Degenerate Quantum Gases
manipulation on AtomChips
Francesco Saverio Cataliotti
Outlook
• Bose-Einstein condensates on a microchip
• Atom Interferometry
• Multipath Interferometry on an AtomChip
• Results and Conclusions
Degenerate atoms
T
e
m
p
e
r
a
t
u
r
a
Fermioni
Bosoni
T < TF
T < TC
EF
Degenerate Atoms
1925: Einstein predicts “condensation” of bosons
60’s: Development of Lasers
80’s: Development of laser cooling
1985: Magnetic Trapping of ultracold atoms
1986: Optical trapping of Na
1987: Na Magneto-Optical Trap
1995: First 87Rb Bose-Einstein Condensate
Huge playground for fundamental physics:
- BEC with Li, Na, K, Cs, Fr…
- Optical gratings, collective excitations…
First applications:
- Interferometry
- Earth and Space sensors
- Quantum Information
2001: First BEC of 87Rb
on an Atom Chip
Route to BEC in dilute gases
  n  2.612
3
dB
T  300 K
  10-20
laser cooling
T  10 K
  10-6
evaporative cooling
T 100 nK
  2.6
Magneto Optical Trap
(MOT)
F=- v-kz
cooling trapping
Evaporative cooling
remove highest
velocities
thermalization through
elastic collisions
cooling
temperature
Forced evaporation
in a magnetic trap
(conservative
potential)
E
x
BEC on a chip
Macroscopic trap
Micro-trap
I
Current ~ 100 A
n = 10-100 Hz
Power ~ 1.5 kW
Ultra High Vacuum ~ 10-11 Torr
double MOT system:
Laser power ~ 500 mW
Large BEC 106 atoms
but
production cycle > 1 min
Current < 1 A
Power < 10 W
n = 1-100 kHz
High Vacuum ~ 10-9 Torr
single MOT system:
Laser power ~ 100 mW
BEC 105 atoms
and
production cycle ~ 1 s
Laser Cooling close to a surface
s+
s+
s-
s-
s+
s-
BEC on a chip
Bbias =
{0,3.3,1.2} Gauss
8
7
6
5
4
3
2
1
1000
2000
3000
4000
5000
z (m)
Iwir= 1
3 A ; Bbias= {0,3.3,1.2} Gauss
|B| (Gauss)
Bwir (Iwir= 3A)
|B| (Gauss)
• Planar Geometry  gold microstrips on silicon substrates
2000
8
7
6
5
4
3
2
1
1000
1000
x (m)
2000
BEC on a chip
BEC Generation Routine
time [ms]
5000
action
MOT in reflection loading
10^8 atoms
5450
MOT transfer close to the chip (~1mm)
5485
CMOT + Molasses
5 x 10^7 atoms @ T ~ 10 μK
5490
Optical pumping
Ancillary magnetic trap (big Z wire)
20 x 10^6 atoms @ T ~ 12 μK
5740
Compression and transfer to the
magnetic trap on chip (chip Z wire)
20 x 10^6 atoms @ T ~ 50 μK (~200 μm)
8300
Evaporation (big U under the chip)
BEC with 30x10^3 atoms, Tc=0.5 μK
23000
End of the cycle
Imaging cold atoms
lens
atoms
CCD camera
BEC on a chip
MOT
~ 10^8 atoms
Molasses phase
~ 5 x 10^7 atoms @ T ~ 15 uK
First Magnetic Trap (big Z wire)
~ 20 x 10^6 atoms @ T ~ 12 uK
Magnetic Trap on Chip (chip Z wire)
~ 20 x 10^6 atoms @ T ~ 50 uK
BEC
~ 20 x 10^3 atoms @ T < 0.5 uK
Free fall of the BEC
Outlook
• Bose-Einstein condensates on a microchip
• Atom Interferometry
• Multipath Interferometry on an AtomChip
• Results and Conclusions
Atom Interferometer
BEC – coherent form of matter , a wavepacket
BEC 1
BEC 2
BEC
1,2
BEC 2
BEC 1,2
different spin states
coupling mechanism
BEC 1
BEC 1
Rabi pulse
separation for measurement
Stern-Gerlach experiment
BEC on a chip
Atomic Ramsey
Interferometer
- Theory Solve GPE for the BEC
2
Δ=ω 0 -ω
ω
ω0
start from
mix two states
1
let them evolve
for time T
Solve SE for 1 atom
for the non-interacting BEC
mix them up again
Rabi Oscillations
Stern-Gerlach method
mf=2
mf=1
BEC
mf=2
space
Tp
Δ
mf=2
B
time
- pulse
Rabi frequency
BEC
mf=1
Rabi Oscillation
mf
-2
-1
π/2
0
1
2
Rabi frequency ~ 50KHz
Experimental Scheme:
Ramsey Interferometer
π/2
π/2
Δ
mf=2
mf=2
space
B
mf=1mf=2
mf=1
time
Ramsey Interferometer
Oscillation frequency = 1/RF = 1/650KHz = 1.5 μs
Outlook
• Bose-Einstein condensates on a microchip
• Atom Interferometry
• Multipath Interferometry on an AtomChip
• Results and Conclusions
Parameters of the
Interferometric Signal
amplitude
D’Ariano & Paris, PRA (1996)
Resolution:
Working range:
background
Sensitivity:
Weihs et al., Opt. Lett. (1996)
24
Multi-path Interferometer
Multi-Path
interferometer

Funny enougn for N>3 the system can
be aperiodic since frequencies are
incommensurable
Even more fun they are the solutions of a
complex Fibonacci Polynomial
Fn1 ( x)  xFn ( x)  Fn1 ( x)



0  0 0 0


 0  0 0 
0  0  0


 0 0  0 
0 0 0  0


Multi-Path
interferometer
There does not exist a p/2 pulse.
To obtain the best resolution from
the interferometer one has to
optimize pulse area
Multi-Path
interferometer
Multi-Path
interferometer
Outlook
• Bose-Einstein condensates on a microchip
• Atom Interferometry
• Multipath Interferometry on an AtomChip
• Results and Conclusions
What can you use it for?
Detection of a Light-Induced Phase Shift
Polarisation σ+
Polarisation σ-
Light-pulse detuning from F=2  F=3 was 6.8GHz.
32
Conclusions
• We have demonstrated a compact time-domain multi-path
interferometer on an atom chip
• Sensitivity can be controlled by an RF pulse acting as a controllable
state splitter.
• Resolution superior to that of an ideal two-path interferometer.
•Simultaneous measurement of multiple signals at the output enables
a range of advanced sensing applications in atomic physics and
optics
• Integration of interferometer with a chip puts it into consideration
for future portable cold-atom based measurement systems.
Those who really did it
our typical signal
Ivan Herrera
Jovana Petrovic
Pietro Lombardi
Atom Chip
Team
Who did it?
A typical BEC
Jovana Petrovic
Ivan Herrera
Pietro Lombardi