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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!