Astronomical Applications of Quantum Optics

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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).

6 November 2006   Liege Inst. d'Astrophysique                  1
              Main topics of the talk
                  1. The time domain
    2. Quantum properties of (non-thermal) light
        3. Intensity interferometry (HBTII)
               4. Clocks and Detectors
             5. Quanteye for 100m OWL
        6. Aqueye, our Precursor for Asiago
   7. The Photon Orbital Angular Momentum (light
                     beam vorticity)

            For quantum optics activites in Padova see:
                       www.abfgroup.com
6 November 2006           Liege Inst. d'Astrophysique     2
          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 ?

6 November 2006     Liege Inst. d'Astrophysique   3
From milliseconds           All of astronomy
•Pulsars                                                                 The giant pulses
•Quasi-periodic
oscillations                                                             observed from
•Lunar and stellar                                                       0.4 to 8.8 GHz
Occultations
•Milli-, micro-and                                                       with
femto-lensing                                                            nanosecond
•Accretion
instabilities
                                                                         resolution are
•Photon-gas                                                              the brightest
effects                                                                  pulses in the
•Neutron-star
oscillations                                                             Universe.
•Photon emission                                                         The source must
mechanisms
•Coherent                                                                be smaller than
radiation bursts                                                         1 meter in size!
•Photon quantum                                                          (Cordes et al.,
statistics
•Etc.                                                                    2004, Ap.J. 612,
                                                                         pp. 375-388),
                                                                         and subsequent.
To picoseconds

   Notice that atmospheric turbulence is poorly known at these very high frequencies.
      6 November 2006               Liege Inst. d'Astrophysique                     4
 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).

 6 November 2006         Liege Inst. d'Astrophysique          5
  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.

  6 November 2006         Liege Inst. d'Astrophysique           6
          First order correlation function - 1
 The temporal coherence of light is quantified by the first order
 correlation function:
                                          (t ) (t   )
                       g (1) ( ) 
                                                  02
whose modulus is also equal to the fringe visibility in the Michelson
interferometer:
                                         I m ax  I m in
                       g ( )  V ( ) 
                         (1)

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

  6 November 2006              Liege Inst. d'Astrophysique          7
    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 r and time t. The different
                                                            classes are collected in this
                                                            Figure.
                                                             E is the amplitude of the field,
                                                            < > denotes time average, and *
                                                            complex conjugate.

All such 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.
   6 November 2006            Liege Inst. d'Astrophysique                              8
 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.

 6 November 2006       Liege Inst. d'Astrophysique        9
                  A drastic example




6 November 2006      Liege Inst. d'Astrophysique   10
   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:

                         I (t ) I (t   )
      g   ( 2)
                 ( )                        g ( 2 ) (  )
                              I (t ) 2
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.


   6 November 2006            Liege Inst. d'Astrophysique               11
  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.

  6 November 2006             Liege Inst. d'Astrophysique                  12
     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.
    6 November 2006                  Liege Inst. d'Astrophysique                         13
           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.
     6 November 2006                   Liege Inst. d'Astrophysique                          14
                     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.

   6 November 2006      Liege Inst. d'Astrophysique   15
        Photon statistics, antibunching,
         quantum optical spectroscopy




                                 Antibunching in
                                 Resonance                  Classically
Photon Statistics Laser and      Fluorescence               Identical
     Gaussian Sources            H.Kimble,                  Spectral Lines
F.T.Arecchi,                     M.Dagenais,                May Differ In
Phys.Rev.Lett. 15, 912           L.Mandel                   Photon
(1965)                           Phys.Rev.Lett. 39,         Statistics
                                 691 (1977)
   6 November 2006            Liege Inst. d'Astrophysique                16
               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)
  6 November 2006          Liege Inst. d'Astrophysique             17
Advantages of very large telescopes

Telescope diameter   Intensity <I>          Second-order           Fourth-order photon
                                           correlation <I2>           statistics <I4>
        3.6 m                         1                        1                     1


        8.2 m                        5                       27                   720


       4 x 8.2 m                     21                     430               185,000


       50 m                      193                      37,000       1,385,000,000


       100 m                     770                 595,000        355,000,000,000



6 November 2006             Liege Inst. d'Astrophysique                              18
             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
 6 November 2006      Liege Inst. d'Astrophysique        19
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.

6 November 2006             Liege Inst. d'Astrophysique                     20
             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.
  6 November 2006            Liege Inst. d'Astrophysique               21
 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


 6 November 2006       Liege Inst. d'Astrophysique       22
       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
  6 November 2006                 Liege Inst. d'Astrophysique                            23
                     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.
   6 November 2006               Liege Inst. d'Astrophysique                     24
                                                  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).


    6 November 2006                Liege Inst. d'Astrophysique                       25
                     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 in intensity. 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).

   6 November 2006            Liege Inst. d'Astrophysique               26
                                 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)
    6 November 2006                       Liege Inst. d'Astrophysique                                27
                     Expected improvements
 The HBTII sensitivity is expressed by:
S / N  Kinstr  (QE)  AreaTelescope  T  Electr.BW  f (m)  g (sky)

                                             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,
   6 November 2006          Liege Inst. d'Astrophysique                         28
             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.

6 November 2006           Liege Inst. d'Astrophysique                29
            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.
    6 November 2006           Liege Inst. d'Astrophysique                   30
                  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!
6 November 2006          Liege Inst. d'Astrophysique   31
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 .
6 November 2006       Liege Inst. d'Astrophysique         32
     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)




     6 November 2006   Liege Inst. d'Astrophysique   33
Far Future: Distribution of entangled photons




QIPS: Weinfurter, Zeilinger,
 Rarity, Barbieri. ESA


6 November 2006     Liege Inst. d'Astrophysique   34
                  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
6 November 2006      Liege Inst. d'Astrophysique                 35
                    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.


 6 November 2006           Liege Inst. d'Astrophysique              36
         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
Cons:                                                  devices have been
no CCD- type array, 70 nsecond dead time               acquired.
 6 November 2006         Liege Inst. d'Astrophysique                   37
   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.
   6 November 2006             Liege Inst. d'Astrophysique                   38
                 The electronics of Quanteye
                                                               The arrival time of each
                                                               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.
   6 November 2006               Liege Inst. d'Astrophysique                           39
         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).
 6 November 2006             Liege Inst. d'Astrophysique                 40
     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

     V          T(2)    T(3)               T(2), T(3) = indicative time
                                           needed to detect deviations from
    10.0       0.02 s   140 s              Poisson distribution of 2 or 3
    12.5       1.63 s   (39 h)             simultaneous photons. The
                                           Table is a vivid illustration that
    15.0       163 s                       Quantum Astronomy needs the
    17.5       4.5 h                       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
   6 November 2006               Liege Inst. d'Astrophysique                    41
                                          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).

6 November 2006   Liege Inst. d'Astrophysique                         42
                                                        AFOSC




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

  6 November 2006         Liege Inst. d'Astrophysique           43
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.


  6 November 2006         Liege Inst. d'Astrophysique   44
The optical design of Aqueye - 2




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


  6 November 2006               Liege Inst. d'Astrophysique   45
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.

6 November 2006           Liege Inst. d'Astrophysique                 46
               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
      SPAD 0
                                            1

                                            2                 TDC              PXI o VME
                                            3
                                                               CAEN                             PC Controller
                                                                               Optionally:                      DATA BUS
               SPAD 3                           External ref. (input)
                                                                               Optical Bridge




                                            10 Mhz clock (output)


    Under                                                    Clock                                 External
Investigation                                                                                      Storage
In the frame
    of the
  Harrison                                           GPS/GALILEO
   project                                             Receiver


  6 November 2006                                          Liege Inst. d'Astrophysique                                 47
       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
 6 November 2006        Liege Inst. d'Astrophysique         48
                  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..
6 November 2006       Liege Inst. d'Astrophysique                          49
 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
        V            Counts/s     Average time                performances for eanch
                                between 2 counts              individual SPAD. Given
                                                              that the dead time is 70 ns,
         0           1.31x108        7.6 ns                   the linear regime starts at V
         5           1.31x106       0.76 s                   = 2.5, and ends around the
                                                              16th dark counts
        10           1.31x104       0.76 ms                   dominate). By conbning the
        15           1.31x102        76 ms                    4 channels with proper
        20           1.31x100        0.76 s                   statistical analysis we could
                                                              do certainly better.

   6 November 2006              Liege Inst. d'Astrophysique                           50
              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                           Stroboscopic observations by
     telescope; OPTIMA (MPE) +                            Andrej Cadez with the Vega
     QVANTOS Mark II (Lund)                               telescope (70 cm) in Lubiana.
  6 November 2006           Liege Inst. d'Astrophysique                             51
          Lunar and KBO Occultations




      Theoretical model of an A0-V star occultation by a Kuiper Belt Object
6 November 2006              Liege Inst. d'Astrophysique                  52
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.

6 November 2006        Liege Inst. d'Astrophysique                    53
                                                   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.
   6 November 2006         Liege Inst. d'Astrophysique                      54
                   Atmospheric Scintillation




D.Dravins, L. Lindegren, E.Mezey & A.T.Young, ATMOSPHERIC
INTENSITY SCINTILLATION OF STARS. I. Statistical
Distributions and Temporal Properties PASP 109, 173-207 (1997),
and 2 more papers.
 6 November 2006        Liege Inst. d'Astrophysique         55
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. A 45, 8185 (1992)).
Beams having as much as ℓ = 300 ћ OAM have been
realized in the laboratory.
 6 November 2006    Liege Inst. d'Astrophysique   56
  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
M. Padgett, J. Courtial,
L. Allen, Phys.Today              beam is focused.
May 2004, p.25
   6 November 2006                Liege Inst. d'Astrophysique      57
                      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.
    6 November 2006           Liege Inst. d'Astrophysique                  58
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)?



6 November 2006    Liege Inst. d'Astrophysique      59
  How POAM can be generated in the lab
                  ℓ = -1         ℓ = +1
                                                  The generation of beams
                                                  carrying OAM proceeds thanks
                                                  to the insertion in the optical
                                                  path of a phase modifying
          N=1                                     device which imprints a certain
                                                  vorticity on the incident beam.
                                                  One of such devices is the fork
                                                  hologram. If the hologram
    ℓ=0
                                                  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. B 4,
                                                  S47 (2002)). A l = 1 fork
                                                  hologram was kindly lent us by
                                                  Prof. A. Zeilinger (Vienna
                                                  University)
6 November 2006            Liege Inst. d'Astrophysique                        60
             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.
  6 November 2006             Liege Inst. d'Astrophysique           61
    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.
 6 November 2006        Liege Inst. d'Astrophysique        62
            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.
 6 November 2006       Liege Inst. d'Astrophysique                        63
          The achieved resolution




          The achieved angular resolution corresponds
          approximately to 40% of the Rayleigh criterium.
6 November 2006          Liege Inst. d'Astrophysique        64
   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.
  6 November 2006       Liege Inst. d'Astrophysique       65
   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

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.
  6 November 2006                    Liege Inst. d'Astrophysique                                 66