Marco Genovese QFPPP 2014 CERN

1. Improving interferometers by quantum light: is possible testing quantum gravity on an Optical bench? Marco Genovese QFPPP 2014CERN

2. Acknowledgements • This work hasbeensupported by: • EU Projects: BRISQ2 • John TempletonFoundation • Italian Minister of Research: FIRB projects RBFR10YQ3H and RBFR10UAUV; Progettopremiale P5 • BankFoundation: Compagnia di San Paolo.

3. INRIM QUANTUM OPTICS GROUP “Carlo Novero lab” Responsible: M. Genovese 8 quantum optics labs 5 permanent staff (M.G., G. Brida, I. Degiovanni, M.Gramegna, I.Ruo Berchera) 8 non permanent staff (G.Adenier,A.Avella, A. Meda, G.Giorgi,E.Moreva, F. Piacentini, M.Roncaglia,P.Traina); 1 PhD students (N.Samantaray) several undergraduate students G. Brida, I. P.Degiovanni,M.G.,Alice Meda, E.D. (Lisa) Lopaeva, I. Ruo Berchera Stefano Olivares (Univ. Milano) + undergraduate students

4. PDC: a brief summary Type-I PDC Type-II PDC

5. Photon number correlations in twin beams/ideal case FAR FIELD Plane Wave Pump signal(s) x1 q=0 -x1 idler (i) Two-Mode Entangled State (squeezed vacuum) Two-Mode Photon number correlation

6. Photon number correlations in twin beams/gaussian pump Noisy Intensity Pattern, where the typical scale is the Coherence Area Gaussian Pump wp (2)‏ uncertainty in the propagation directions of twin photons Relaxation of the phase matching condition To detect quantum correlation, the detector size must be larger than the single spatial mode [Brambilla et al. Phys Rev A 69, 023802 (2004)]. 6

7. Quantum sensing with twin beams Sub shot noise imaging [G.Brida,M.G.,I.Ruo Berchera, Nature Photonics 4 (10) 227 G.Brida,M.G.,A.Meda,,I.Ruo Berchera,PRA 83 (2011) 033811] (N=10) (N=100)

8. - Phase measurements can be improved by using entangled states as N00N states - Can quantum correlations of twin beams find application in interferometry?

9. Application to interferometry • The dream of building a theory unifying general relativity and quantum mechanics, the so called quantum gravity has been a key element in theoretical physics research for the last 60 years. • A HUGE theoretical work: string theory, loop gravity, …. • However, for many years no testable prediction emerged from these studies. In the last few years this common wisdom was challenged: a first series of testable proposals concerned photons propagating on cosmological distances [AmelinoCamelia et al.], with the problem of extracting QG effects from a limited (uncontrollable) observational sample affected by various propagation effects.

10. Several QG theories (string theories, holographic theory, heuristic arguments from black holes,…) predict non- commutativity of position variables at Planck scale Sort of space-time uncertainty principle (L= radial separation)

11. Recently, effects in interferometers connected to non-commutativity of position variables in different directions were considered both for cavities with microresonators [Pikovsky et al.] and two coupled interferometers the so called ``holometer'‘ [Hogan]. In particular this last idea led to the planning of a double 40m interferometer at Fermilab • Here we show how the use of photon number correlations in twin beams can largely improve the sensibility of this interferometer

12. Holographic Noise (HN) and interferometry Two Interferometers Single Interferometer (┴) (‖) time M1 M2 «Separated» space-time volume «Overlapping» space-time volume BS • HOLOMETER : principle of operation • Evaluate the cross-correlation between two equal Michelson interferometers occupying the same space-time volume (‖ conf.) • HNs are correlated while Shot Noises are uncorrelated vanishing over a long integration time • Control measurement can be performed «turned off» HN correlation just by separating the space-time volumes ( ┴ conf.)

13. Holographic Noise (HN) and interferometry G. Hogan, Phys. Rev. D 85, 064007 (2012). G. Hogan, Arxiv: 1204.5948

14. Quantum light in the Holometer Squeezed light in gravitational wave detectors!! A sub-shot-noise PS measurement in a single interferometer (e.g. gravitational wave detector) was suggested exploiting squeezed light Caves, PRD 23, 1693 (1981) Kimble et al., PRD 65, 022002 (2001) Long Story and huge literature… and recently realized at Geo 600 and Ligo R. Schnabel et al., Nature Commun. 1, 121 (2010) Ligo, Nature Phys. 7, 962 (2011)

17. The Model «separated spacetime» «Overlapping spacetime» (‖) • (┴) • d d

18. The Model «separated spacetime» «Overlapping spacetime» (‖) • (┴) • d d Quantum EV

19. The Model «separated spacetime» «Overlapping spacetime» (‖) • (┴) • d d P.D.F of the phases due to HN Quantum EV

20. The Model «separated spacetime» «Overlapping spacetime» (‖) • (┴) • Phase Covariance

21. The Model Phases covariance uncertainty:

22. The Model Phases covariance uncertainty: linearization 0-th order • 0-th order independent from phase fluctuations (i.e. HN) • 0-th order Photon noise (shot-noise level in the classical @FermilabHolometer) IQIS2013, 24-26 September 2013, Como

23. The Model Phases covariance uncertainty: linearization 0-th order 2-nd order • 0-th order independent from phase fluctuations (i.e. HN) • 0-th order Photon noise (shot-noise level in the classical @FermilabHolometer) • 2-nd order phase dependent (Radiation pressure effect etc..) 0-th order contribution to phase covariance uncertainty:

24. The Model Phases covariance uncertainty: linearization 0-th order 2-nd order • 0-th order independent from phase fluctuations (i.e. HN) • 0-th order Photon noise (shot-noise level in the classical @FermilabHolometer) • 2-nd order phase dependent (Radiation pressure effect etc..) 0-th order contribution to phase covariance uncertainty:

25. d d d d

26. d d d d PRL 110, 213601 (2013)

27. Results ideal case (no losses, no radiation pressure) In the ideal case of absence of losses: µ mean photon number of coherent state  mean photon number of squeezed state µ >>  >> 1

28. Results for moderate quantum resources PN +RP CL SQ TWB Quantum Enhancement Uncertainty PN +RP photonsmomentum PN +RP dfRP =

29. Results for strong quantum resources CL= Shot Noise Level Ph+RP Ph+RP TWB Ph Ph SQ

30. Role of the entanglement

31. Role of the entanglement Is Entanglement related to the TWB quantum enhanchement? Indeed a clear role of entanglement, measured by negativity, is demonstrated. This is due to the fact that the scheme requires not only perfect photon number correlation, but also a defined phase of the TWB for a coherent interference with the classical coherent field at the Beam Splitter.

32. Regimes of interests for a real experiment For real life losses, in terms of absolute sensitivity, the most promising setup is still by far the double squeezing. CL TWB SQxSQ Shot noise HN (40m arms) SQxSQ

33. CONCLUSIONS • We studied for the first time the use of quantum light in coupled interferometers • This is of extreme interest for the new developments of fundamental physics (testing holographic principle, quantum gravity ecc..) • Quantum light enhance the sensitivity of the Holometer below the “Shot-Noise” limit • Squeezed light provides an enhancement of the order of the mean number of photon of the squeezed light • Twin-Beam provides a complete suppression of the shot-noise contribution (0!!!!) • Losses (effectively) affect this enhancement • Radiation pressure is not an problem (for affordable light power level) PRL 110, 213601 (2013)