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Astronomical Applications of Quantum Optics This talk originates from a study ( Quanteye ) performed in 2005 in the frame of ESO’s OWL (then a 100m telescope) instrumentation, but which is valid for all Extremely Large Telescopes (ELTs). Main topics of the talk The time domain

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astronomical applications of quantum optics
Astronomical Applications of Quantum Optics

This talk originates from a study (Quanteye) performed in 2005 in the frame of ESO’s OWL (then a 100m telescope) instrumentation, but which is valid for all Extremely Large Telescopes (ELTs).

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main topics of the talk
Main topics of the talk

The time domain

Quantum properties of (non-thermal) light

Intensity interferometry (HBTII)

Clocks and Detectors

Quanteye for 100m OWL

Aqueye, our Precursor for Asiago

The Photon Orbital Angular Momentum (light beam vorticity)

For quantum optics activites in Padova see: www.abfgroup.com

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1 time domain in astronomy
1 - Time domain in astronomy

Astronomy expands by pushing parameter envelopes, e.g.

. in wavelength

. in spatial resolution

Future:

Extremely High-Time Resolution Astrophysics? Non-thermal processes and ’Quantum’ properties of light?

Well below t  1x10-6 s, a “new” window to the Universe ?

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all of astronomy
All of astronomy

From milliseconds

  • Pulsars
  • Quasi-periodic oscillations
  • Lunar and stellar Occultations
  • Milli-, micro-and femto-lensing
  • Accretion instabilities
  • Photon-gas effects
  • Neutron-star oscillations
  • Photon emission mechanisms
  • Coherent radiation bursts
  • Photon quantum statistics
  • Etc.

The giant pulses observed from 0.4 to 8.8 GHz with nanosecond resolution are the brightest pulses in the Universe.

The source must be smaller than 1 meter in size!

(Cordes et al., 2004, Ap.J. 612, pp. 375-388), and subsequent.

To picoseconds

Notice that atmospheric turbulence is poorly known at these very high frequencies.

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2 quantum optics in astronomy 1
2 - Quantum optics in astronomy - 1
  • Photons are more complex than is generally appreciated.
  • Classical astrophysics merges all radiation of a certain wavelength into the quantity "intensity". When instead treating radiation as a three-dimensional photon gas, other effects also become significant, e.g. higher-order coherence and the temporal correlation between photons.
  • Glauber (1963a, 1963b, Nobel Prize 2005) showed that an arbitrary state of light can be specified with a series of coherence functions essentially describing one-, two-, three-, etc. photon-correlations with respect to position r and time t.
  • See also D.Dravins, ESO Messenger 78, 9 (1994).

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2 quantum optics in astronomy 2
2 - Quantum optics in astronomy - 2

These quantum correlation effects are fully developed over timescales equal to the inverse bandwidth of light. For example, a 1 A bandpass filter in the visible gives a frequency bandwidth of  1011 Hz, and the effects are then fully developed on timescales of 10-11 seconds. Instrumentation with such continuous resolutions is not yet available, but it is (hopefully) possible to detect the effects, albeit with a decreased amplitude, also at the more manageable 50 to 100 picosecond timescales.

The largest possible flux of photons is then necessary: Extremely Large Telescopes are absolutely needed to bring non-linear optics to astronomy.

Quantum optics and ELTs could thus become a fundamentally new information channel to the Universe.

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first order correlation function 1
First order correlation function - 1

The temporal coherence of light is quantified by the first order correlation function:

whose modulus is also equal to the fringe visibility in the Michelson interferometer:

Any realization of a photometer, spectrometer and phase interferometer (Michelson, Mach-Zender) measures some properties of this first order correlation function (see next slides).

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first order correlation function 2
First order correlation function - 2

All classical optical instruments measure properties of light that can be deduced from the first-order correlation function of light, g(1), for two coordinates in space rand time t. The different classes are collected in this Figure.

E is the amplitude of the field, < > denotes time average, and * complex conjugate.

Allsuch measurements can be ascribed to quantities of type E*E, corresponding to intensity I, which in the quantum limit means observations of individual photons or of statistical one-photon properties.

Thus classical measurements do not distinguish light sources with identical G(1).Possible multi-photon phenomena in the photon stream reaching the observer are not identified, not even in principle.

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first order correlation function 3
First order correlation function - 3
  • Therefore, conventional astronomical instruments measure properties of light such as its intensity, spectrum, polarization or first-order coherence. However, such properties are generally insufficient, even in principle, to determine the physical conditions under which light has been created (e.g. thermal processes versus stimulated emission), or subsequent scattering processes.
  • Yet, different types of light may have quantum-statistical differences regarding collective multi-photon properties in the photon gas. Such properties are known for light from laboratory sources and might ultimately become experimentally measurable also for astronomical sources.

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a drastic example
A drastic example

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second order correlation function 1
Second order correlation function - 1

The description of collective multi-photon phenomena in a photon gas requires a quantum-mechanical treatment since photons have integer spin, and therefore constitute a boson fluid with properties different from a fluid of classical distinguishable particles. The second order correlation describes the correlation of intensity between two coordinates in space r and time t.

With respect to time, the second order correlation function is defined by:

For any classical wave the degree of coherence should always be less than g(2)(0) . This result is contradicted for quantum states of light.

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second order correlation function 3
Second Order correlation function - 3

In thermodynamic equilibrium, photons occupy the energy levels according to Bose-Einstein (BE) distribution.

However, away from equilibrium, photons may deviate from BE. For example, in the laboratory, one can observe how the physical nature of the photon gas gradually changes from chaotic (g(2) = 2) to ordered (g(2)= 1) when a laser is "turned on“, and the emission gradually changes from spontaneous to stimulated.

Therefore, by measuring g(2) and knowing the laser parameters involved, it is possible to deduce the atomic energy level populations, which is an example of an astrophysically important parameter (non-LTE departure coefficient) which cannot be directly observed with classical measurements of one-photon properties.

To determine whether one individual photon is due to spontaneous or stimulated emission requires the study of statistical properties of the boson fluid.

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second order correlation function 4
Second Order correlation function - 4

Fundamental quantities measured in two-photon experiments. All such measurements can be ascribed to quantities of type I*I, i.e. intensity multiplied by itself, which in the quantum limit means observations of pairs of photons, or of statistical two-photon properties.

In the Hanbury Brown Twiss intensity interferometer (HBTII) this is measured for r1r2 but t1 = t2: <I(0,0) I(r,0)>, thus deducing angular sizes of stars, reminiscent of a classical interferometer.

For r1 = r2 but t1t2 we instead have an intensity-correlation spectrometer, which measures <I (0,0) I (0,t)>, determining the spectral width of e.g. scattered laser light.

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additional properties
Additional Properties

For a source with g(2)  2, neither an intensity interferometer nor an intensity-correlation spectrometer will yield correct results. Additional measurements are required to fully extract the information content of light.

Many different quantum states of optical fields exist, not only those mentioned above which can be given classical analogs, but also e.g. photon antibunching with g(2) = 0, which is a purely quantum-mechanical state. This implies that neighboring photons "avoid" one another in space and time. While such properties are normal for fermions (e.g. electrons), which obey the Pauli exclusion principle, ensembles of bosons (e.g. photons) show such properties only in special situations. An antibunching tendency implies that the detection of a photon at a given time is followed by a decreased probability to detect another immediately afterward.

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slide15

Photon Arrival Times

R. Loudon The Quantum Theory of Light (2000)

0 is the typical time scale, e.g. around 10 picosecond for monochromatic thermal visible light.

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photon statistics antibunching quantum optical spectroscopy
Photon statistics, antibunching, quantum optical spectroscopy

Antibunching in

Resonance Fluorescence

H.Kimble, M.Dagenais, L.Mandel

Phys.Rev.Lett. 39, 691 (1977)

Classically

Identical

Spectral Lines

May Differ In

Photon

Statistics

Photon Statistics Laser and Gaussian Sources

F.T.Arecchi, Phys.Rev.Lett. 15, 912 (1965)

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a laboratory example
A laboratory example

The different statistical properties of thermal and laser laboratory sources

Adapted from D.Dravins, H.O.Hagerbo, L.Lindegren, E.Mezey, B.Nilsson: SPIE 2198, 289 , 1994)

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advantages of very large telescopes
Advantages of very large telescopes

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cosmic lasers in action
Cosmic Lasers in Action

A (too) early paper on optical astronomical laser :

D.H. Menzel, :Laser Action in Non-Lte Atmospheres, in Spectrum Formation in Stars with Steady-State Extended Atmospheres, Proceedings of IAU Colloq. 2, 1969 in Munich, Germany. Edited by H. G. Groth and P. Wellmann, National Bureau of Standards Special Publication 332.

Abstract: The radiative transfer equation is written in microscopic form, and from some simplifications on the ratio of occupation numbers for upper and lower level, a laser action is suggested.

Two (more recent) review papers:

M.Elitzur: Masers in the Sky, Scientific American, 272, No.2, 52 (Feb. 1995), for radio masers

C. H. Townes, Astronomical masers and lasers, in Quantum Electron., 1997, 27 (12), 1031-1034

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an overall vision of astrophysical lasers
An overall vision of astrophysical lasers

Letokhov, V. S.

Astrophysical Lasers

Quant. Electr. 32, 1065 (2002) = Kvant. Elektron. 32, 1065 (2002)

Masers and lasers in the active medium particle-density vs. dimension diagram.

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laser emission in eta car 1
Laser emission in Eta Car -1

Observations with HST have identified a gas cloud that acts as a natural ultraviolet laser, near Eta Carinae. The interstellar laser may result from Eta Carinae's violently chaotic eruptions, in which it blasts parts of itself out into space, like an interstellar geyser.

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laser emission in eta carinae 2
Laser Emission in Eta Carinae - 2

See the Papers:

S. Johansson, V.S. Letokhov:

- Possibility of Measuring the Width of Narrow Fe II Astrophysical Laser Lines in the Vicinity of Eta Carinae by means of Brown-Twiss-Townes Heterodyne Correlation Interferometry.

- Astrophysical laser operating in the OI 8446-Å line in the Weigelt blobs of η Carinae, MNRAS, Volume 364, Issue 1, pp. 731-737, 2005

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3 the hbt intensity interferometer
3 - The HBT Intensity Interferometer

The crucially important laboratory work by Hanbury Brown, Twiss and Purcell was performed around 1955. It really was at the basis of the previous considerations (see Glauber and Arecchi).

Subsequently (1965), they built a large optical intensity interferometer at Narrabri, Australia. Each 'mirror' was a mosaic of 252 small hexagonal mirrors, 38 cm.

The composite mirrors were approximately of paraboloidal shape, but great optical accuracy was not sought, since it was only required that the starlight be directed onto the photocathodes.

The light-gathering power of the 6.5 m diameter mirrors, the detectors, electronics etc. allowed the Narrabri interferometer to operate down to magnitude +2.0

See the book by R. Hanbury Brown, 1974

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the hbtii correlator
The HBTII correlator

The two 'mirrors' directed the starlight to two photomultipliers (RCA Type 8575, photocathode 42 mm diameter, stellar image about 25 mm). The starlight was filtered through a narrow-band interference filter.

The most-used filter was 443 nm ± 5 nm.

The photocurrent is sent to a wide-band amplifier, then through a phase-reversing switch, and then through a wide-band filter that passes 10-110 MHz. The signals from the two photomultipliers then are multiplied in the correlator in that frequency range.

This bandwidth excludes seeing frequencies, thus eliminating their effects.

In the jargon of the first slides, we would today consider the HBTII as the first astronomical instrument capable to measure the second order correlation coefficient in the photon strem.

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the rails
The rails

The mirrors were mounted on two carriages that ran on a circular railway of 188 m diameter. A central cabin containing the controls and electronics was connected to the carriages by TV-type coaxial cables from a tower.

The separation of the mirrors could be varied from 10 m up to 188 m. The mirrors rotated on three axes to follow the star. The available baseline distances permitted measurements of angular diameters from 0.011" to 0.0006".

The electrical bandwidth (100 MHz) implies that the paths from the photomultipliers to the correlator must be equal to about 1 ns (30 cm in length) to avoid loss of correlation due to temporal coherence: it is much easier to equalize electrical transmission lines that optical paths (in the Michelson stellar interferometer, the paths must be equal to 1 or so).

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signal processing
Signal processing

The filtered starlight is a quasi-monochromatic signal, in which the closely-spaced frequency components can be considered to beat against one another to create fluctuations inintensity. The accompanying fluctuations in phase were lost (notice, this loss of phase information is not necessarily true, see the recent papers by Ofir and Ribak, MNRAS 2006).

The normalized correlation is proportional to |γ|2, the square of the fringe visibility in the Michelson case. Although the phase information was gone, the magnitude of the degree of coherence was still there, allowing the measurement of diameters (and possibly of limb-darkening if higher S/N ratio could have been reached in the second lobe).

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results of hbtii
Results of HBTII

Measurements were finally made on 30 or so stars of spectral types B0 to F5 (the sensitivity increases very rapidly with the temperature of the star ).

Measurements could not be made on Betelgeuse, since the mirrors could not be brought closer than 10 m apart, and the 6.5 m mirrors would themselves resolve the star, reducing the correlation to zero.

CHANGE OF CORRELATION WITH BASELINE (a) Beta Cru (B0 IV); (b) Alpha Eri (B5 IV); (c) Alpha Car (F0 II)

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expected improvements
Expected improvements

The HBTII sensitivity is expressed by:

independent on the optical BW and weakly dependent on the optical quality- Being a second order effect it is intrinsically very low: the original HBT limit was around the 6th mag in one week of integration!

The figure shows the expected gain over the original HBT realization with modern detectors (QE 0.4 instead of 0.2) and time tagging capabilities (100 ps instead of 100 MHz), and precursors like VLTs, LBT, MAGIC, and finally with the 100 m OWL. The curves refer to 1, 2 and 3 hours of integration,

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future of hbtii with elts
Future of HBTII with ELTs?

In my opinion, the interest in HBTII will survive in the ELTs era.

I wish to recall the following points:

1- ease of adjusting the time delays of the channels to equality within few centimeters (electronic instead of optical compensation);

2 - immunity to seeing: adaptive optics is not required

4 - blue sensitivity, with the possibility to utilize the large body of data from Michelson-type interferometers and to supplement their data with observations in this spectral region.

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very long baseline optical intensity interferometry
Very Long Baseline Optical Intensity Interferometry

The most exciting development of the HBT interferometer is the an Intensity Interferometry with two distant telescopes, therefore an optical (intensity) VLBI!

No optical link is indeed needed, only time tagging to better than say 100 ps and proper account of atmospheric refraction and delays.

The concept could be tested immediately with two or all telescopes of the ESO VLT and/or with the two apertures of the LBT!

LBT would provide essential (almost) zero-delay information.

MAGIC I+II on the Roque is also a very attractive possibility.

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4 clocks and detectors
4 - Clocks and Detectors

A few words now about clocks and detectors.

There is a substantial difference, which applies both to clocks and to detectors, between the astronomical applications and other applications such as nuclear physics, laser ranging, laboratory correlation spectroscopy etc:

we require a continuous functioning, no room for signal gating, coincidences, integrations etc.

The photons from the celestial source will arrive when they want!

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time distribution among two distant telescopes
Time Distribution among two distant telescopes
  • The existing GPS and probably also the future Galileo fall short of the needed precision (say 100 ps or better).
  • The problem of distributing a very precise and extremely well synchronized time among distant observers is bound to become easier and easier in the next years.
  • VLBI indeed is not the only science requiring this accurate time: terrestrial and interplanetary communications will act as a most powerful driver .

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an example of very accurate time distribution feasible today
An example of very accurate time distribution – feasible today

A proposed ESA system:

Only one master clock is needed on the ground

(courtesy of Carlo Gavazzi Space)

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far future distribution of entangled photons
Far Future: Distribution of entangled photons

QIPS: Weinfurter, Zeilinger, Rarity, Barbieri. ESA

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the harrison project
The Harrison Project

In the frame of a large contract with the Galileo Navigation Satellite System managed by the Consortium Torino Time, we have recently granted some funding with the following objectives

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detectors
DETECTORS

Inside Quanteye, we performed a market survey for detectors suitable for High-Time-Resolution Astrophysics & Quantum Optic, such as PMTs, Streak Cameras, Hybrid Photo Detectors, Avalanche Photodiodes etc. and available in 2004-2005.

The technology is rapidly advancing, especially under the push of telecommunications, in particular of quantum cryptography.

We selected for that study, and for the precursor for Asiago a Single Photon Avalanche Photodiode (SPAD) produced in Italy by MPD.

Other products are now available, from SENS-L in Ireland, id-Quantique in Suisse, The Czeck Technical University in Prage, the Max-Planck-Institute for Solid State in Munich, etc.

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mpd spads
MPD SPADs

Our detector is the Single Photon Avalanche Photodiode (SPAD)from MPD,originally developed by Prof. S. Cova in Milano, and used already in several AdOpt devices in Italy (LBT) and at ESO.

One advantage is the low cost. The active area is 50 micrometers. Four devices have been acquired.

Cons:

no CCD- type array, 70 nsecond dead time

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5 quanteye for the 100m owl 1
5 - QuantEYE for the 100m OWL - 1

The baseline solution of focal reducer plus 10x10 lenslet array. The focus of each lenset is brought to a distributed array of 10x10 SPADs.

The filters are inserted in the parallel beam. A number of very narrow ( 1 A) bandpass filters, 4 linear polarizers, a number of broad band filters (e.g. BVRI) were considered.

Quanteye thus behaves as a fixed-aperture, non-imaging photometer.

The 10x10 outputs are stored in separate memories and can be analyzed in a variety of modes.

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the electronics of quanteye
The electronics of Quanteye

The arrival time ofeach photon is acquired and stored. An on-line correlator allows real time control of the observation. An asynchronous post processing guarantees data integrity for future scientific investigation.

The huge amount of data can be handled by present-day technology. For example, a run of 1 minute at 1 GHz produces 3 TBytes per head; existing hard drives of 300 GBytes for each of the 25 lines insure two such runs before reading out the data.

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the overall design of quanteye
The overall design of Quanteye

Two reading heads (one fixed on the optical axis, one moving over the scientific field to point a reference star), a real time cross-correlator, a large storage unit, and a clock (e.g. a Hydrogen Maser unit).

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the photometric capabilities of quanteye
The photometric capabilities of Quanteye

Quantum Optics mode: full 100m OWL aperture, 6 mirrors, no integration allowed, 1 A wide filter, SPAD QE = 0.4 at 540 nm, 1 linear polarizer, dark = 100 c/s correspondent to V = 13.9

T(2), T(3) = indicative time needed to detect deviations from Poisson distribution of 2 or 3 simultaneous photons. The Table is a vivid illustration that Quantum Astronomy needs the largest possible collector!

In a more conventional broad band High Time Resolution Astrophysics, Quanteye would be the fastest photometer, with an exceptionally high dynamic range (more than 25 mag, from the 5th to the 30th). It could also reproduce 10x10 telescopes observing the star in 10x10 colors, polarization states, etc

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6 aqueye
6 - AQUEYE

Aqueye (the Asiago Quantum Eye) is being built for the 182 cm Copernicus Telescope at Cima Ekar as a proof-of-concept instrument with very limited resources.

Aqueye will act as a single-aperture photometer with a FoV of 3” (slightly worse than the average seeing).

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afosc
AFOSC

We are making the best use of the exisiting AFOSC imaging spectrograph, which already provides an intermediate pupil.

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the optical design of aqueye 1
The optical design of Aqueye - 1

The pupil is sub-divided in 4 sub-apertures.

The lenses are low cost commercial devices.

The pyramid is custum built.

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the optical design of aqueye 2
The optical design of Aqueye - 2

Optical performances are very good at all wavelengths from 420 to 750 nm.

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the mechanical design of aqueye
The Mechanical Design of Aqueye

One can use the filters of AFOSC, or insert 4 different filters and polarizers in the parallel section of each beam after the pyramid.

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electronics with commercial boards
Electronics with commercial boards

The selected commercial boards are used in nuclear physics applications.

Max output rate = 10 Mhz

Typical rate = 100 Khz

SPAD precision = 30 ps

0

PC Controller

TDC

CAEN

SPAD 0

1

PXI o VME

Optionally:

Optical Bridge

2

3

SPAD 3

DATA BUS

External ref. (input)

Clock

External

Storage

10 Mhz clock (output)

Under

Investigation

In the frame of the Harrison project

GPS/GALILEO

Receiver

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the detector system on the bench
The detector system on the bench

From right to left:

Two SPADs connected to the VME-TDC unit, the dedicated PC, the 1 TeraByte storage unit, the PC screen

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quantum algorithms
Quantum Algorithms

QuantEYE (and even Aqueye) would generate enormous, multidimensional (color, polarization) data strings.Quantum algorithms could prove advantageous over classical methods, especially if the quantum computer materializes in the near future. This computational task is one our planned activities inside the Engineering Dept..

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expected photometric capabilities of aqueye for htra
Expected photometric capabilities of Aqueye for HTRA

1.82 m aperture divided in 4 channels, 2 mirrors+pyramid+ 4 lenses + 200 A filter at 50% transmission, no polarizer.SPAD: QE = 0.45 a 550 nm, dark = 50 c/s = V 16.0 star, V = 19 mag/(arcsec)2 star, FoV 3 arcsec  Vsky = 17.3. Vega (V=0) at Zenith: 800 phcm-2s-1 A-1.

This table shows the performances for eanch individual SPAD. Given that the dead time is 70 ns, the linear regime starts at V = 2.5, and ends around the 16th dark counts dominate). By conbning the 4 channels with proper statistical analysis we could do certainly better.

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what can be observed with aqueye
What can be observed with Aqueye?

The 182 cm telescope is too small to detect quantum effects, however we can try very high time resolution photometry on different astrophysical problems, starting of course with the mighty Crab pulsar.

Skinakas Observatory 1.3 m telescope; OPTIMA (MPE) + QVANTOS Mark II (Lund)

Stroboscopic observations by Andrej Cadez with the Vega telescope (70 cm) in Lubiana.

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lunar and kbo occultations
Lunar and KBO Occultations

Theoretical model of an A0-V star occultation by a Kuiper Belt Object

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the crab pulsar from asiago and slovenia
The Crab pulsar from Asiago and Slovenia

Skinakas Observatory 1.3 m telescope; OPTIMA (MPE) + QVANTOS Mark II (Lund).

Stroboscopic observations by A. Cadez with the Vega telescope (70 cm) near Lubiana.

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exoplanets transits
Exoplanets transits

By determining the absolute transit time over several years one could detect the presence of Earth-like planets.

Adapted from (Matthew J. Holman and Norman W. Murray, The Use of Transit Timing to Detect Terrestrial-Mass Extrasolar Planets

SCIENCE, 25 FEBRUARY 2005 VOL 307, 1288)

I have chosen this example to remind that UTC is a discontinuous time, and that at the 10 picosecond level everything is difficult.

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atmospheric scintillation
Atmospheric Scintillation

D.Dravins,  L. Lindegren,  E.Mezey  &  A.T.Young, ATMOSPHERIC INTENSITY SCINTILLATION OF STARS. I.  Statistical Distributions and Temporal Properties PASP  109,  173­207  (1997), and 2 more papers.

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6 photon orbital angular momentum 1
6 - Photon Orbital Angular Momentum - 1

Photons have spin angular momentum ± ћ along their direction of propagation.

However, any electromagnetic field containing a phase term exp( i ℓ φ) (e. g. Laguerre-Gaussian and Bessel modes) also carries a quantity of OAM, because the Poynting vector and the linear momentum density of these beams have an azimuthal component ℓ. The carried POAM is equal to ℓ ħ per photon

(L. Allen et al. Phys. Rev. A45, 8185 (1992)).

Beams having as much as ℓ = 300 ћ OAM have been realized in the laboratory.

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poam 2

Wavefront Intensity Phase

POAM - 2

The wavefront has an helical shape composed by ℓ lobes disposed around the propagation axis z. A phase singularity called optical vortex is nested inside the wavefront, along the axis z.

For helically phased beams, the phase singularity on the axis dictates zero intensity there: the cross−sectional intensity pattern of all such beams has an annular character that persists no matter how tightly the beam is focused.

M. Padgett, J. Courtial,

L. Allen, Phys.Today

May 2004, p.25

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cosmic sources with poam
Cosmic Sources with POAM??
  • In astrophysics, POAM could be induced by (M. Harwit ApJ, 597, 1266, 2003):
  • interstellar media with density discontinuities on wide scales (edges of shocked domains) might induce POAM on a maser beam.
  • intense beams from pointlike sources such as pulsars or Kerr black holes,
  • the blackbody radiation of the cosmic microwave background
  • SETI. A very clever population could artificially generate photons with PAOM (and also entanglement).
  • Considerable theoretical effort is needed to elucidate these possibilities.

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photon orbital angular momentum 3
Photon Orbital Angular Momentum -3

So our idea was:

Can POAM be used for nulling the ‘normal’ light from a star on the optical axis of the telescope (as with a coronagraph), and then provide a different way to help the discovery of faint objects close to a bright source (e.g. extrasolar planets)?

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how poam can be generated in the lab

ℓ = -1

ℓ = +1

N = 1

ℓ = 0

How POAM can be generated in the lab

The generation of beams carrying OAM proceeds thanks to the insertion in the optical path of a phase modifying device which imprints a certain vorticity on the incident beam. One of such devices is the fork hologram. If the hologram presents N dislocations, then at the m-th diffraction order it imposes a OAM value equal to N m ħ (A. Vaziri et al. J. Opt. B4, S47 (2002)). A l = 1 fork hologram was kindly lent us by Prof. A. Zeilinger (Vienna University)

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off axis beams

On-axis

Off-axis

Off-axis beams

When the axis of the incoming beam is not centered with the hologram’s dislocation, the intensity distribution of the output beam has generally a non-symmetric pattern. The wavefront of the output beam contains an off-axis optical vortex and the carried OAM may have a non-integer value. Also focused (non-Gaussian) and tilted beams are not described by a single L-G mode (L. E. Helseth Opt. Comm. 229, 85 (2004) and M. V. Vasnetsov et al. New J. Phys.7, 46 (2005)). When we observe two distinct sources having different positions with respect to the center of the hologram, the superposition of their L-G modes will draw a complicated non-symmetric pattern. So we can detect the presence of a very close companion by analyzing the deviations observed from the L-G modes expected from a single source centered with the hologram.

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sub rayleigh and coronagraphy
Sub-Rayleigh and coronagraphy

Therefore, POAM could find applications to astronomical coronagraphy.

Swartzlander (Opt. Lett. 26, 497 (2001)) proposed to peer into the darkness of an optical vortex to enhance the contrast of a faint source placed very close to a star (below the Rayleigh limit).

Foo et al. (Opt. Lett. 30, 3308 (2005)) proposed to place in the first focal plane of a Lyot coronagraph a phase mask that generates a ℓ = 2 optical vortex.

In laboratory test of this coronagraphic setup (J. H. Lee et al. Phys. Rev. Lett. 97, 053901 (2006)), two close laser sources with intensity contrast of 95% were clearly resolved.

Liege Inst. d'Astrophysique

our sub rayleigh experiment
Our sub-Rayleigh experiment

Rayleigh criterion limit (α /D)

We (seeTamburini et al. Phys. Rev. Lett. 97, 163903, 2006) demonstrated the possibility to achieve sub-Rayleigh separability of monochromatic and white light sources with non-integer optical vortex generated by a ℓ = 1 blazed fork-hologram.

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the achieved resolution
The achieved resolution

The achieved angular resolution corresponds approximately to 40% of the Rayleigh criterium.

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a first experiment at the telescope
A first experiment at the telescope

In a first campaign of observations in 2005, we tested the ℓ = 1 fork-hologram at the f/16 Cassegrain focus of the 122 cm telescope of Asiago. We observed a double star with a fast CCD camera (frame rate of 0.07 seconds), to freeze the seeing effects.

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the first star

Ras Algethi (α Her, not spatially filtered)

Spatially unfiltered OVs generated by the double system

4”.7

Optical singularities (dark centers of the L-G modes)

ℓ = 0

ℓ = 1

The first star

Bad seeing gave rise to severe problems, in particular we were not able to obtain clear “doughnut” patterns from the star. We are now improving on this preliminary apparatus, planning for further observations in a near future. At any rate, we think we have demonstrated the potential interest of the technique, especially for telescopes equipped with adaptive optics devices, and in space.

Liege Inst. d'Astrophysique