Transcript Margalit - The Racah Institute of Physics

A self-interfering clock as a
“which-path” witness
Yair Margalit
The Atom Chip Group
Ben-Gurion University
www.bgu.ac.il/atomchip
+
Y. Margalit, Z. Zhou, S. Machluf, D. Rohrlich, Y. Japha,
and R. Folman, Science 349, 1205 (2015).
1
Outline
• The atom chip
• Our main tool: a Stern-Gerlach beam
splitter
• Clock interferometry
• Some speculations
2
A quick reminder of what the atom chip is:
Drawing from paper by Jakob Reichel; conveyer belt – invention by Ted Haensch
“where material engineering meets quantum optics”
First attempts 15 years ago in Innsbruck, Munich and Harvard.
3
Two unique properties of the atom chip
which we use here
1. High field gradients, example:
I=2A r=10microns => B=400G => B’=40kG/mm.
2. Low inductance of wires enables quick on/off times (~1ms).
In addition: low power needed.
4
Reminder II:
Stern-Gerlach 1922
Otto Stern
Nobel prize 1943
A plaque at the Frankfurt institute
commemorating the experiment
mF=-2
mF=-1
mF=0
mF=+1
mF=+2
Stern-Gerlach in cold atoms @ BGU
5
Two reasons why a
Stern-Gerlach Interferometer
should not work
The SG interferometer:
An idea almost
a century old…
1. External noise couples differently
to different spin states
Previous attempts used 3 layer shields
(we don’t have shields at all because of the speed
of the magnetic pulses)
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2. Is the wave packet like Humpty-Dumpty? (Englert, Scully, et al.)
The quantum analogue of the arrow of time in the breaking glass.
Magnetic curvatures cause phase dispersion, and very sensitive to fluctuations.
Heisenberg (1930), Wigner (1963): separation of the partial
beams will introduce a large dispersion of phases within the
individual beams.
Bohm (1951), Englert (1988), Schwinger (1988), Scully (1989):
The required precision is very high.
But we get 99% (nor.) visibility
(even though 1015 electrons
couple directly to the atoms!)
As far as we know: this is the first spatial SG interferometer realization
S. Machluf, Y. Japha, RF. Nature Comm. 4, 2424 (2013).
7
Devereux, Michael. "Reduction of the atomic wavefunction in the Stern–Gerlach
magnetic field." Canadian Journal of Physics 93.11 (2015): 1382-1390.
8
Atom chip
Interferometry with the field
gradient beam splitter (FGBS)
|1〉
|2〉
|2〉
BEC of 104 87Rb
Time100
of|1〉
flight,
atoms,
mm
below
the atom
expansion
andchip
overlap
𝜓𝑖𝑛 = |2, 𝑝 = 0, 𝑧0 〉
𝜋/2
1 + |2〉 |𝑝 = 0, 𝑧0 〉
𝜕𝐵/𝜕𝑧
𝜋/2
→ Interference
1, 𝒑1 + |2, 𝒑2 〉 |𝑧0 〉
(|2, 𝒑2 〉 − 2, 𝒑1
+ 1, 𝒑1 + 1, 𝒑2 )|𝑧0 〉
𝜕𝐵/𝜕𝑧
z
𝜓𝑓 = 2, 𝒑𝑓 , 𝑧1 + |2, 𝒑𝑓 , 𝑧2 〉
Beam splitter output: spatial
superposition of the same internal and
momentum states.
S. Machluf, Y. Japha, and R. Folman, Nat. Commun. 4, 2424 (2013).
9
𝐹, 𝑚𝐹 = 2,2 ≡ 2 ; 2,1 ≡ |1〉
Clock Interferometry
motivation: study the interplay of QM and GR
Not only a phase shift due to the gravitational potential, but also a reduction
of visibility due to distinguishability induced by gravitational red-shift.
M. Zych, F. Costa, I. Pikovski, and Č. Brukner, Nat. Commun. 2, 505 (2011).
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Quantum mechanics meets GR
Classical potential gives
a phase shift.
Matter-wave
interferometer
(neutron)
We are searching
for visibility shifts!
“Observation of gravitationally induced quantum interference”, Colella, R., Overhauser, A.
W. & Werner, S. A. Phys. Rev. Lett. 34, 1472–1474 (1975).
necessarily
upon
both
the gravitational
“OpticalOutcome
clocks and relativity”,
C. W.depends
Chou, D. B.
Hume,
T. Rosenband,
and D. J. Wineland,
Science constant
329, 1630 (2010).
and the Planck's constant.
Simplest clock: utilizing Rb as a (magnetic sensitive) 2-level clock
1. Non-linear Zeeman effect helps
us make a good 2-level system
25MHz
25MHz+180kHz
2
1
0
780nm
-1
mF=-2
2. Initiate the clock
3. The clock tick rate depends on
the Zeeman splitting and this is
how we create a synthetic GR red-shift
12
13
Do we have a clock in a coherent spatial
superposition?
The answer is YES.
14
TG = 0 ms
Df = f0 (= 84o)
15
TG = 2 ms
16
TG = 4 ms
17
TG = 6 ms
18
TG = 8 ms
19
Orthogonal clock states,
“which path” information
exists – no fringes
TG = 10 ms
Df = f0+DwTG = p
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TG = 14 ms
21
TG = 18 ms
22
TG = 22 ms
23
TG = 26 ms
24
Identical clock states,
revival of the
interference fringes
TG = 30 ms
Df = f0+DwTG = 2p
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Varying the clock orthogonality

Observing complementarity (V2+D2=1) in action.
Redshift
Complementarity expects revivals of the visibility
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Complementarity inequality: V2+D2≤1
D = sin(Df/2)
27

Varying the preparation of the clock
Clock preparation
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Required precision to measure the redshift
Gravitational time dilation at Earth’s surface:
𝜏 ≃ Δ𝑇 (1 + 𝑔𝑅/𝑐 2 )
For a 1 meter separation, 1 second interferometer time, the
proper time difference is
Δ𝑇𝑔Δℎ
−16 𝑠𝑒𝑐
Δ𝜏 =
≃
10
𝑐2
optical
Kovachy,
al. "Quantum
at the
M. Zych,T.,F.et
Costa,
I. Pikovski,superposition
and Č. Brukner,
Nat.half-metre
Commun. scale."
2, 505 Nature
(2011). 528.7583
(2015): 530-533.
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Some speculations for the end:
Gravity induced decoherence?
The internal frequencies are
modified => this correlates
the internal states and the
centre-of-mass position of
the molecule
“Universal decoherence due to gravitational time dilation”. I. Pikovski, M. Zych, F.
Costa, Č. Brukner, Nat. Phys.10.1038/nphyS3366 (Jun.,2015).
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An even wilder speculation: post-quantum theories
A very naïve example of a post-quantum theory: V^2+D^2>1 ??
Vm - measured visibility; VQM - visibility
predicted by quantum mechanics
• High visibility because of Bohmian
trajectories
• High distinguishability because of GR red
shift
Conclusions:
1. The atom chip has enabled to realize a coherent spatial Stern-Gerlach beam
splitter with high phase stability (99% normalized visibility) – what is the limit?
2. This allowed for the first time to put a clock in a spatial superposition.
3. We simulated red shift with a magnetic gradient. Our experiment can thus be
completely explained by standard QM, but it simulates an experiment that cannot
be explained only by QM (i.e. without GR).
4. Time is a which path witness! Enables to study the interplay between QM and GR.
5. Next step is to do it with better clock states (|1,0> and |2,0>), for which a bias field
is not required. We can again use our SG as the second order force is strong
enough.
6. Speculating: the connection between gravity and quantum
dephasing may be significant. (and may even lead to wave
function collapse e.g. Penrose)
7. Speculating some more, perhaps we can learn something about
post-quantum directions.
8. Speculating^2, perhaps we can even learn something new on time
itself.
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A self-interfering clock as a “which path” witness
Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha,
Ron Folman
Technical:
Financing:
Acknowledgements
Zina Binstock, BGU nanofabrication facility
Israel Science Foundation
EC “MatterWave” consortium
German-Israeli Project Cooperation (DIP)
Council for Higher Education (PBC)
Ministry of Immigrant Absorption
John Templeton Foundation
Atom Chip Group
http://www.bgu.ac.il/atomchip/
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Ilse Katz Institute for Nanoscale Science and Technology http://www.bgu.ac.il/en/iki
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The gravitational time dilation they’re talking about as making the “which-way” distinction is,
near the surface of the Earth, approximately: T ~ T0 ( 1+ gR/c2)
where T is the time between ticks for the clock a distance R from the center of the Earth
(something not too different from the radius of Earth), T0 the time for a clock far away
from anything massive, and g the strength of gravity near the surface of the Earth. If you
plug numbers in for two clocks at different elevations, this is a shift of about one part in
1016 per meter of difference.
(As a sanity check, that’s about what they see in the aluminum-ion clock experiment at NIST:
they raised one clock above the other by about 33cm, and see a shift of a bit under 5 parts
in 1017. So I’m not completely off base, here…)
The largest separation between paths I’m aware of in an atom interferometer is the
10-meter tower interferometer in the group of my old boss, Mark Kasevich. That’s from
2013, with a separation of a centimeter and a half. I have heard, but not seen solid
documentation of, that they’ve expanded this to half a meter or so.
To get the interference-destroying effect, they applied a phase shift of π to one arm, which
would correspond to half a “tick” of the clock– that is, half the oscillation period. To see this
gravitationally, you would need to have that part-in-1016 shift amount of a difference of one
oscillation period over the time in the interferometer (a couple of seconds for the 10-m tower).
For a microwave clock transition like you have in the rubidium used in the Kasevich group,
you’re a factor of a million away– the frequency is about 7,000,000,000Hz, so the shift would
be on the short side of a microhertz. That’s not going to do much.
You might, however, get somewhere with one of the optical clock atoms, like strontium. the “clock”
transition in Sr is in the visible region, at around 400,000,000,000,000Hz, so a part-in-1016 shift is close
to 1Hz. Over a couple of seconds, that’s probably enough phase shift to significantly degrade the
contrast, based on the graph in the new paper. How plausible is that? Well, it’s not ridiculous.
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Phase stability
Single shots
138 shots average
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The Atom Chip definition is broadening
Atom Chips: From 3 in 2000 to many today,
The atom chip technology is advancing rapidly so that
eventually, all the different particles such as Rydberg,
molecules, atom-like (NV), ions, cold electrons,
anti-matter, etc. may be put on the chip,
including entanglement to a quantum surface.
The monolithic integration dream
Tim Freegarde
Ion and permanent magnet chips
@ BGU for Mainz and Amsterdam
+ Nottingham Sagnac…
+ near field optics,
plasmonics, etc.
More information on the atom chip in:
• book on atom chips,
RF, Philipp Treutlein and Joerg Schmiedmayer,
(Eds: Jakob Reichel and Vladan Vuletic)
• special issue on QIP
(Journal of Quantum Information Processing
Editors :Howard Brandt & RF )
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What is Normalized visibility?
What effects does it take out?