ENTANGLED BRIGHT SQUEEZED VACUUM Quantum Radiation group Max-Planck Institute for the Science of Light ENTANGLED BRIGHT SQUEEZED VACUUM Maria Chekhova*,**, Ivan Agafonov**, Timur Iskhakov*, Bhaskar Kanseri*, Angela Perez*, Kirill Spasibko**, Gerd Leuchs* *Max-Planck Institute for the Science of Light, Erlangen, Germany **M.V.Lomonosov Moscow State University, Moscow, Russia    

OUTLINE Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

BRIGHT SQUEEZED VACUUM p pump collinear nondegenerate PDC pump noncollinear degenerate PDC pump collinear degenerate PDC ‘Macroscopic’ state Interactions with matter (atoms, mechanical systems, ...), with itself (nonlinear optics) Is it entangled?

Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

ENTANGLEMENT QWP S A B PBS

MACROSCOPIC ENTANGLEMENT PBS QWP A B S

MACROSCOPIC BELL STATES pump a b The states produced this way can be called macroscopic Bell states as they are very similar to the two-photon Bell states. And they are produced the same way, and with the same Hamiltonian. Experimentally this can be realized through parametric down-conversion but one should employ, in addition to 2 polarization modes, also 2 other modes. We use wavelength. So a,b denote different wavelengths, H and V polarization. The states obtained this way can be directly derived from the shape of the Hamiltonian. But it is more instructive to write the state explicitly. Then we see that there are correlations between two pairs of modes. The number of photons in mode Ha is exactly equal to the number of photons in mode Vb.

EXPERIMENTAL PREPARATION 600 720 840 - 1 2 a n g l e , d wavelength, nm PBS BBO type-I BBO type-I DP B: 805 nm A: 635 nm PBS We produce these states in a MZ interferometer where the pump enters through a polarization BS, so it has orthogonal polarizations in the two arms. In each arm, there is a type-I BBO crystal, and it produces a nondegenerate PDC at wavelengths 805 nm and 635 nm. These two beams of orthogonally polarized squeezed vacuums are overlapped on another PBS, losslessly. The pump is cut off. With the phase pi here, the Hamiltonian is the one generating Phi- state. In the diagonal basis, it turns into the Hamiltonian generating Psi+. And then, there is a special dichroic waveplate that leads to the appearance of a minus here as it causes an oe delay for the two wavelengths differing by exactly pi. This setup and the generation of macroscopic Bell states are described in this paper. In the diagonal basis: DP : T. Sh. Iskhakov, M.V.Chekhova, G.O.Rytikov, and G.Leuchs, PRL 106, 113602 (2011).

HOW TO VERIFY ENTANGLEMENT? Ch. Simon and D. Bouwmeester, PRL 91, 053601 (2003); T.Sh. Iskhakov et al., arXiv:1111.2073v3 [quant-ph] (2011). Theoretically, for

MODE MATCHING Correlated points But for different wavelengths, the selected angles should be different. This is clear from the wavelength-angular spectrum of PDC: correlated points correspond to different angles. The diameters of the apertures should have the same ratio as the wavelengths.

EXPERIMENTAL SETUP Separate angular filtering for the two wavelengths In the new version of our setup, we separated the wavelengths and filtered them separately. The rest is the same, except that we tried very hard… Separate angular filtering for the two wavelengths

VIOLATION OF SEPARABILITY CONDITION D2 fixed at 8.9 mm And we finally violated this separability condition. This is the sum of the three variances, as a function of the diameter of one of the apertures. The other one is fixed. This is the boundary for the separability, and you can see that we get below it.

HOW MUCH ENTANGLED? The state is already written as a Schmidt decomposition, ‘Fedorov ratio’, an operational measure Entanglement reduced due to losses and multimode detection Not operational!

MEASUREMENT RESULTS Very little entanglement accessible, due to losses and noise: in theory, R~300

Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

POLARIZATION PROPERTIES Photon-number correlations in polarization modes polarization squeezing S1 triplet singlet S1 S2

POLARIZATION QUASIPROBABILITY W-function K.B.Wolf, Opt. Commun. 132, 343 (1996); V.P.Karassiov and A.V.Masalov, J. Opt. B 4, 366 (2002) One can calculate all mean values (moments of all orders) through algebraic averaging:

POLARIZATION TOMOGRAPHY P.A.Bushev, V.P.Karassiov, A.V.Masalov, and A.A.Putilin, Optics and Spectroscopy 91, 526 (2001) tomogram of a Stokes measurement Reconstruction:

TOMOGRAPHY OF MACROSCOPIC BELL STATES j 635 nm 805 nm PBS BBO type - I DP GP HWP QWP Nd:YAG 3 w OG PREPARATION MEASUREMENT d t A B. Kanseri, T. Sh. Iskhakov, I.N.Agafonov, M. V. Chekhova, and G. Leuchs , PRA 85, 022126 (2012).

TOMOGRAPHY HWP step 2.50 QWP step 50 HWP QWP PBS

RESULTS: TRIPLET AND SINGLET STATES Electronic noise Noise subtracted B. Kanseri, T. Sh. Iskhakov, I.N.Agafonov, M. V. Chekhova, and G. Leuchs , PRA 85, 022126 (2012).

COMPARISON WITH A COHERENT STATE B. Kanseri, T. Sh. Iskhakov, I.N.Agafonov, M. V. Chekhova, and G. Leuchs , PRA 85, 022126 (2012).

Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

SINGLE MODE SELECTION So far, no single-mode squeezed vacuum Several applications require a single mode, namely: - conditional Fock-state preparation; - super-resolution; - achieving high entanglement; - ...

SINGLE MODE SELECTION BBO type-I PBS HWP NPBS 1013 photons/mode

bunching: for each mode of two-mode squeezed vacuum, g(2)=2 g(2) MEASUREMENT superbunching: for single-mode squeezed vacuum, g(2)=3 bunching: for each mode of two-mode squeezed vacuum, g(2)=2 T. Sh. Iskhakov, A.Perez, K.Yu. Spasibko, M. V. Chekhova, and G. Leuchs , Optics Letters, 37, 11 (2012).

PHOTON-NUMBER DISTRIBUTIONS T. Sh. Iskhakov, A.Perez, K.Yu. Spasibko, M. V. Chekhova, and G. Leuchs , Optics Letters, accepted (2012).

SINGLE-MODE STATISTICS Collinear nondegenerate (thermal statistics) Collinear degenerate experiment theory

Bright squeezed vacuum Entanglement Polarization properties Single mode selection Conclusions

2. An operational measure of entanglement proposed CONCLUSIONS 1. Demonstration of BSV entanglement 2. An operational measure of entanglement proposed 3. Polarization tomography of BSV states 4. Single mode selected 5. Next: lossless Schmidt mode selection

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