# Pedagogical Introduction

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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. - PowerPoint PPT Presentation

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• Pedagogical IntroductionWe 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.

• : 2 kinds . We do this. We dont do this.(One-photon interferometry)

• 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 students experiment in 1909. Geoffrey Taylor (student of J.J. Thompson). NB: Max Plancks theory of quanta (1900). Taylor 1909, Proc. Camb. Phil. Soc., 15, 114

• Geoffrey Taylors 1909 prototype of the Plateau de Bure interferometer.

Taylors 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. Taylors 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 ! Conclusions: Photon not a wave.Can identify path.No interference. NOT WHAT WE DO.What saves us?

DetectorDetectorGrangier, Roger, Aspect (1986)1 photon2 photonsBeam splitterCorrelation vs. photon number

• 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.Single-photon inputAntenna 1 pathAntenna 2 path

• One photon input to M-Z: fringes as function of path delay.

Grangier, Roger, Aspect,1986, Europhys. Lett., 1, 173

• Hanbury Browns radio interferometer of 1952. Almost right for us.

BUT WE DONT 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 & Rodda1965, Proc. IRE, 55, 166

Bell Labs,Holmdel, N.J.Lasers on shock-mounted concrete bloc, in a concrete vault.

• Can two lasers interfere? Yes, if you phase-lock. This is Youngs 2-slit experiment, without the slits !!

• ``One photon comes from two lasers !! Now Repeat Taylors 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. )

• Another way to think of it.Loudon,Quantum Theory of Light, in agreement with W.E. Lambs ``Anti-photon critique. A ``photon is not a globule of light, traveling like a bullet through the interferometer.Regard the interferometer as a tuned, (phase-locked) resonant cavity, that allows traveling-wave 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.The 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.

• 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. Its a snapshot at an instant in time.

• Radio interferometryAn interferometers measures coherence in the electric field between pairs of points (baselines).wavefrontCorrelatorBDirection to sourceBsinIncoming signals are corrected for geometric delay t and multiplied to yield a complex visibility, V = |V|ei, which has an amplitude and phase.ctT1T2(courtesy Ray Norris)Usual diagram of

• 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 ConceptsAn interferometer measures coherence in the electric field between pairs of points (baselines).Direction to sourceBecause of the geometric path difference ct, the incoming wavefront arrives at each antenna at a different phase.wavefrontCorrelatorBBsinctT1T2(courtesy Ray Norris)

• Aperture SynthesisAs the source moves across the sky (due to Earths rotation), the baseline vector traces part of an ellipse in the (u,v) plane.B sin = (u2 + v2)1/2v (kl)u (kl)T1T2Actually we obtain data at both (u,v) and (-u,-v) simultaneously, since the two antennas are interchangeable. Ellipse completed in 12h, not 24!BBsinT1T2

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