Transcript a pedagogical / historical introduction (D. Downes)

Pedagogical Introduction
 We
do multiplying interferometry. (correlator)
 We do ``1-photon’’ interferometry,
not ``2-photon’’ interferometry.
 We measure phases. We need phase stability.
We must phase-lock oscillators.
 ``Detection” occurs in the correlator.
 We cannot detect individual photons.
.
We do this.
(One-photon interferometry)
: 2 kinds
We don’t do this.
We REALLY do ``one-photon’’
interferometry:
 Example:
 Typical
flux density at 3mm~ 1 mJy
= 1.3E-7 photons / sec / m2 / Hz.
 2 x 15-m dishes => collecting area = 230 m2.
 In 1-MHz band, power to 2 dishes = 30 photons/sec.
 For clock rate of 320 MHz, sample time = 3.1 nsec.
 So we record ~10 million samples before getting one
photon from the sky.
 Is this OK ? Can we get interference?
``1-photon’’ interference: A student’s
experiment in 1909.
 Geoffrey Taylor
(student of J.J. Thompson).
 NB: Max Planck’s theory of quanta (1900).
 Taylor 1909, Proc. Camb. Phil. Soc., 15, 114
Geoffrey Taylor’s 1909 prototype of the
Plateau de Bure interferometer.
Taylor’s physics
experiment, built at home:
Left: strong, many-photon
light.
Right: 1-photon at a time.
(no difference).
``A photon only interferes with itself’’.
--- Dirac (1932)
Dirac got this by pure thought. Taylor’s paper
was long-forgotten. (In fact, only ``probabilty
amplitudes’’ interfere, not the photons).
But what about the 2-path,
2-dectector interferometer?
Suppose you send it only
``one photon’’ at a time?
Try it in the lab.
Detectors
One beam splitter: 2 paths, 2 detectors
post-detection correlation;
try one photon: get zero correlation !
Detector
 Conclusions:
 Photon
not a wave.
 Can identify path.
 No interference.
 NOT WHAT WE DO.
 What saves us?
Detector
Beam splitter
Correlation vs. photon number
1 photon
Grangier, Roger, Aspect (1986)
2 photons
Add a 2nd beam-splitter: (Mach-Zehnder)
now have 2 paths, correlate at end, just
like our mm interferometer.
M-Z like Plateau de Bure interferometer:
2 paths, correlate at end.
Antenna 1 path
Singlephoton
input
Antenna 2 path
One photon input to M-Z:
fringes as function of path delay.
Grangier, Roger, Aspect,
1986, Europhys. Lett., 1, 173
Hanbury Brown’s
radio interferometer
of 1952.
Almost right for us.
BUT WE DON’T DO THIS :
Our ``detector’’ is here : 
( the Correlator )
Note: Cables not necessary.
Hanbury-Brown used
WiFi (in 1952 !!).

Importance of phase-locking: Can
lasers interfere?
Enloe & Rodda
1965, Proc. IRE,
55, 166
Bell Labs,
Holmdel, N.J.
Lasers on shockmounted concrete bloc,
in a concrete vault.
Can two lasers interfere?
Yes, if you phase-lock.
This is Young’s 2-slit experiment, without the slits !!
Now Repeat Taylor’s experiment of 1909. Reduce flux to 1-photon.
Just like PdB mm –interferometer: 2 phased paths, 1-photon-at-a-time.
The interference pattern will still build up. ( ``A photon only interferes
with itself.” )
``One photon comes from two lasers !! ’’
Another way to think of it.
Loudon,Quantum Theory of Light, in agreement
with W.E. Lamb’s ``Anti-photon’’ critique.
.
1.
2.
3.
A ``photon’’ is not a globule of light, traveling
like a bullet through the interferometer.
Regard the interferometer as a tuned, (phaselocked) resonant cavity, that allows travelingwave modes.
A 1- photon excitation of a mode is
distrubuted over the entire interferometer,
including the two internal paths.
Yet another way to think of it:
 Think
of the two antennas (2 slits) as a filter.
 The filter takes one QM state and gives you
another (like an ``operator’’ on a Hilbert space).
 The filter convolves 2 delta-functions of
position with the original state to give you a
different state on the other side of the 2 slits.
 In contrast, you give the detector a QM state,
and it gives you back a number.
 Filters and detectors are very different things.
The ``quantum limit’’ for receivers is
irrelevant for interferometry.
receiver ``quantum limit’’ means k TR = h .
 So the receiver steadily emits 1 photon in (1/) sec.
 In a 1-MHz band, a receiver at the ``quantum limit’’
emits 106 photons /sec.
 But in a 1-Mhz band, 2 x 15m antennas looking at a
1-mJy source at 3mm collect only 30 photons/sec.
 So there is no way we can recognize that an
individual photon comes from the sky.
 The
Question in an interferometry course:
Suppose we could detect an individual
photon (e.g. on a hard disk at one antenna
of the Plateau de Bure interferometer).
Then how can we get interference?
The usual way to think of it.
The usual diagram of radio
interferometry is a space-space diagram.
It’s a snapshot at an instant in time.
Usual diagram of

Radio interferometry
An interferometers measures coherence in the electric
field between pairs of points (baselines).
Direction to source
ct

B
T2
T1
(courtesy Ray Norris)
Correlator
• Incoming signals are corrected for geometric delay t and
multiplied to yield a complex visibility, V = |V|ei, which
has an amplitude and phase.
Another way: a space-time diagram:
1 Photon in from sky to interferometer
which is at rest in space, moving only in
time (vertical straight line).
Change the Lorentz frame:
One photon in, two photons out.
One is an induced photon,
One is spontaneous emission.
Which is which?
No way to tell.
Hence we cannot identify the path.
Hence we can do inteferometry.
Basic Concepts

An interferometer measures coherence in the electric
field between pairs of points (baselines).
Direction to source
ct

B
T2
T1
(courtesy Ray Norris)
Correlator
• Because of the geometric path difference ct, the
incoming wavefront arrives at each antenna at a different
phase.
Aperture Synthesis

As the source moves across the sky (due to Earth’s
rotation), the baseline vector traces part of an ellipse in
the (u,v) plane.
v (kl)


T1
B
T1
B sin  = (u2 + v2)1/2
T2
u (kl)
T2
• Actually we obtain data at both (u,v) and (-u,-v)
simultaneously, since the two antennas are
interchangeable. Ellipse completed in 12h, not 24!