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NONLINEAR INTERFEROMETRY II: INDUCED COHERENCE
Maria Chekhova
Max-Planck Institute for the Science of Light,Erlangen, Germany
Max-Planck Institute for the Science
of Light
Quantum Radiation group
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
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NONLINEAR INTERFEROMETER: ANALOGY WITH THE RAMSEY INTERFEROMETER
Light and matter exchange roles
Nonlinear
Ramsey
N. F. Ramsey, Phys. Rev. 78, 695 (1950).
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SU(1,1) INTERFEROMETER
B. Yurke, S.L. McCall, and J.R. Klauder, PRA 33, 4033 (1986)
OPA1 OPA2
pump
idler
signal
Two optical parametric amplifiers – degenerate or nondegenerate
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OPTICAL PARAMETRIC AMPLIFIER
Parametric gain for SPDC
for FWM
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SU(2) and SU(1,1)
SU(2) AND SU(1,1) INTERFEROMETERS
8/40B. Yurke, S.L. McCall, and J.R. Klauder, PRA 33, 4033 (1986)
SU(2) interferometer
*1122
*1221
212
211
,
,1
,
UUUU
UU
ba
ba
in
in
out
out
=−=
=+
=
U
ina
inb
outa
outb
‘beamsplitter’, SU(2) group
SU(1,1) interferometer
*2212
*2111
221
222
212
211 ,1,1
,][][
SSSS
SSSS
ba
ba
in
in
out
out
=
=−=−
=
++
S
ina
inb
outa
outb
‘Bogolyubov’, SU(1,1) group
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VARIOUS GEOMETRIES
M. V. Chekhova and Z. Y. Ou, Advances in Optics and Photonics 8, 104 (2016)
‘Mach-Zehnder’ ‘Young’
crystal pump
idler
signal
double slit
signalidler
crystalpump
idler
signal
‘Michelson’
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‘SAGNAC’
B. S. Shi and A. Tomita, PRA 69, 013803 (2004)
Signal and idler beams do not pass through the same crystal again!
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
12 4/ 0
OPA1 OPA2
pump
idler
signal
Only biphotons!
LOW PARAMETRIC GAIN
13 40/
SLIGHTLY MISALIGNED SU(1,1)
OPA 1 OPA 2
pumpsignal 1
idler
signal 2
M. V. Chekhova and Z. Y. Ou, Nonlinear Interferometers in Quantum Optics. AOP 8, 104 (2016)
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‘INDUCED COHERENCE’ EFFECT
signal1
signal2
L.J. Wang, X.Y. Zou, and L. Mandel, PRA 44, 7 (1991)
Parametric gain is low -> ‘induced coherence without induced emission’
interference
No interference (Feynman’s distinguishability principle)
pis ωωω =+
idler
Measure
Detect Measurement with undetected photons
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‘INDUCED COHERENCE’ EFFECT
signal1
signal2
L.J. Wang, X.Y. Zou, and L. Mandel, PRA 44, 7 (1991)
idlertransmission Interference
fringe visibility
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DEPENDENCE ON THE TRANSMISSION
X.Y. Zou, L.J. Wang, and L. Mandel, PRL 67, 3 (1991)
Condition for the interference: the idler beam/photon should be common for both OPAs.
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POLARIZATION EFFECTS
T. J. Herzog, P. G. Kwiat, H. Weinfuhrter, and A. Zeilinger, PRL75, 3034 (1995)
Interference in one beam is observed if the conjugate beam has the same frequency, wavevector, and polarization on both passes.
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WHAT HAPPENS AT HIGH GAIN?
A. V. Belinsky and D. N. Klyshko, Phys. Lett. A 166, 303 (1992)
signal1
signal2
transmission
But the visibility becomes 100% if the intensities in arms 1,2 are balanced!
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POSSIBILITIES FOR SPECTROSCOPY AND OTHER APPLICATIONS
signal1
signal2 interference
pis ωωω =+
idler
Measure
Detect
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QUESTIONS?
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
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MEASUREMENT OF IR ABSORPTION OF THE CRYSTAL
A.V.Burlakov et al., JETP 93, 55 (2001); G.Kh. Kitaeva et al., J Infrared Milli Terahz Waves 32, 1144 (2011).
Young’s scheme
pump
crystal
Low absorption: angular lineshape
High absorption (α-HIO3)
THz range
LiNbO3
IR range
α-HIO3
Absorption at idler wavelength reduces the interference visibility at signal wavelength.
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“CROSSED DISPERSION” SCHEME
J. P. Budin, B. Godard, abd J. Ducuing, IEEE J. Q. Electr. 4, 831 (1968); D.N.Klyshko, A.N.Penin, B.F.Polkovnikov, JETP Lett. 11, 5 (1970).
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MEASUREMENT OF IR DISPERSION FOR LINEAR MATERIALS
D.Yu.Korystov, S.P.Kulik, A.N.Penin, JETP Lett. 73, 214 (2001).
Dispersion in the linear gap determines the frequency-angular spectrum of SPDC.
Mach-Zehnder scheme
pump
crystal1 crystal2
Linear material
Paraffin oil in the gap One crystal
Dispersion of paraffin oil
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INFRARED SPECTROSCOPY WITH VISIBLE LIGHT
D.A. Kalashnikov, A.V. Paterova, S.P.Kulik, and L.A. Krivitsky, Nat. Phot. 10, 98 (2016).
Measurement of dispersion and absorption near a resonance of CO2 gas
p=0: high visibility
p=7.7 Torr: fringes moved
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INFRARED SPECTROSCOPY WITH VISIBLE LIGHT
D.A. Kalashnikov, A.V. Paterova, S.P.Kulik, and L.A. Krivitsky, Nat. Phot. 10, 98 (2016).
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TERAHERTZ RANGE
E.I. Malkova, S.P. Kovalev, K.A. Kuznetsov, G.Kh. Kitaeva, EPJ Web of Conferences 195, 06020 (2018)
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TERAHERTZ RANGE
M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter & G. von Freymann, arXiv:1909.06855 [quant-ph]
Stokes anti-Stokes
~1THz
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
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IMAGING WITH UNDETECTED PHOTONS
Interference in the signal radiation is seen only where the idler radiation passes through the mask.
signal1
signal2interference2
1
I1-I2
G.B. Lemos, V. Borish, G.D. Cole, S. Ramelow, R. Lapkiewicz, & A. Zeilinger, Nature 512, 409 (2014).
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EXPERIMENT
G.B. Lemos, V. Borish, G.D. Cole, S. Ramelow, R. Lapkiewicz, & A. Zeilinger, Nature 512, 409 (2014).
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PHASE IMAGING
G.B. Lemos, V. Borish, G.D. Cole, S. Ramelow, R. Lapkiewicz, & A. Zeilinger, Nature 512, 409 (2014).
Image of a phase object: an etched silicon plate
OUTLINE
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1. Nonlinear interferometer: a reminder2. Induced coherence effect3. Spectroscopy with undetected photons4. Imaging with undetected photons5. Optical coherence tomography with undetected
photons6. Conclusions
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OPTICAL COHERENCE TOMOGRAPHY
Source (white light)
Reference
Sample
Camera
Microscale and sometimes sub-micron resolution;
3D images;
In-vivo testing of biological samples, especially in ophthalmology and cardiology
Can one move to the MIR range?
(For testing paint layers, pharmaceutic coatings etc. )
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OPTICAL COHERENCE TOMOGRAPHYWITH UNDETECTED PHOTONS
signal1
signal2
A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, PRA97, 023824 (2018).
532 nm
1550 nm
810 nm
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MORE OF OPTICAL COHERENCE TOMOGRAPHY
A. Paterova, H. Yang, Ch. An, D. Kalashnikov, and L. Krivitsky, Quantum Sci. and Tech. 3, 025008 (2018).
532 nm, 488 nm
1543 nm, 2140 nm, 2504 nm, 3011 nm
Different surfaces of a Thorlabs compound waveplate
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MORE POSSIBILITIES
A. Vanselow, P. Kaufmann, I. Zorin, B. Heise, H. Chrzanowski, and S. Ramelow, Quantum Information and Measurement (QIM) V: Quantum Technologies © OSA 2019
Fourier transform to retrieve group delays
Transverse position accessed by scanning
ceramics paint
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POLARIMETRY
A. Paterova, H. Yang, Ch. An, D. Kalashnikov, and L. Krivitsky, Optics Express 27, 2589 (2019).
HWP or QWP
Testing polarization rotation in the IR range
A review:
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40 40/
NONLINEAR INTERFEROMETER WITH LOW-GAIN OPAs
- is similar to a Ramsey interferometer;
- can be used for spectroscopy with undetected photons;
- can be used for imaging and OCT with undetected photons
THANK YOU FOR YOUR ATTENTION!