of BEC
I
BEC: state of matter in which all atoms occupy lowest
quantum state (ground state)
I
S.N. Bose (1924)
quantum statistical treatment of photons
I
A. Einstein (1924/25)
extended Bose’s idea to material particles
predicted BEC in an ideal quantum gas
I
W. Ketterle, E. Cornell & C. Wieman (1995)
produced the first gaseous condensate
Nobel Price of Physics (2001)
About Bose-Einstein Condensation (BEC)
History of BEC
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What is a BEC
I
About Bose-Einstein Condensation (BEC)
High temperature T : weak interacting gas
Describe with thermal velocity v , number density n,
distance between atoms d
What is a BEC
5 / 28
c Stefan Kienzle
What is a BEC
I
High temperature T : weak interacting gas
Describe with thermal velocity v , number density n,
distance between atoms d
I
Low temperature T : quantum mechanical description
s
λDB =
h2
2πmkB T
De-Broglie Wavelength
with Planck constant h, Boltzmann constant kB and
mass of atoms m
About Bose-Einstein Condensation (BEC)
What is a BEC
5 / 28
c Stefan Kienzle
What is a BEC
I
High temperature T : weak interacting gas
Describe with thermal velocity v , number density n,
distance between atoms d
I
Low temperature T : quantum mechanical description
s
λDB =
h2
2πmkB T
De-Broglie Wavelength
with Planck constant h, Boltzmann constant kB and
mass of atoms m
I
About Bose-Einstein Condensation (BEC)
T = TC : wavepackets start to overlap and form a
BEC
What is a BEC
5 / 28
c Stefan Kienzle
What is a BEC
I
High temperature T : weak interacting gas
Describe with thermal velocity v , number density n,
distance between atoms d
I
Low temperature T : quantum mechanical description
s
λDB =
h2
2πmkB T
De-Broglie Wavelength
with Planck constant h, Boltzmann constant kB and
mass of atoms m
About Bose-Einstein Condensation (BEC)
I
T = TC : wavepackets start to overlap and form a
BEC
I
T = 0 K: pure BEC, described by one single
wavefunction
What is a BEC
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Prerequisites
I
Ultracold bosonic gases, Ultra-high vacuum
About Bose-Einstein Condensation (BEC)
Prerequisites
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Prerequisites
I
Ultracold bosonic gases, Ultra-high vacuum
I
Bosons: integer spin
Fermions: half integer spin and governed by
Pauli-Principle
About Bose-Einstein Condensation (BEC)
Prerequisites
6 / 28
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Prerequisites
I
Ultracold bosonic gases, Ultra-high vacuum
I
Bosons: integer spin
Fermions: half integer spin and governed by
Pauli-Principle
I
Ultralow temperatures
λDB ≈ d = n−1/3 ⇒ TC (n) =
h2
· n2/3
2πmkB
with critical temperature Tc (n)
I.e. TC (n) ≈ 100 nK for dilute gases at densities of
1014 cm−3
About Bose-Einstein Condensation (BEC)
Prerequisites
6 / 28
c Stefan Kienzle
Prerequisites
I
Ultracold bosonic gases, Ultra-high vacuum
I
Bosons: integer spin
Fermions: half integer spin and governed by
Pauli-Principle
I
Ultralow temperatures
λDB ≈ d = n−1/3 ⇒ TC (n) =
h2
· n2/3
2πmkB
with critical temperature Tc (n)
I.e. TC (n) ≈ 100 nK for dilute gases at densities of
1014 cm−3
I
Phase-space density D crucial for BEC
D = n · λ3DB
About Bose-Einstein Condensation (BEC)
D > 2.612
Prerequisites
6 / 28
c Stefan Kienzle
BEC Dynamics
I
Many-body ground state
ψ(~r , t) = ψ(~r )e −iµt
with ground state energy / chemical potential µ
About Bose-Einstein Condensation (BEC)
BEC Dynamics
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BEC Dynamics
I
Many-body ground state
ψ(~r , t) = ψ(~r )e −iµt
with ground state energy / chemical potential µ
I
Dynamic: Gross-Pitaevski equation
h2
∂
· ∇2 + U(~r ) + Ũ|ψ(~r , t)|2 ψ(~r , t)
i h ψ(~r , t) = −
∂t
2m
with harmonic potential U(~r ) = 12 m(ω2x x 2 + ω2y y 2 + ω2z z 2 ) and Ũ = 4πh2 a/m
describing two body collisions
About Bose-Einstein Condensation (BEC)
BEC Dynamics
7 / 28
c Stefan Kienzle
BEC Dynamics
I
Many-body ground state
ψ(~r , t) = ψ(~r )e −iµt
with ground state energy / chemical potential µ
I
Dynamic: Gross-Pitaevski equation
h2
∂
· ∇2 + U(~r ) + Ũ|ψ(~r , t)|2 ψ(~r , t)
i h ψ(~r , t) = −
∂t
2m
with harmonic potential U(~r ) = 12 m(ω2x x 2 + ω2y y 2 + ω2z z 2 ) and Ũ = 4πh2 a/m
describing two body collisions
I
Thomas-Fermi limit (nŨ hωx,y ,z ): neglect term for kinetic energy ⇒ density of
condensate
µ − U(~r )
,0
nc (~r ) = |ψ(~r , t)|2 = max
Ũ
About Bose-Einstein Condensation (BEC)
BEC Dynamics
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Outline
1 About Bose-Einstein Condensation (BEC)
2 BEC Production
3 Evaporative Cooling
4 Absorption Imaging
5 Interference Between Two Bose Condensates
6 Summary
Zeeman-Slowing
I
reduces velocity & temperature by Laser-cooling
BEC Production
Zeeman-Slowing
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Zeeman-Slowing
I
reduces velocity & temperature by Laser-cooling
I
provides high flux (1012 slow atoms per second) which enables more than 1010 atoms
to be loaded into the MOT in one or two seconds
BEC Production
Zeeman-Slowing
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Zeeman-Slowing
I
reduces velocity & temperature by Laser-cooling
I
provides high flux (1012 slow atoms per second) which enables more than 1010 atoms
to be loaded into the MOT in one or two seconds
I
Zeeman-slowed Sodium beam has velocity of 30 m/s corresponding to kinetic energy
of 1 K
BEC Production
Zeeman-Slowing
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Magneto-Optical-Trap (MOT)
I
BEC Production
S. Chu, C. Cohen-Tannoudji & W. D. Phillips
received the Nobel Prize of Physics for development of methods to
cool and trap atoms with laser light in 1997
Magneto-Optical-Trap (MOT)
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Magneto-Optical-Trap (MOT)
BEC Production
I
S. Chu, C. Cohen-Tannoudji & W. D. Phillips
received the Nobel Prize of Physics for development of methods to
cool and trap atoms with laser light in 1997
I
Cooling in optical molasses
Magneto-Optical-Trap (MOT)
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Magneto-Optical-Trap (MOT)
BEC Production
I
S. Chu, C. Cohen-Tannoudji & W. D. Phillips
received the Nobel Prize of Physics for development of methods to
cool and trap atoms with laser light in 1997
I
Cooling in optical molasses
I
Reduces temperature to 1 mK or below
Magneto-Optical-Trap (MOT)
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Magneto-Optical-Trap (MOT)
BEC Production
I
S. Chu, C. Cohen-Tannoudji & W. D. Phillips
received the Nobel Prize of Physics for development of methods to
cool 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 higher
densities (1010 - 1012 cm−3 )
Magneto-Optical-Trap (MOT)
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Magneto-Optical-Trap (MOT)
BEC Production
I
S. Chu, C. Cohen-Tannoudji & W. D. Phillips
received the Nobel Prize of Physics for development of methods to
cool 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 higher
densities (1010 - 1012 cm−3 )
I
Provides phase-space density D ≈ 10−7 : still too low for phase
transitions
Magneto-Optical-Trap (MOT)
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Polarization-Gradient Cooling (Sisyphus-cooling)
I
Technique already present in the center of the MOT
BEC Production
Polarization-Gradient Cooling (Sisyphus-cooling)
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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 adding
short cycle (few ms) of optimized Polarization-Gradient Cooling
BEC Production
Polarization-Gradient Cooling (Sisyphus-cooling)
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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 adding
short cycle (few ms) of optimized Polarization-Gradient Cooling
I
I.e. for sodium temperatures between 50 µK and 100 µK
BEC Production
Polarization-Gradient Cooling (Sisyphus-cooling)
11 / 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 adding
short 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)
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Magnetic Trapping
I
Magnetic Trapping of neutral atoms first observed in 1985
BEC Production
Magnetic Trapping
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Magnetic Trapping
I
Magnetic Trapping of neutral atoms first observed in 1985
I
Major role: Accomodate pre-cooled atoms and compress them ⇒ high collision rates
and evaporative cooling
BEC Production
Magnetic Trapping
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Magnetic Trapping
I
Magnetic Trapping of neutral atoms first observed in 1985
I
Major role: Accomodate pre-cooled atoms and compress them ⇒ high collision rates
and evaporative cooling
I
Atoms trapped by interactions of magnetic dipole with external magnetic field
Energy levels in a magnetic field E (mF ) = g µB mF B
BEC Production
Magnetic Trapping
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Magnetic Trapping
I
Magnetic Trapping of neutral atoms first observed in 1985
I
Major role: Accomodate pre-cooled atoms and compress them ⇒ high collision rates
and evaporative cooling
I
Atoms trapped by interactions of magnetic dipole with external magnetic field
Energy levels in a magnetic field E (mF ) = g µB mF B
I
Maxwell ⇒ only confines weak-field seeker
BEC Production
Magnetic Trapping
12 / 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 rates
and evaporative cooling
I
Atoms trapped by interactions of magnetic dipole with external magnetic field
Energy levels in a magnetic field E (mF ) = g µB mF B
I
Maxwell ⇒ only confines weak-field seeker
I
Excellent tool for evaporative cooling
BEC Production
Magnetic Trapping
12 / 28
c Stefan Kienzle
Outline
1 About Bose-Einstein Condensation (BEC)
2 BEC Production
3 Evaporative Cooling
4 Absorption Imaging
5 Interference Between Two Bose Condensates
6 Summary
Concepts and History
I
Evaporative Cooling
Continously removing trapped high-energy atoms to
reach TC
Concepts and History
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Concepts and History
Evaporative Cooling
I
Continously removing trapped high-energy atoms to
reach TC
I
Evaporated atoms carry away more than average
energy ⇒ temperature decreases
Concepts and History
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Concepts and History
Evaporative Cooling
I
Continously removing trapped high-energy atoms to
reach TC
I
Evaporated atoms carry away more than average
energy ⇒ temperature decreases
I
Suggested by H. Hess in 1985 with trapped atomic
hydrogen
Concepts and History
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Concepts and History
Evaporative Cooling
I
Continously removing trapped high-energy atoms to
reach TC
I
Evaporated atoms carry away more than average
energy ⇒ temperature decreases
I
Suggested by H. Hess in 1985 with trapped atomic
hydrogen
I
Technique was extended to alkali atoms in 1994 by
combining Evaporative Cooling with Laser 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 turns
into repulsive force and expels atoms from trap
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
RF-Field
Distance to
trap center
I
I
Radio frequented (RF) radiation flips atomic spin ⇒ attractive trapping force turns
into repulsive force and expels atoms from trap
Energy selective ⇒ only atoms with E > h|mF |(ωRF − ω0 )
with rf frequenzy ω0 which induces spinflips at the bottom of the trap
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
RF-Field
Distance to
trap center
I
I
I
Radio frequented (RF) radiation flips atomic spin ⇒ attractive trapping force turns
into repulsive force and expels atoms from trap
Energy selective ⇒ only atoms with E > h|mF |(ωRF − ω0 )
with rf frequenzy ω0 which induces spinflips at the bottom of the trap
Other atoms rethermalyze
Evaporative Cooling
RF Induced Evaporation
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c Stefan Kienzle
RF Induced Evaporation
RF-Field
Distance to
trap center
I
I
I
I
Radio frequented (RF) radiation flips atomic spin ⇒ attractive trapping force turns
into repulsive force and expels atoms from trap
Energy selective ⇒ only atoms with E > h|mF |(ωRF − ω0 )
with rf frequenzy ω0 which induces spinflips at the bottom of the trap
Other atoms rethermalyze
Advantage: No need to weaken trapping potential in order to lower depth.
Atoms evaporate from whole surface where RF resonance condition is fullfilled ⇒ 3D
in velocity space
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
I
Rethermalization: Scattering processes lead to new distribution
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
I
Rethermalization: Scattering processes lead to new distribution
I
Favorable ratio between elastic collision rate (provides Evaporative Cooling) and
inelastic collision rate (leads to trap loss and heating) required
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
I
Rethermalization: Scattering processes lead to new distribution
I
Favorable ratio between elastic collision rate (provides Evaporative Cooling) and
inelastic collision rate (leads to trap loss and heating) required
I
Provides phase-space density D > 2.612
Evaporative Cooling
RF Induced Evaporation
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RF Induced Evaporation
I
Evaporative Cooling
Horizontal sections taken through center of velocity
distribution
RF Induced Evaporation
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RF Induced Evaporation
Evaporative Cooling
I
Horizontal sections taken through center of velocity
distribution
I
Lower values show appearance of condensate fraction
RF Induced Evaporation
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RF Induced Evaporation
Evaporative Cooling
I
Horizontal sections taken through center of velocity
distribution
I
Lower values show appearance of condensate fraction
I
Above 4.23 MHz: single Gaussian-like distribution
RF Induced Evaporation
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RF Induced Evaporation
Evaporative Cooling
I
Horizontal sections taken through center of velocity
distribution
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
RF Induced Evaporation
17 / 28
c Stefan Kienzle
RF Induced Evaporation
Evaporative Cooling
I
Horizontal sections taken through center of velocity
distribution
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; the
noncondensate & condensate fraction
RF Induced Evaporation
17 / 28
c Stefan Kienzle
RF Induced Evaporation
Evaporative Cooling
I
Horizontal sections taken through center of velocity
distribution
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; the
noncondensate & condensate fraction
I
At 4.1 MHz: just little remains of noncondensate fraction
RF Induced Evaporation
17 / 28
c Stefan Kienzle
Outline
1 About Bose-Einstein Condensation (BEC)
2 BEC Production
3 Evaporative Cooling
4 Absorption Imaging
5 Interference Between Two Bose Condensates
6 Summary
Absorption Imaging
I
Switching off trap ⇒ condensate falling down (gravity) and ballistically expands
Absorption Imaging
Absorption Imaging
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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 on
charge-coupled device camera (CCD-camera)
Absorption Imaging
Absorption Imaging
19 / 28
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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 on
charge-coupled device camera (CCD-camera)
I
Cloud heats up by absorbing photons (about one recoil energy per photon)
Absorption Imaging
Absorption Imaging
19 / 28
c Stefan Kienzle
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 on
charge-coupled device camera (CCD-camera)
I
Cloud heats up by absorbing photons (about one recoil energy per photon)
I
Single destructive image
Absorption Imaging
Absorption Imaging
19 / 28
c Stefan Kienzle
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 on
charge-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 and
thermal clouds can be inferred
Absorption Imaging
Absorption Imaging
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Absorption Imaging
I
2D probe absorption images after 6 ms time of flight
Width of images is 870 µm
Absorption Imaging
Absorption Imaging
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Absorption Imaging
I
2D probe absorption images after 6 ms time of flight
Width of images is 870 µm
I
Velocity distribution of cloud just above transition point
Absorption Imaging
Absorption Imaging
20 / 28
c Stefan Kienzle
Absorption Imaging
I
2D probe absorption images after 6 ms time of flight
Width of images is 870 µm
I
Velocity distribution of cloud just above transition point
I
Shows difference between isotropic thermal distribution and elliptical core attributed
to expansion of dense condensate
Absorption Imaging
Absorption Imaging
20 / 28
c Stefan Kienzle
Absorption Imaging
I
2D probe absorption images after 6 ms time of flight
Width of images is 870 µm
I
Velocity distribution of cloud just above transition point
I
Shows difference between isotropic thermal distribution and elliptical core attributed
to expansion of dense condensate
I
Almost pure condensate (after further evaporative cooling)
Absorption Imaging
Absorption Imaging
20 / 28
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Absorption Imaging
I
Produced in vapor of
Absorption Imaging
87
Rb atoms
Absorption Imaging
21 / 28
c Stefan Kienzle
Absorption Imaging
87
I
Produced in vapor of
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
Absorption Imaging
Rb atoms
Absorption Imaging
21 / 28
c Stefan Kienzle
Absorption Imaging
87
I
Produced in vapor of
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
Absorption Imaging
Rb atoms
Absorption Imaging
21 / 28
c Stefan Kienzle
Absorption Imaging
87
I
Produced in vapor of
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
Absorption Imaging
Rb atoms
Absorption Imaging
21 / 28
c Stefan Kienzle
Absorption Imaging
87
I
Produced in vapor of
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 quantum
state of magnetic trap
Absorption Imaging
Rb atoms
Absorption Imaging
21 / 28
c Stefan Kienzle
Outline
1 About Bose-Einstein Condensation (BEC)
2 BEC Production
3 Evaporative Cooling
4 Absorption Imaging
5 Interference Between Two Bose Condensates
6 Summary
Interference
I
Interference Between Two Bose Condensates
Evidence for coherence of BEC’s
Interference Between Two Bose Condensates
23 / 28
c Stefan Kienzle
Interference
Interference Between Two Bose Condensates
I
Evidence for coherence of BEC’s
I
Cut atom trap in half (double-well potential) by
focusing far-off-resonant laser light into center of
magnetic trap
Interference Between Two Bose Condensates
23 / 28
c Stefan Kienzle
Interference
Interference Between Two Bose Condensates
I
Evidence for coherence of BEC’s
I
Cut atom trap in half (double-well potential) by
focusing far-off-resonant laser light into center of
magnetic trap
I
Cool atoms in these two halves to form two
independent condensates
Interference Between Two Bose Condensates
23 / 28
c Stefan Kienzle
Interference
Interference Between Two Bose Condensates
I
Evidence for coherence of BEC’s
I
Cut atom trap in half (double-well potential) by
focusing far-off-resonant laser light into center of
magnetic trap
I
Cool atoms in these two halves to form two
independent condensates
I
Quickly turn off laser and magnetic fields, allowing
atoms to fall and expand freely
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference
Interference Between Two Bose Condensates
I
Evidence for coherence of BEC’s
I
Cut atom trap in half (double-well potential) by
focusing far-off-resonant laser light into center of
magnetic trap
I
Cool atoms in these two halves to form two
independent condensates
I
Quickly turn off laser and magnetic fields, allowing
atoms to fall and expand freely
I
Both condensates start to overlap and interfere with
each other
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference
I
Interference pattern of two expanding condensates after 40 ms time of flight for 2
different powers of Argon-ion laser light (3 & 5 mW)
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
24 / 28
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Interference
I
Interference pattern of two expanding condensates after 40 ms time of flight for 2
different powers of Argon-ion laser light (3 & 5 mW)
I
Fringe periods 20 & 15 µm
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
24 / 28
c Stefan Kienzle
Interference
I
Interference pattern of two expanding condensates after 40 ms time of flight for 2
different powers of Argon-ion laser light (3 & 5 mW)
I
Fringe periods 20 & 15 µm
I
Fields of view: horizontally: 1.1 mm
vertically: 0.5 mm
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
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Interference Drop Tower
I
Interference Between Two Bose Condensates
Recent experiment: drop tower (Center of Applied Space
Technology and Microgravity ’ZARM’ Bremen)
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference Drop Tower
Interference Between Two Bose Condensates
I
Recent experiment: drop tower (Center of Applied Space
Technology and Microgravity ’ZARM’ Bremen)
I
Height: 146 m (outside); 120 m (inside)
Delivers 4.74 s of near weightlessness
Interference Between Two Bose Condensates
25 / 28
c Stefan Kienzle
Interference Drop Tower
Interference Between Two Bose Condensates
I
Recent experiment: drop tower (Center of Applied Space
Technology 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)
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference Drop Tower
Interference Between Two Bose Condensates
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Recent experiment: drop tower (Center of Applied Space
Technology and Microgravity ’ZARM’ Bremen)
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Height: 146 m (outside); 120 m (inside)
Delivers 4.74 s of near weightlessness
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Capturing cold atoms in magneto-optical trap (MOT)
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Loading Ioffe-Pritchard trap, creating BEC consisting of
104 87 Rb atoms
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference Drop Tower
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Evolution of BEC and asymmetric Mach-Zehnder interferometer (AMZI) visualized
by series of absorption images of atomic densities separated by 1 ms
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
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c Stefan Kienzle
Interference Drop Tower
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Evolution of BEC and asymmetric Mach-Zehnder interferometer (AMZI) visualized
by series of absorption images of atomic densities separated by 1 ms
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Interferometer starts at time t0 after release of BEC
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
26 / 28
c Stefan Kienzle
Interference Drop Tower
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Evolution of BEC and asymmetric Mach-Zehnder interferometer (AMZI) visualized
by 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 coherent
superposition of two wave packets that drift apart, redirects and partially recombines
them
Interference Between Two Bose Condensates
Interference Between Two Bose Condensates
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c Stefan Kienzle
Summary
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BEC is a state of matter in which all atoms occupy the ground state
Summary
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c Stefan Kienzle
Summary
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BEC is a state of matter in which all atoms occupy the ground state
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Phase transistions for D > 2.612
Summary
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c Stefan Kienzle
Summary
I
BEC is a state of matter in which all atoms occupy the ground state
I
Phase transistions for D > 2.612
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Condensate has anisotropic density distribution
Summary
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c Stefan Kienzle
Summary
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BEC is a state of matter in which all atoms occupy the ground state
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Phase transistions for D > 2.612
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Condensate has anisotropic density distribution
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Interference between two condensates is evidence for coherence of BEC’s
Summary
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c Stefan Kienzle
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: Science
269, 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. Müntinga 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 understanding
Bose-Einstein caondesates http://arxiv.org/abs/cond-mat/9904034