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Some recent experiments on weak measurements and quantum state generation. Aephraim Steinberg Univ. Toronto (presently @ Institut d'Optique, Orsay). Let's Make a Quantum Deal!. Let's Make a Quantum Deal!. Let's Make a Quantum Deal!. OUTLINE. The 3-box problem
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(presently @ Institut
Let's Make a Quantum Deal!
Let's Make a Quantum Deal!OUTLINE
PDFs:Morgan Mitchell Marcelo Martinelli (back Brazil)
Optics: Kevin Resch(Zeilinger) Jeff Lundeen
Krister Shalm Masoud Mohseni (Lidar)
Reza Mir[real world(?)] Rob Adamson
Karen Saucke (back )
Atom Traps: Jalani Fox Stefan Myrskog (Thywissen)
Ana Jofre (NIST?) Mirco Siercke
Samansa Maneshi Salvatore Maone ( real world)
Some of our theory collaborators:
Daniel Lidar, János Bergou, Mark Hillery, John Sipe, Paul Brumer, Howard Wiseman
But back up: is there any physical sense in which this is true?
What if you try to observe where the particle is?
PA = < |A><A| >wk = (1/3) / (1/3) = 1
PB = < |B><B| >wk = (1/3) / (1/3) = 1
PC = < |C><C|>wk = (-1/3) / (1/3) = -1.
Prepare a particle in a symmetric superposition of
three boxes: A+B+C.
Look to find it in this other superposition:
Ask: between preparation and detection, what was
the probability that it was in A? B? C?
were these postselected particles really all in A and all in B?
can this negative "weak probability" be observed?
[Aharonov & Vaidman, J. Phys. A 24, 2315 ('91)]
Aharonov et al., PRA 67, 42107 ('03)
Spatial Filter: 25um PH, a 5cm and a 1” lens
cf. Ritchie et al., PRL 68, 1107 ('91).
The position of each photon is uncertain to within the beam waist...
a small shift does not provide any photon with distinguishing info.
But after many photons arrive, the shift of the beam may be measured.
OR: STUDY CORRELATIONS OF PA & PB...
- if PA and PB always move together, then
the uncertainty in their difference never changes.
- if PA and PB both move, but never together,
then D(PA - PB) must increase.
Resch &Steinberg, PRL 92,130402 ('04)
Use two pointers (the two transverse directions)
and couple to both A and B; then use their
correlations to draw conclusions about PAB.
We have shown that the real part of PABW can be extracted from such correlation
(PAB = 1)Non-repeatable data which happen to look the way we want them to...
The result should have been obvious...
is identically zero because
A and B are orthogonal.
Even in a weak-measurement sense, a particle
can never be found in two orthogonal states at
the same time.
The bomb must be there... yet
my photon never interacted with it.
(AKA: The Elitzur-Vaidman bomb experiment)
A. Elitzur, and L. Vaidman, Found. Phys. 23, 987 (1993)
P.G. Kwiat, H. Weinfurter, and A. Zeilinger, Sci. Am. (Nov., 1996)
Consider a collection of bombs so sensitive that
a collision with any single particle (photon, electron, etc.)
is guarranteed to trigger it.
Suppose that certain of the bombs are defective,
but differ in their behaviour in no way other than that
they will not blow up when triggered.
Is there any way to identify the working bombs (or
some of them) without blowing them up?
Only detector C fires
Measurement, by definition, makes some quantity certain.
This may change the state, and (as we know so well), disturb conjugate variables.
How can we measure where the bomb is without disturbing its momentum (for
But if we disturbed its momentum, where did the momentum go? What exactly
did the bomb interact with, if not our particle?
It destroyed the relative phase between two parts of the particle's wave function.
D+ e- was in
D- e+ was in
But … if they were
both in, they should
We've got to be careful about how we interpret these
You're not always free to reason classically about what would
have happened if you had measured something other than what
you actually did.
(Do we really have to buy this?)
K. J. Resch, J. S. Lundeen, and A. M. Steinberg, Phys. Rev. Lett. 87, 123603 (2001).
2LO- PUMP =
PUMP - 2 x LO
Det. V (D+)
Det. H (D-)
V Pol DC
407 nm Pump
[Y. Aharanov, A. Botero, S. Popescu, B. Reznik, J. Tollaksen, quant-ph/0104062]
Upcoming experiment: demonstrate that "weak
measurements" (à la Aharonov + Vaidman) will
bear out these predictions.
An experimental implementation of Hardy’s Paradox is now possible.
Suppose we perform a which-path measurement using a
microscopic pointer, e.g., a single photon deposited into
a cavity. Is this really irreversible, as Bohr would have all
measurements? Is it sufficient to destroy interference? Can
the information be “erased,” restoring interference?
The fringe pattern (momentum distribution) is clearly changed –
yet every moment of the momentum distribution remains the same.
To find the probability of a given momentum transfer,
measure the weak probability of each possible initial
momentum, conditioned on the final momentum
observed at the screen...
Glass plate in focal
P(pi) weakly (shifting
photons along y)
in image plane measures
CCD in Fourier plane measures
<y> for each position x; this
determines <P(pi)>wk for each
final momentum pf.
(finite width due to finite
width of measuring plate)
Note: not delta-functions; i.e., momentum may have changed.
Of course, these "probabilities" aren't always positive, etc etc...
Note: the distribution
extends well beyond h/d.
On the other hand, all its moments
are (at least in theory, so far) 0.
Weak-measurement theory can predict the output of meas-urements without specific reference to the measurement technique.
Morgan W. Mitchell et al., to appear
The single-photon superposition state |1,0> + |0,1>, which may be
regarded as an entangled state of two fields, is the workhorse of
The output of a Hong-Ou-Mandel interferometer is |2,0> + |0,2>.
States such as |n,0> + |0,n> ("high-noon" states, for n large) have
been proposed for high-resolution interferometry – related to
A number of proposals for producing these states have been made,
but so far none has been observed for n>2.... until now!
(But cf. related work in Vienna)
[See for example
H. Lee et al., Phys. Rev. A 65, 030101 (2002);
J. Fiurásek, Phys. Rev. A 65, 053818 (2002)]
A "noon" state
A really odd beast: one 0o photon,
one 120o photon, and one 240o photon...
but of course, you can't tell them apart,
let alone combine them into one mode!
Okay, we don't even have single-photon sources.
But we can produce pairs of photons in down-conversion, and
very weak coherent states from a laser, such that if we detect
three photons, we can be pretty sure we got only one from the
laser and only two from the down-conversion...
|0> + e |2> + O(e2)
|3> + O(2) + O( 2)
+ terms with <3 photons
|0> + |1> + O(2)
Yes, it's that easy! If you see three photons
out one port, then they all went out that port.
How to combine three non-orthogonal photons into one spatial mode?
(or <2 photons)
But how do you get the two down-converted photons to be at 120o to each other?
More post-selected (non-unitary) operations: if a 45o photon gets through a
polarizer, it's no longer at 45o. If it gets through a partial polarizer, it could be
Tunneling times et cetera:
Hauge and Støvneng, Rev. Mod. Phys. 61, 917 (1989)
Büttiker and Landauer, PRL 49, 1739 (1982)
Büttiker, Phys. Rev. B 27, 6178 (1983)
Steinberg, Kwiat, & Chiao, PRL 71, 708 (1993)
Steinberg, PRL 74, 2405 (1995)
Aharonov & Vaidman, PRA 41, 11 (1991)
Aharonov et al, PRL 60, 1351 (1988)
Ritchie, Story, & Hulet, PRL 66, 1107 (1991)
Wiseman, PRA 65, 032111
Brunner et al., quant-ph/0306108
Resch and Steinberg, quant-ph/0310113
Scully et al, Nature 351, 111(1991)
Storey et al, Nature 367 (1994) etc
Wiseman & Harrison, N 377,584 (1995)
Wiseman, PLA 311, 285 (2003)
Hardy, PRL 68, 2981 (1992)
Aharonov et al, PLA 301, 130 (2001).
The 3-box problem:
Aharonov et al, J Phys A 24, 2315 ('91);
PRA 67, 42107 ('03)
Resch, Lundeen, & Steinberg, quant-ph/0310091