1. 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

2. OUTLINE
Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

3. Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

4. BRIGHT SQUEEZED VACUUMp
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?

5. Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

6. ENTANGLEMENT
QWP S A B
PBS

7. MACROSCOPIC ENTANGLEMENT
PBS
QWP A B S

8. 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.

9. 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, (2011).

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

11. 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.

12. 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

13. 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.

14. 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!

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

16. Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

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

18. 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:

19. 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:

20. TOMOGRAPHY OF MACROSCOPIC BELL STATESj
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, (2012).

21. TOMOGRAPHY
HWP step 2.50
QWP step 50
HWP
QWP
PBS

22. 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, (2012).

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

24. Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

25. 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;
- ...

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

27. 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).

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

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

30. Bright squeezed vacuum
Entanglement
Polarization properties
Single mode selection
Conclusions

31. 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

32. THANK YOU FOR YOUR ATTENTION!