Download The amazing story of Laser Cooling and Trapping

The amazing story of Laser
Cooling and Trapping
following Bill Phillips’ Nobel Lecture
http://www.nobelprize.org/nobel_prizes/physics/
laureates/1997/phillips-lecture.pdf
Laser cooling of atomic beams
1
Na is not a “two-level” atom!
Problem: unwanted optical pumping
(a) The optical pumping process preventing cycling transitions in alkalis like Na;
(b) (b) use of a repumping laser to allow many absorption-emission cycles.
2
sciencewise.anu.edu.au
Another problem: Doppler shift
In order for the laser light to be resonantly absorbed by a counterpropagating
atom moving with velocity v, the frequency ϖ of the light must be kv lower
than the resonant frequency for an atom at rest.
As the atom repeatedly absorbs photons, slowing down as desired, the Doppler
shift changes and the atom goes out of resonance with the light.
The natural linewidth Γ/2π of the optical transition in Na is 10MHz (full width
at half maximum). A change in velocity of 6 m/s gives a Doppler shift this large,
so after absorbing only 200 photons, the atom is far enough off resonance
that the rate of absorption is significantly reduced.
The result is that only atoms with the ‘‘proper’’ velocity to be resonant with
the laser are slowed, and they are only slowed by a small amount.
3
Cooling an atomic beam with a fixed frequency laser
after cooling
before cooling
The dotted curve is the velocity distribution before cooling, and the solid curve is
after cooling. Atoms from a narrow velocity range are transferred to a slightly
narrower range centered on a lower velocity.
Zeeman slower
The laser is tuned so that, given the field induced Zeeman shift and the velocity-induced
Doppler shift of the atomic transition frequency, atoms with velocity v0 are resonant with the
laser when they reach the point where the field is maximum.
Those atoms then absorb light and begin to slow down. As their velocity changes, their
Doppler shift changes, but is compensated by the change in Zeeman shift as the atoms move
to a point where the field is weaker. At this point, atoms with initial velocities slightly lower
than v0 come into resonance and begin to slow down.
The process continues with the initially fast atoms decelerating and staying in resonance while
initially slower atoms come into resonance and begin to be slowed as they move further
down the solenoid.
4
Zeeman Cooling
http://es1.ph.man.ac.uk/AJM2/Atomtrapping/Atomtrapping.htm
Note: optical pumping problem is avoided
By shutting off the cooling laser beam
and delaying observation until the
slow atoms arrived in the observation
region, Prodan, Phillips, and Metcalf
(1982) were able to detect atoms as
slow as 40 m/s with a spread of 10 m/s,
corresponding to a temperature (in the
atoms’ rest frame) of 70 mK.
The next step was to get these atoms to
come to rest in the observation region.
5
Magnetic trapping
The idea of magnetic trapping is that in a
magnetic field, an atom with a magnetic
moment will have quantum states whose
magnetic or Zeeman energy increases with
increasing field and states whose energy
decreases, depending on the orientation of
the moment compared
to the field.
The increasing-energy states, or low-field
seekers, can be trapped in a magnetic field
configuration
having a point where the magnitude of the
field is a relative minimum.
(a) Spherical quadrupole trap with lines of B-field.
(b) Equipotentials of our trap (equal field magnitudes in millitesla),
in a plane containing the symmetry (z) axis.
Magneto-optical trapping (MOT)
6
Doppler cooling in one dimension
Laser beams are tuned slightly below the atomic resonance frequency.
An atom moving toward the left sees that the laser beam opposing its motion is Doppler
shifted toward the atomic resonance frequency.
It sees that the laser beam directed along its motion is Doppler shifted further from its
resonance. The atom therefore absorbs more strongly from the laser beam that opposes its
motion, and it slows down.
The same thing happens to an atom moving to the right, so all atoms are slowed by this
arrangement of laser beams.
Optical molasses
A sodium atom cooled to the Doppler limit has
a ‘‘mean free path’’ (the mean distance it
moves before its initial velocity is damped out
and the atom is moving with a different,
random velocity) of only 20 mm, while the size
of the laser beams doing the cooling might
easily be one centimeter.
Thus, the atom undergoes diffusive, Brownianlike motion, and the time for a laser cooled
atom to escape from the region where it is
being cooled is much longer than the ballistic
transit time across that region.
This means that an atom is effectively ‘‘stuck’’
in the laser beams that cool it. This stickiness,
and the similarity of laser cooling to viscous
friction, prompted the Bell Labs group (Chu et
al., 1985) to name the intersecting laser beams
‘‘optical molasses.’’
7
Optical molasses
Experimental molasses lifetime (points)
and the theoretical decay time (curve) vs
detuning of molasses laser from
resonance.
Doppler cooling limit
This cooling process leads to a temperature whose lower limit is on the order of ħΓ,
where Γ is the rate of spontaneous emission of the excited state (Γ-1 is the excited state
lifetime). The temperature results from an equilibrium between laser cooling and the
heating process arising from the random nature of both the absorption and emission of
photons.
The random addition to the average momentum transfer produces a random walk of the
atomic momentum and an increase in the mean square atomic momentum.
This heating is countered by the cooling force F opposing atomic motion.
8
Time-of-flight method for measuring laser cooling temperatures
The predicted lower limit
of Doppler cooling: 240 mK
Time-of-flight method for measuring laser cooling temperatures
The experimental TOF distribution
(points) and the predicted distribution
curves for 40 mK and 240 mK (the
predicted lower limit of Doppler cooling).
Conclusion: atoms were much colder
than the Doppler limit!
9
‘‘Sisyphus’’ cooling
The atom is now
again at the bottom
of a hill, and it again
must climb, losing
kinetic energy, as it
moves.
(a) Interfering, counterpropagating beams having orthogonal, linear polarizations create a
polarization gradient.
(b) The different Zeeman sublevels are shifted differently in light fields with different
polarizations; optical pumping tends to put atomic population on the lowest energy level, but
nonadiabatic motion results in ‘‘Sisyphus’’ cooling.
‘‘Sisyphus’’ cooling
http://www.nobelprize.org/nobel_prizes/physics/laureates/1997/illpres/doppler.html
10
Heterodyne spectrum of fluorescence from Na atoms in optical molasses. The
broad component corresponds to a temperature of 84 µK, which compares well
with the temperature of 87 µK measured by time-of-flight measurement . The
narrow component indicates a sub-wavelength localization of the atoms.
Atoms in optical lattices
An optical lattice works as follows. When atoms are exposed to a laser field
that is not resonant with an atomic optical transition (and thus does not excite the
atomic electrons), they experience a conservative potential that is proportional to
the laser intensity. With two counterpropagating laser fields, a standing wave is
created and the atoms feel a periodic potential. With three such standing waves
along three orthogonal spatial directions, one obtains a three-dimensional optical
lattice. The atoms are trapped at the minima of the corresponding potential wells.
Adapted from: Eugene Demler
11
Sodium laser cooling experiment (1992)
WK and Dark SPOT
Wolfgang Ketterle, Meridian Lecture
Nobel Prize in Physics 1997
Steve Chu
Claude Cohen-Tannoudji
Bill Phillips
12
fromTheodor W. Hänsch‘s Nobel Lecture
Evaporative cooling
13
Quantum gases: bosons and fermions
Ideal gas at
zero temperature
Bose-Einstein
Fermi-Dirac
EF
Bose-Einstein : integer spin
Fermi-Dirac : half-integer spin
In neutral atoms Nelectrons = Nprotons
Salomon
et al.,
ENS
Statistical properties are governed by the
number of neutrons in an atom Nneutrons :
Boson if Nneutrons is even
Fermion if Nneutrons is odd
Nobel Prize in Physics 2001
Eric Cornell
Wolfgang Ketterle
Carl Wieman
14
Sodium BEC I experiment (2001)
Wolfgang Ketterle, Meridian Lecture
Atomic clocks and variation
of fundamental constants
15
Clocks
16
Cesium microwave
atomic clock
9 192 631 770 periods
per second
timeandnavigation.si.edu
Current definition of a second:
1967: the second has been defined as the duration of
9 192 631 770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground
state of the cesium 133 atom.
1997: the periods would be defined for a cesium atom at rest,
and approaching the theoretical temperature of absolute
zero (0 K).
17
Cesium atomic clock
A gas of cesium atoms enters
the clock's vacuum chamber.
Six lasers slow the movement
of the atoms, cooling them to
near absolute zero and force
them into a spherical cloud at
the intersection of the laser
beams.
The ball is tossed
upward by two lasers
through a cavity filled
with microwaves. All of
the lasers are then
turned off.
Gravity pulls the ball of cesium
atoms back through the microwave
cavity. The microwaves partially alter
the atomic states of the cesium
atoms.
http://www.nist.gov/public_affairs/releases/n99-22.cfm
Cesium atomic clock
Cesium atoms that were altered in the microwave cavity emit light when hit
with a laser beam.
This fluorescence is measured by a detector (right).
The entire process is repeated many times while the microwave energy in
the cavity is tuned to different frequencies until the maximum fluorescence
of the cesium atoms is determined.
This point defines the natural resonance frequency of cesium, which is
used to define the second.
http://www.nist.gov/public_affairs/releases/n99-22.cfm
18
NIST Cs clock
http://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm
19
How to build a better clock?
9 192 631 770 periods
per second
timeandnavigation.si.edu
20
What is a clock?
Schematic view of an optical atomic clock: the local oscillator (laser) is resonant with
the atomic transition. A correction signal is derived from atomic spectroscopy that is fed back
to the laser. An optical frequency synthesizer (optical frequency comb) is used to divide the
optical frequency down to countable microwave or radio frequency signals.
From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2
How good is a clock?
There are two principal characteristics that we consider when evaluating state-ofthe-art clocks: stability and uncertainty.
Stability is a measure of the precision with which we can measure a quantity
(think of how widely scattered a group of arrows red at target might be), and is
usually stated as a function of averaging time since for many noise processes the
precision increases (i.e., the noise is reduced through averaging) with more
measurements. The stability is usually set by the combination of the inherent
frequency purity of the physical system and the signal-to-noise ratio with which we
can measure the system.
In contrast, the (absolute) uncertainty for an atomic clock tells us how well we
understand the physical processes that can shift the measured frequency from its
unperturbed (“bare"), natural atomic frequency (think of how off-centre our group of
arrows might be). Small absolute uncertainty is clearly an essential part of a good
primary frequency standard and requires extensive evaluation of all known physical
shifts (usually called “systematic effects").
From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2
21
Clock unstability
Let us first consider the formula for clock instability, σy, in the regime where it is
limited by fundamental (as opposed to technical) noise sources, such as atomic
statistics based on the number of atoms:
spectroscopic linewidth of the clock system
the time required for a single
measurement cycle
the averaging period
clock transition
frequency
the number of atoms or
ions used in a single measurement
How to build a better clock?
22
Cesium microwave
atomic clock
Strontium optical atomic clock
9 x 109 periods
per second
4.3 x 1014 periods per second
http://www.nist.gov/pml/div689/20140122_strontium.cfm
Counting optical frequencies
Laser frequency (563 nm):
Interclock comparisons:
• Other optical standards (Al+, Ca, Yb, Sr, etc.)
Difference frequency:
• Microwave standards
Difference frequency:
Problem:
Fastest electronic counters:
Solution:
Femtosecond laser frequency comb
33
from Jim Bergquist’ talk
23
from John Hall’s Nobel Lecture
fromTheodor W. Hänsch‘s Nobel Lecture
24
Femtosecond Ti:Sapphire Laser
Pulsed output
Pump laser
Pulse duration:
Repetition rate:
23
from Jim Bergquist’ talk
25
Strontium optical atomic clock
Strontium optical atomic clock
http://www.nist.gov/pml/div689/20140122_strontium.cfm
26
Atomic frequency standards
Microwave
Transitions
Optical
Transitions
Neutral atoms in
optical lattices
Single ion
Th: nuclear clock?
Cs: 4×10-16
Sr: 6.4×10-18
M. A. Lombardi, T. Heavner, and S. Jefferts,
Measure: J. Meas.Sci. 2, 74 (2007).
B. J. Bloom et al., Nature 506, 71 (2014)
From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2
27
MOTIATION: NEXT GENERATION
ATOMIC CLOCKS
Next - generation
ultra precise atomic clock
http://CPEPweb.org
Atoms trapped by laser light
NIST Yb clock
The ability to develop more precise optical frequency standards is essential for
new tests of fundamental physics, search for the variation of fundamental
constants, and very-long-baseline interferometry for telescope array
synchronization.
More precise clocks will enable the development of extremely sensitive
quantum-based tools for geodesy, hydrology, and climate change studies,
inertial navigation, and tracking of deep-space probes.
ARE
FUNDAMENTAL
CONSTANTS
CONSTANT???
Being able to compare and reproduce experiments is at the
foundation of the scientific approach, which makes sense
only if the laws of nature do not depend on time and space.
J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003)
28
Note: we are still measuring them …
From NIST Tech Beat: July 19, 2011
29
Which fundamental constants to consider?
A pragmatic approach: choose a theoretical framework so
that the set of undetermined fixed parameters is fully known.
Then, try to determine if these values are constant.
It only makes sense to consider the variation of
dimensionless ratios:
Fine-structure constant α EM =
e2
~ 1/137.036
c
Electron or quark mass/QCD strong interaction scale
me
The electron-proton mass ratio
MP
me,q
Λ QCD
…
Possible sources for variation of the
fundamental constants
Unification theories
Extra space dimensions
Variation of the fundamental
constants in an expanding
universe
Scalar fields ?
Life needs very specific fundamental constants!
30
Life needs very specific fundamental constants!
α
~1/137
ħ
www.economist.com
If α is too big → small nuclei can not exist
Electric repulsion of the protons > strong nuclear binding force
α~1/10
α~1/137
will blow carbon apart
Life needs very specific fundamental constants!
α ~1/137
ħ
www.economist.com
α~1/137
Nuclear reaction in stars are particularly sensitive to α.
If α were different by 4%: no carbon produced by stars. No life.
31
Life needs very specific fundamental constants!
α
~1/137
ħ
www.economist.com
α~1/132
No carbon produced by stars:
No life in the Universe
???
Scientific American Time 21, 70 - 77 (2012)
32
How to test if α changed with time?
Atomic transition energies depend on α2
Mg+ ion
Scientific American Time 21, 70 - 77 (2012)
Astrophysics searches for variation of α:
looking for changes in quasar light
Scientific American Time 21, 70 - 77 (2012)
33
Julian Berengut, UNSW, 2010
Astrophysical searches for α−variation
Alkali-doublet method
3p3/2
∆EFS ∝ ( Zα )
3p1/2
2
Observed at red shift z

1  [ ∆EFS ]Z
= 
− 1

α
2  [ ∆EFS ]0

∆α
3s
Na, Mg+, Si3+
Murphy et al. (2001)
Observed on Earth
∆α
α
= −0.5(1.3) ×10−5
34
Astrophysical searches for α−variation
Many-multiplet method: compare spectra of different atoms
Relativistic correction
to the energy
Contributions of
many-body effects

∆
1
1
2
∝
−C
( Zα ) 
E n*
 j + 1/ 2

Transition energies depend on α2,
Need atomic calculations to find corresponding factor q
Observed from quasar
absorption spectra
  α 2 
EZ = E0 + q   Z  − 1
  α0 



Laboratory frequency
Conflicting results
Murphy et al., 2003: Keck telescope,
143 systems, 23 lines, 0.2<z<4.2
Quast et al, 2004: VL telescope,
1 system, Fe II, 6 lines
∆α α = −0.4(1.9)(2.7) ×10−6
∆α α = −0.12(1.8) ×10−6
∆α α = 5.7(2.7) ×10−6
Molaro et al., 2007
Z=1.84
Srianand et al, 2004: VL telescope, 23
systems, 12 lines,
Fe II, Mg I, Si II, Al II, 0.4<z<2.3
Murphy et al., 2007
∆α α = −0.54(12) ×10 −5
∆α α = −0.06(0.06) ×10 −5
∆α α = −0.64(36) ×10−5
V.V. Flambaum, Variation of Fundamental Constants
35
Astrophysical searches for α−variation: the problem of the isotopic abundances
On Earth at the present time:
7.6%
92.4%
Astrophysical searches for α−variation: the problem of the isotopic abundances
Early Universe
?%
?%
36
Astrophysical searches for α−variation: the problem of the isotopic abundances
The isotopic abundance ratios in gas clouds in the early universe
could vary significantly from those on earth at the present time, and the
resulting change in isotope shift (IS) can mimic the variation of α.
This effect is similar in magnitude to detected α−variation (Murphy et
al., 2003).
The separation of the IS from actual α-variation is possible by using
“anchor” combinations of atomic frequencies that are insensitive to
both effects and “probe‘” combinations of atomic frequencies that
are insensitive to IS (Kozlov et al., 2004).
Astrophysical searches for α−variation and probes of chemical evolution of the
Universe
One can form “probe” combinations that are sensitive to only isotope
shifts (IS) to measure isotopic abundances in the early universe at the
10-20% level.
This is crucially important for testing models of nuclear reactions in
stars and supernovae and the chemical evolution of the universe.
Use of “probe” and “anchor” combinations requires knowledge of the
isotope shifts for lines that can be used in astrophysical studies,
including Mg I, Mg II, Si II, Si IV, Ti II, Cr II, Fe II, Ni II, Zn II, and Ge II.
Very few IS measurements exist in these systems. Present IS accuracy
that varies from 2% for Mg I to 70% for Ni II is insufficient.
37
Can we look for α−variation in a lab?
Different optical atomic clocks use transitions that have different
contributions of the relativistic corrections to frequencies.
Therefore, comparison of these clocks can be used to search for
α−variation.
The most precise laboratory test of α−variation has been carried out
at NIST [1] by measuring the frequency ratio of Al+ and Hg+ optical
atomic clocks with a fractional uncertainty of 5.2×10-17.
Repeated measurements during the year yielded a constraint on the
temporal variation of α α = −1.6(2.3) × 10−17.
[1] T. Rosenband et al.,Science 319, 1808 (2008).
38
Laboratory searches for α−variation
Different atomic clocks use transitions that have different
contributions of the relativistic corrections to frequencies.
ν ( x) = ν 0 + qx
2
x = (α α 0 ) − 1
Therefore, comparison of different clocks can be used to
search for α−variation.
NIST [Rosenband et al., Science 319, 1808 (2008)]
Al+ / Hg+ atomic clocks
α α = −1.6(2.3) ×10−17 y −1
199Hg+ Energy Levels
5d106p
5d96s2
5d106s
• Atomic line
• State detection by electron shelving.
3
from Jim Bergquist’ talk
39
Trapped ions in an rf trap
• No static E or B fields;
Trap acts on total charge of ion,
not internal structure
• Trap ion at trap center where
trapping fields approach zero
~
rf
• Can operate in tight-confinement (Lamb-Dicke) regime
⇒ First-order doppler free.
2nd-order doppler shift (time dilation)
due to micromotion will limit accuracy
from Jim Bergquist’ talk
11
Liquid Nitrogen
Magnetic Shield
Cryostat Wall
77 K Shield
Liquid Helium
Helical Resonator
4 K Copper Shield
around trap
13
• Long storage times
• Environmental isolation
- Low collision rate
- Low blackbody
from Jim Bergquist’ talk
40
Some facts about Al+
1P
1
3P
• 8 mHz linewidth clock transition
167 nm
267 nm
1121 THz
• Small quadratic ZS (6x10-16 /Gauss2)
• Negligible electric-quadrupole shift (J=0)
1S
0
0
• Smallest known blackbody shift (8x10-18 at 300K)
I = 5/2
• Linear ZS 4 kHz/Gauss (easily compensated)
• Light mass (2nd order Doppler shifts)
• No accessible strong transition for
cooling & state detection
from Jim Bergquist’ talk
Clock state transfer to Be+
(simplified)
1. Cool to motional quantum ground state with Be+
2. Depending on clock state, add vibrational energy via Al+
3. Detect vibrational energy via Be+
from Jim Bergquist’ talk
41
Using two ions
Clock ion (Al+) for very accurate spectroscopy
Logic ion (Be+) for cooling and readout
Coulomb-force couples the motion of the ions
⇒ Cooling Be+ leads to cooling of Al+
Ion motion is quantized (n=0, 1, …)
Transfer information Al+ Motion Be+
from Jim Bergquist’ talk
from Jim Bergquist’ talk
Al+/Hg+ Comparison
fs-comb locked to Hg+
measure beat with Al+
1126 nm
laser
1070 nm
laser
fiber
×2
×2
fiber
×2
199Hg
Hg++
×2
fb,Hg
n frep+ fceo
9Be+
fb,Al
27Al+
m frep+ fceo
42
from Jim Bergquist’ talk
Al+/Hg+ Comparison
-17
νAl/νHg × 10
15
- 1 052 871 833 148 990
α-dot / α = (1.433 +/- 1.702) x 10
2
/ yr χ =2.9674
0.5
10-16
0.4
2006
2007
2007
Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec
NEED MORE
PRECISE
FREQUENCY
STANDARDS:
NEW CLOCK
PROPOSALS
43
Electronic bridge:
How to run Th3+ nuclear clock?
Th nuclear clock:
Nuclear isomer
transition in 229
Thorium has been
suggested as an
etalon transition in a
new type of optical
frequency standard.
Need calculations to find usable electronic transitions.
Correlation and relativistic effects in actinide ions,
M. S. Safronova and U. I. Safronova, Phys. Rev. A 84, 052515 (2011).
HIGHLYHIGHLY-CHARGED IONS ???
100
Cl6+
102 nm
200
300
400
500
Al+
267 nm
600
Wavelength nm
Mg
458 nm
Si2+
190 nm
3s2 1S0 – 3s3p 3P0 transition in Mg-like ions
44
HIGHLYHIGHLY-CHARGED IONS !
Optical transitions
are possible due to level crossings !
Sn-like ions
(current work)
[Kr] 4d105s2 core
Sn
5p6s 3P0
5p2 1S0
1D
289 nm
2
2
3
5p P0,1,2
Sn –like Ba6+
5p2 1S0
1D
2
3P
2
3P
1
5p2 3P0
Sn-like Pr9+
5p4f J=3
163 nm
495(13) nm
5p2 3P0
45