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Lecture I: Controlling Single Atoms
38th International Nathiagali Summer College on Physics and Contemporary Needs
01. July 2013
D. Meschede, Institut für Angewandte Physik, Universität Bonn
Single Atoms: Controlling the Quantum World
Lecture I: Controlling Single Atoms
„ ...dass man ebenso wenig
mit einzelnen Atomen
experimentieren kann,
wie wir imstande sind,
Ichtyosaurier in einem Zoo
zu züchten.“
Erwin Schrödinger (1952)
Lecture I: Controlling Single Atoms
Portrait of a
Single Caesium Atom
A. Alberti, W. Alt, A. Rauschenbeutel, M. Spurny, A. Widera
Lecture I: Controlling Single Atoms
Why are we interested in controlling neutral atoms?
- Considered 1 of 7 seven potential routes towards
Quantum Information Processing (QIP)
Unique advantages:
* all atoms identical;
* „bottum up“ approach known (this lecture)
* „top down“ approach known (Mott insulators)
Disadvantages:
quantum gates difficult
(= controlled reversible interactions)
Perhaps more importantly:
Illustrating, exploring and controlling the quantum world
Lecture I: Controlling Single Atoms taming?
(c) 2007 ER!K · Personal Entertainment
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
Apparatus for manipulating single neutral atoms
Photon-
Counter
Imaging Optics
MOT-
Laser beams
1 Cs-Atom
1 µm/Pixel
Lecture I: Controlling Single Atoms
ca. 30 kg copper wire
Lecture I: Controlling Single Atoms
Real time movies with about 20-50 atoms
Lecture I: Controlling Single Atoms
Single Atom MOT
0 atoms
1 atoms
2 atoms
3 atoms
Lecture I: Controlling Single Atoms
500 nm
U0=
1.3 mK z
Wz
Characteristics of the optical dipole potential
MOT
LASER
Lecture I: Controlling Single Atoms
Laser Sequence
MOT Dipole Trap
N=0
N=2
N=4
N=3
0 10 20 30 40 50
Time [s]
Time (s) 0
1
5
ato
ms
ph
oto
n C
ount
Rate
[ 1
00 k
Hz ]
Lecture I: Controlling Single Atoms
Moerner, ... Single Ions
Walther, Haroche
1975 1980 1985 1990 1995 2000 2005
Kimble
Ertmer
Meschede
Rempe
Lu
McClelland
Grangier/Browaeys
Chapman
Single Neutral Atoms
Single Molecules
2010
Toschek, .Dehmelt, Blatt, Wineland, ...
Reichel, Kuhr, Saffman, ..
Lecture I: Controlling Single Atoms
Applications beyond basic quantum physics:
Atom number counting for
ATTA: Atom Trap Trace Analysis (Z. Lu, Argonne; M. Oberthaler, Heidelberg)
Laser-Based Methods for Ultrasensitive Trace-Isotope Analyses (Feature review article)
Z.-T. Lu and K.D.A. Wendt, Review of Scientific Instruments 74, 1169 (2003)
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
Optical conveyor belt (single atom tweezers)
A O M
A O M
Nd:YAG-Laser
Photon-
Counter
Imaging Optics
MOT-
Laser beams
Lecture I: Controlling Single Atoms
Frequency
Laser 1
Frequency
Laser 2
Lecture I: Controlling Single Atoms
"sort" atoms
coupling between
arbitrary pairs of
atoms
Two perpendicular conveyor-belts
Lecture I: Controlling Single Atoms
initial state:
target state:
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Dx Dx
Lecture I: Controlling Single Atoms
position of
vertical DT
after loading from MOT
after rearranging
six atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Light induced chemical reaction
(now called „parity check“)
Could make formation of a single molecule possible …
Lecture I: Controlling Single Atoms
more controlled motion:
spin dependent transport
P. Jessen , I. Deutsch, PRL 82 (1999), D. Jaksch et al.,ibid.
O. Mandel et al., PRL 91, 010407 (2003); D. Weiss (unpublished)
33
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
spin dependent transport (Caesium, l = 866 nm)
Lecture I: Controlling Single Atoms
Position
Tim
e
¼
¼
¼
UEOM
mirror EOM ¸ = 4
experimental
realization
(@ magic wavelength)
inital
final
Lecture I: Controlling Single Atoms
It works!
Lecture I: Controlling Single Atoms
2011: transport efficiency in excess of 99%/step!
2009
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
We need ´perfect` position control: Measuring the house number of the atom
28 29
30 31
32
Lecture I: Controlling Single Atoms
How to improve the precision for 2 or more neighbouring atoms?
optical instrument
EMCCD
input output
input output
Lecture I: Controlling Single Atoms
Imaging equation for a sampled light distribution
object
f ( x )
sampling noise
convolution sampling
“inverse” process
deconvolution regularization filtering
blurring
( f ¤ g ) ( x ) ( f ¤ g ) ( x i ) ( f ¤ g ) ( x
i ) + n ( x
i )
Lecture I: Controlling Single Atoms
44 PRL 102, 053001 (2009)
Lecture I: Controlling Single Atoms
Distribution of
atoms
Distribution of atom
pairs
45
now called “parity” Used to be “light induced losses”
M. Karski et al., PRL 102, 053001 (2009)
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
Quantum-Bit (Qubit)
y1
y0
y = ay1 + by0
Classical Bit
1
0
{ 1,0 }
Good atoms have 2 levels only! {↑,↓}
Lecture I: Controlling Single Atoms
survival probability:
P(F = 3) > 99 %
P(F = 4) < 0.5 % F = 4
F = 3
F´ = 5
"push-out" laser Cs
(1) „Push-out“ technique
Lecture I: Controlling Single Atoms
Microwave radiation
at 9.2 GHz couples the
up/down quantum states
y1
y0
y = ay1 + by0
Lecture I: Controlling Single Atoms
Contrast close to 100%, detection efficiency > 90%
Coherence times: Circumstantial! 1 ms < t < 1 s
Rabi oscillations
Lecture I: Controlling Single Atoms
``HOT´´ atoms COLD atoms
F = 4
F = 3
dCOLD
dHOT
d
Lecture I: Controlling Single Atoms
t
p/2 p/2
delay
p
p
0 20 40 60 80 100 120 140 160 0
5
10
15
20
25
30
35
40
delay [ms]
po
pu
latio
n in
F=
3 [%
]
Lecture I: Controlling Single Atoms
0 50 100 150 200 250 300 0
5
10
15
20
25
30
35
40
delay [ms]
p
0 50 100 150 200 250 300 0
5
10
15
20
25
30
35
40
delay [ms]
p
popula
tion in F
=3 [%
]
Lecture I: Controlling Single Atoms
Controlling neutral atoms:
Tswitch > 16 µs
(mK)
Lecture I: Controlling Single Atoms
55
0
mF = -4
4
mF = -3
9.2 GHz
F = 4
F = 3 3
Site Selection –
Turn MRI around !
Caesium hyperfine structure
55
Use Microwaves
and B-Field Gradients:
Lecture I: Controlling Single Atoms
• prepare atoms
• initialize register
• write into register
• read register
Lecture I: Controlling Single Atoms
The optical lattice spectrum analyzer:
magnetic field gradient maps spectrum into spatial distribution
spin flip spectrum (p-pulse for d=0)
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
New J. Phys. 12, 065027 (2010).
Beautiful 2D images
by
M. Greiner, Harvard
S. Kuhr/I. Bloch, MPQ
„Quantum gas microscope“ Ref: Physics Today, Oct 2010
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
… beyond playing marbels with atoms …
Ref: Wikipedia
Lecture I: Controlling Single Atoms
Displacement
allows microwave
transitions with Dn ≠ 0
High order sidebands! 62
Quantum states
|𝑛, ↑⟩ |𝑛, ↓⟩
Dn = 0 for
identical potentials
carrier transitions only
Lecture I: Controlling Single Atoms
tunable Franck-Condon/Lamb-Dicke factor!
Lecture I: Controlling Single Atoms
Microwave Spectroscopy
(associated with dark state cooling, Raman cooling)
Lecture I: Controlling Single Atoms
Spectral lineshapes are well understood
(transverse motion)
Lecture I: Controlling Single Atoms
Microwave Cooling
(associated with dark state cooling, Raman cooling)
Lecture I: Controlling Single Atoms
Microwave
Repumping
Lecture I: Controlling Single Atoms
Cooling removes energy …
… kinetic … … potential …
Lecture I: Controlling Single Atoms
Coherent Motional Control
(associated with dark state cooling, Raman cooling)
Lecture I: Controlling Single Atoms
70
Coherent excitation for Dn = 1 - 17
70
Lecture I: Controlling Single Atoms
Motion and Polarization Control
(associated with dark state cooling, Raman cooling)
Lecture I: Controlling Single Atoms
Carrier 1st Blue 2nd Blue
Carrier
1st Blue
2nd Blue
Position on the
Poincaré sphere
defined to
better than 10-3 !
Lecture I: Controlling Single Atoms
Check for smallest
excitation in sidebands:
This is our sweet
point!
red
blue Even more sensitive
with phases?
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
• Rb: some 10000 atoms
T ~ 250 nK detection:absorption imaging
• Cs: single atoms
T ~ 30 µK detection: fluorescence
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Thermalization of single Cs atoms • Cs cooled to Rb temperature
• Immersion of Cs into Rb gas, strong interaction
• |aRbCs| > 450 Angstrom
Lecture I: Controlling Single Atoms
3 body collisons limit the
life time of the atoms
N. Spethmann, Thesis (2012)
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
- Preparing & Moving Atoms
- Single Atom Detection
- Qubits and Adressable Atoms
- Motional Atom Control
- Single Atoms in Ultracold Gases
- Interfering Atom Trajectories
Lecture I: Controlling Single Atoms
• Splitting a Single Atom
Position
time
¿
„proto-entanglement“
p/2 pulse
+d shift
+d shift
p pulse
idle
p/2 pulse
+d shift
+d shift
p pulse
Lecture I: Controlling Single Atoms
single atom interferometer
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
programming
long
sequences
need coherence!
Lecture I: Controlling Single Atoms
500:1 !
2011: 10 µm
2012/3: 1 mm ??
Lecture I: Controlling Single Atoms
Contrast
Phase/2p
Lecture I: Controlling Single Atoms
86
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
Lecture I: Controlling Single Atoms
- Sources of Single Atoms
1-10 atoms for 1 minute
- Optical Conveyor Belts
spin dependent transport, microwave cooling
- Single Atom Adressability
use field gradients/composite pulses
- Single Site Detection
next neighbors resolved!
- Split Atoms with Macroscopic Separations
sensitive single atom interferometer
- Single Impurities for Ultracold Gases
the coldest single atoms?