Upload
ami-fowler
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
►Coherent Stern-Gerlach splitting on an atom-chip
China, Sep 2013
Shimon Machluf
Ben-Gurion University of the Negev
www.bgu.ac.il/atomchip
S. Machluf, Y. Japha, R. FolmanNature Communications 4, 2424 (2013)
Views from the desert
OutlineOutline
• Motivation for interferometry on a chip
• Why Stern-Gerlach Interferometers should not work
• Our two level system
• Our Stern-Gerlach method
• Results
• Conclusions
What we want to do with chip interferometryWhat we want to do with chip interferometry
I: Surface physics – use the atoms as a probee.g. Mesoscopic transport, Johnson noise, shot noise of fractional charge
I: Surface physics – use the atoms as a probee.g. Mesoscopic transport, Johnson noise, shot noise of fractional charge
Non-interferometric atom-chip measurements
Example: electron transport
BGU+HD, Science (2008)
State of the art: RF and MW double-well splitting
II: Many bodye.g. Squeezing, collisional dephasing, thermodynamics
II: Many bodye.g. Squeezing, collisional dephasing, thermodynamics
e.g. an example of recent work done on an atom chip (Science, 2012)
PS single atom physicsis also still interesting! (x3)
III: momentum splitting for metrologyIII: momentum splitting for metrology
Ken Takase / Mark Kasevich 2008
e.g. Large area and large effective area
Could be used for sensing technology or fundamental studies:e.g. Chu, Holger Muller, Mark Kasevich
Fundamental tests with matter-wave interferometersFundamental tests with matter-wave interferometers
State-of-the-art in momentum splittingState-of-the-art in momentum splitting
Typically, accurate beam splitters are done with light: quantum accuracy (!) but hard to get large momentum
Is there an alternative, and can classical systems also do the job?
The differential force of the Stern-Gerlach experiment
Stern-Gerlach 1922
A plaque at the Frankfurt institute
commemorating the experiment
Stern-Gerlach in cold atoms @ BGU
Otto SternNobel prize 1943
Two reasons why aStern-Gerlach Interferometer
should not work
Two reasons why aStern-Gerlach Interferometer
should not work
1. External noise couples differently to different spin states
Heisenberg (1930), Wigner (1963): separation of the partialbeams will introduce a large dispersion of phases within theindividual beams.Bohm (1951), Englert (1988), Schwinger (1988), Scully (1989):The required precision is very high.
2. Is the wave packet like Humpty-Dumpty?
Quantum systems in our labQuantum systems in our labAlkali vapor Color centers in diamond
Find papers onthese 3 systemson our web site:www.bgu.ac.il/atomchip
The Atom Chip
Vapor work:
Archive 2013
Diamond work:
1-1 0
780nm
F=3F=2F=1F=0
1 20- 1-2F=2
F=15S1/2
5P3/2
Hyperfine structure of Rb 87
Zeeman sub-levels
6.8GHz
780nm
F=3F=2F=1F=0
1 20- 1-2
F=2
F=15S1/2
5P3/2
Lifting the degeneracy of the Zeeman sub-levels
6.8GHz
Same happens in the excited state
Pieter ZeemanNobel 1902
Stern-Gerlach in cold atoms @ BGU
780nm
F=3F=2F=1F=0
1 20- 1-2
F=2
F=15S1/2
5P3/2
Utilizing Rb as a 2-level system
6.8GHz
Same happens in the excited state
Second order Zeeeman
Two unique properties of the atom chip which we use here:
high field gradients and accurate on/off
Two unique properties of the atom chip which we use here:
high field gradients and accurate on/off
Example: I=2A r=10microns => B=400G => B’=40kG/mm
In addition, low inductance of wires enables quick on/off
Field gradient beam splitterField gradient beam splitter
•
•
•
•
•
•
(in our case: )
Gradient may be applied parallel or perpendicular to motion
Norman F. RamseyNobel prize 1989
Isidor Isaac RabiNobel prize 1944
Part we work with
Simple kinematic view:differential acceleration
A. Daniel et al., PRA (2013)
(< 10^6 A/cm^2)
Large distance
10^7 A/cm^2F=μ B’B[G]=2 I[A]/r[mm]
Geometrical factor for finite size:(2z/D)*arctan(D/2z)
Theory includes Breit-Rabi
GP sim.
Figure 1.1 – The Bloch sphere
Z
0
1
YX
Fourier transform view: varying Ramsey frequency
Data fromBGU
Experiment: free fallExperiment: free fall
• Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms
• atoms 100 μm from the surface of the chip
• Zeeman splitting of 25MHz
• Strong enough field to take the transition to the |2,0> out of resonance (250kHz)
• Two π/2 pulses with Rabi frequency 20-25 kHz
• Between the pulses, 2-3 A current in a 2x200 μm gold wire (< 10^6 A/cm^2)
• Measure momentum separation
Characterizing the beam splitter
Error bars are from different runs
The FGBS is very versatileThe FGBS is very versatile
• Large dynamic range
• Can split in the direction, and perpendicular to the direction, of motion
• Can work also in trapped mode for BEC or guided interferometry
• Can work also with the mag. insensitive clock states |1,0> ►|2,0> for low noise:
[ T ]
[ Hz ]
• If you put far away the second π/2, or two FGBS, you create a population interferometer
Choose your signal
spatial
population
Another example of versatility: trapped BECAnother example of versatility: trapped BEC
• Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms
• atoms 250 μm from the surface of the chip
• Trap frequencies 2π x 100 Hz and 2π x 100/1.4 Hz
• Zeeman splitting of 18MHz
• Strong enough field to take the transition to the |2,0> out of resonance (100kHz)
• Two π/2 pulses with Rabi frequency 5-10 kHz (pulses less accurate because of traps)
• Between the pulses, no need for current in the chip wire as traps give acceleration
• Measure momentum separation
vr
GP simulation with no free parameters
Error bars are from different runswith different Rabi frequencies and different TOF.
Bringing the wave packets togetherBringing the wave packets together• For the freely falling atoms, a second gradient is applied
• For trapped atoms, an oscillation time is added
All periodicities fit well with the known estimate:ht/md
1D BEC @ BGU: phase fluctuations –Self-induced interference pattern
Non deterministic fringes
Coherence = deterministic fringesCoherence = deterministic fringes
So why do we see coherence:
1. Wave packets very small2. Different spin for very short time3. And we are lucky that the initial positiondoes not matter
29 runs(1/2 an hourof data)
Outlook: ultimate phase stabilityOutlook: ultimate phase stability
General FGBS:
Our FGBS:
δΦ/ΔΦ , δp/Δp ~ δI/I, δT/T, δz/z
δp in our interferometer is canceledby the second pulse and is dependent on Δp which goes to zero.
δΦ within our FGBS:
If you plug in our 2A 5μs pulse, 100μm distance, δI/I=10^-3, you get δΦ=1 rad
δz/z may be made negligible e.g. in a 3 wire configuration where the trap position isindependent of current, but in any case as shown it affects only the c.m.degree of freedom.
Single shot: Calculate C(t). For BEC C(t)=1 so visibility should be 100% pending purity, population imbalance, imaging resolution, etc.
Shot-to-Shot:
δp/Δp: 10^-7 and beyond.
Comment on trapped BEC
Side remark: A separate project by Shuyu ZhouSide remark: A separate project by Shuyu Zhou
Shuyu explaining his experimentto Peter Zoller and Ignacio Cirac
Quantum coherence in a collision between a BEC and a snake shaped wire
Very preliminary results of phase imprint
Average of 30 images
Shimon Machluf
• The field gradient beam splitter is fast, allows large momentum,is very versatile, and requires no light
• Atom Chips enable the strong pulsed gradients this beam splitter requires
• Applications range from many body, to surface\material science, and metrology.
• We have seen first signs of coherence. We are still very far from shot noiseso there is much to improve.
• It seems that for high momentum transfer, the SG beam-splittermay even have better accuracy than light beam-splitters, but itsstill very early to tell…
To conclude:
My latest anti-gravity experiment….
Pieter ZeemanNobel 1902
A field gradient will produce a force on any magnetic moment
first and secondorders
No two separate wave packets
0
0.25
0.5
0.75
1
0 1 2 3 4 5 6
time
P1(
t)
0
Figure 2.1 – Rabi oscillations
2
2
0
2
220
2
01 ωωΩΩ~
,tΩ~
cos1Ωωω
Ω
2
1(t)P1(t)P
Isidor Isaac RabiNobel prize 1944
Rabi Oscillations in a 2-level system:
π/2 pulse
Bloch sphere
Figure 1.1 – The Bloch sphere
Z
0
1
YX
12
θsine0
2
θcosΨ i
Examples:
Cold atoms @ BGU
Room temperatureatoms in a solid (!) @ BGU
Additional tools we will use:Additional tools we will use:
Bloch sphere
Figure 1.1 – The Bloch sphere
Z
0
1
YX
12
θsine0
2
θcosΨ i
Norman F. RamseyNobel prize 1989Ramsey fringes
022 )()( BFREERAMSEY TT
T
RAMSEYZ dttT0
, ))(cos(cos)(
0
0.2
0.4
0.6
0.8
1
0 5 10T
P1
Detuning =0
Detuning =0.1
Detuning =0.5`
RamseyOscillations@ BGU
Norman Ramsey (Nobel 1989, passed away 2011) and Dan Kleppner - 2005
Atom chip review article: RF et al. Adv. At. Mol. Opt. Phys. 48, 263 (2002)
One of the humble beginnings: RF et al. PRL 84, 4749 (2000)
Applications: clocks, acceleration sensors, gravitational sensors, magnetic sensors, quantum memory and communications, quantum computing
Fundamental science: Decoherence, interferometry, many body, atomic physics,low dimensional systems, atom-surface physics, surface physics, symmetries and fundamental constants
Dra
win
g f
rom
pa
pe
r b
y Ja
kob
Re
ich
el;
con
veye
r b
elt
– in
ven
tion
by
Te
d H
ae
nsc
hA quick reminder of what the atom chip is:
“where material engineering meets quantum optics”
A quick reminder of what the atom chip is: “where material engineering meets quantum optics”
The monolithic integration dreamThe monolithic integration dream
The atom chip technology is advancing very rapidly so that eventually, all the different particles such as Rydberg, molecules, atom-like (NV), ions, cold electrons, etc. may be put on the chip, including entanglement to a quantum surface.
Atom
Chips:
From
3 in 2000 to ~30 today,
• new book on atom chips, RF, Philipp Treutlein and Joerg Schmiedmayer, (Eds: Jakob Reichel and Vladan Vuletic)
• special issue on QIP (Journal of Quantum Information ProcessingEditors :Howard Brandt & RF )
The Atom Chip definition is broadeningThe Atom Chip definition is broadening
More information on the atom chip in:More information on the atom chip in:
+ near field optics, plasmonics, etc.
Highest tem
perature gradient know
n to mankind
Ion and permanent magnet chips@ BGU for Mainz and Amsterdam
A Bose-Einstein CondensationA Bose-Einstein Condensation
1D BEC @ BGU: phase fluctuations –Self-induced interference pattern
3D BEC @ BGU
Phase Imprint
What is phase imprint?
The Process of Phase Imprint
Ucu_Z + Usnake1
Ucu_Z + Usnake2
Icu_Z =32.3A
Isnake1 =30mA
Isnake2 =5mA
Iy_bias =84.7A
Ix_bias =0A
We suddenly reduced the snake current from 30mA to 5mA. The BEC approached the chip surface and came back. After 6ms, about one oscillation cycle, we turned off all currents and released the BEC.After about 9-13ms we probe the density distribution by absorption imaging.
About 38um
About 5um
Experiment result of phase imprint __single shot
Stability_Average of 30 shots