1 NONLINEAR INTERFEROMETER FOR SHAPING THE SPECTRUM OF BRIGHT SQUEEZED VACUUM Maria Chekhova Max-Planck Institute for the Science of Light, Erlangen, Germany M.V.Lomonosov Moscow State University Max-Planck Institute for the Science of Light Quantum Radiation group

2 OUTLINE 1. Bright squeezed vacuum 2. Nonlinear SU(1,1) interferometer 3. Bright squeezed vacuum in a nonlinear interferometer: - tailoring the angular spectrum; - OAM modes; - tailoring the frequency spectrum. 4. Conclusions

3 OUTLINE 1. Bright squeezed vacuum 2. Nonlinear SU(1,1) interferometer 3. Bright squeezed vacuum in a nonlinear interferometer: - tailoring the angular spectrum; - OAM modes; - tailoring the frequency spectrum. 4. Conclusions

4 BRIGHT SQUEEZED VACUUM Strong pump Quadrature squeezed BSV q p q p Twin-beam BSV Superbunching (good for multiphoton effects) Easily

5 PHOTON-NUMBER ENTANGLEMENT OF BSV S B A I.N. Agafonov, M.V. Chekhova, and G.Leuchs, PRA 82, (2010). n n M.V. Chekhova, G.Leuchs, and M. Zukowski, Optics Communications 337, 27 (2015). Weak photon-number entanglement Low-gain PDC (SPDC) High-gain PDC High degree of photon-number entanglement

6 POLARIZATION ENTANGLEMENT OF BSV S QWP PBS B A m m n n T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G.Leuchs, PRL 109, (2012).

7 BELL INEQUALITY FOR BSV S PBS B A m n K. Rosolek, M. Stobinska, M. Wiesniak, M. Zukowski, PRL 114, (2015) Photon numbers n,m as local hidden variables violated by quantum mechanics but loss-sensitive

8 OUTLINE 1. Bright squeezed vacuum 2. Nonlinear SU(1,1) interferometer 3. Bright squeezed vacuum in a nonlinear interferometer: - tailoring the angular spectrum; - OAM modes; - tailoring the frequency spectrum. 4. Conclusions

9 NONLINEAR INTERFEROMETER Nonlinear source 1 Nonlinear source 2 pump Nonlinear Mach-Zehnder interferometer Linear Mach-Zehnder interferometer

10 SU(1,1) INTERFEROMETER B. Yurke, S.L. McCall, and J.R. Klauder, PRA 33, 4033 (1986) Nonlinear source 1 Nonlinear source 2 pump idler signal Parametric down-conversion or four-wave mixing

11 SU(2) AND SU(1,1) INTERFEROMETERS B. Yurke, S.L. McCall, and J.R. Klauder, PRA 33, 4033 (1986) SU(2) interferometerSU(1,1) interferometer ‘beamsplitter’ ‘Bogolyubov’

12 OUTLINE 1. Bright squeezed vacuum 2. Nonlinear SU(1,1) interferometer 3. Bright squeezed vacuum in a nonlinear interferometer: - tailoring the angular spectrum; - OAM modes; - tailoring the frequency spectrum. 4. Conclusions

13 ANGULAR SPECTRUM At large L, a single mode can be obtained. Two crystals far apart: only a narrow angular spectrum is amplified in the second crystal A traveling-wave high-gain optical parametric amplifier: broad spectrum, multimode BSV pump PDC Higher-order modes diffract faster, hence only lowest-order modes survive.

14 SHAPING THE ANGULAR SPECTRUM A. Perez, T.Sh. Iskhakov, S. Lemieux, P. Sharapova, O.V. Tikhonova, M.V. Chekhova and G. Leuchs, Optics Letters 39, 2403 (2014). Frequency filtering (monochro- mator): 1.25 frequency modes. Angular structure: 1.1 angular modes 355nm, 0.2mJ, 1kHz Because for a single mode g (2) =2, measurement of g (2) for the whole beam provides the number of modes: CCD

15 Collinear emission suppressed  (rad)  (rad) MODES WITH ORBITAL ANGULAR MOMENTUM

16 MODES WITH ORBITAL ANGULAR MOMENTUM Modes with optical angular momentum l=-2,-1,1,2 Collinear emission suppressed l=-1 l=0 l=1

17 ANALOGY BETWEEN SPACE AND TIME Spatial case: the angular width Temporal case: ??? By analogy, T.Sh. Iskhakov, S. Lemieux, A.M. Perez, R.W. Boyd, G. Leuchs, and M.V. Chekhova, arXiv: (2015). A.M. Perez, T.Sh. Iskhakov, P.R. Sharapova, S. Lemieux, O.V. Tikhonova, M.V. Chekhova, and G. Leuchs, OL 39, 2403 (2014).

18 SHAPING THE FREQUENCY SPECTRUM OF PDC crystal1 crystal2 Dispersive material BSV pump mode0 mode20 Frequency spectrum from a single crystal: broad, multimode  Higher-order modes spread more in time and do not overlap with the pump pulse in the second crystal t

19 NONLINEAR INTERFEROMETER 3 mm BBO type I Delay line Telescope (1mm) Measurement of frequency and spatial spectra 400 nm, 0.85 ps, 5 kHz 0.05 mJ Interference (3 mm BK7) LP filter Various glasses (BK7, SF6, SF57, …)

20 SPECTRUM NARROWING 2x0.3 cm of BK7 Interference structure 60 nm

21 SPECTRUM NARROWING 2x18 cm of SF6 2 effects: -Phase drift (~20 s); -Intensity fluctuations (~ps) After averaging over intensity fluctuations, envelope width 3.2 nm 3.2 nm

22 SPECTRUM NARROWING 2x18 cm of SF6

23 SPECTRUM NARROWING 5.7 ps pulses, 355 nm pumping 0.85 ps pulses, 400 nm pumping

24 SPECTRUM NARROWING

25 OUTLINE 1. Bright squeezed vacuum 2. Nonlinear SU(1,1) interferometer 3. Bright squeezed vacuum in a nonlinear interferometer: - tailoring the angular spectrum; - OAM modes; - tailoring the frequency spectrum. 4. Conclusions

QUANTUM RADIATION GROUP Mathieu Manceau Angela Perez Timur Iskhakov, Olga Tikhonova, Robert Fickler, Robert Boyd, Gerd Leuchs Samuel Lemieux Polina Sharapova Lina Beltran

27 CONCLUSIONS Bright squeezed vacuum manifests macroscopic entanglement, up to the violation of Bell’s inequalities. By generating it in a nonlinear interferometer, one can - tailor its angular spectrum (up to obtaining single-mode radiation); - tailor its frequency spectrum (up to obtaining single-mode radiation); - obtain it in OAM modes THANK YOU FOR YOUR ATTENTION!

28 SIMPLIFIED MODEL T.Sh. Iskhakov, S. Lemieux, A.M. Perez, R.W. Boyd, G. Leuchs, and M.V. Chekhova, arXiv: (2015). Modes of the first crystal get differently spread due to GVD and are differently amplified in the second one Mode 50 Mode 10 Mode 0 10 cm SF6 60 cm SF6