Optical quantum imaging metrology sensing Marco Genovese EMPIR17

Optical quantum imaging metrology & sensing Marco Genovese EMPIR-17 FUN 01 - Be. COMe Light-matter interplay for optical metrology beyond the classical spatial resolution limits COST Action MP 1405 EMPIR-17 FUN 06 - SIQUST Single-photon sources as new quantum standards FQXi Project FET Open project - Pathos Nato grant G 5263

• 1935 - quantum correlations (entanglement, discord, …) -> on foundation of quantum mechanics BELL inequalities, Schrödinger cat, …… [( | H > + | V > ) ] ______________________________ 2 • ~ 1990 - II quantum revolution -> Quantum Tech: - Quantum information - Quantum metrology & sensing - Quantum Imaging - …. debate

Quantum Imaging: a new quantum technology addressed to exploit properties of quantum optical states for overcoming limits of classical optics • "Real applications of quantum imaging", M. Genovese, Journal of Optics, 18 (2016) 073002. - Ghost imaging [A. Belinskii D. Klyshko Sov. P. JETP 78 (94) 259 ; T. Pittman et al. , PRA 52 (95) R 3429] [A. Gatti PRA 69 (04)133603 ; R. Bennik et al. , PRL 89 (02) 113601 ] - Quantum lithography [A. Boto et al, PRL 85 (00) 2733 ; M. D’Angelo et al. , PRL 87 (01) 13602] - Entangled Images [V. Boyer et al. , Science 321 (08) 544] - Image amplification by PDC [A. Gatti et al. , PRL 83 (99) 1763 ; A. Mosset et al. ; PRL 94 (05) 223603] - Quantum Illumination [S. Tan et al. , PRL 101 (08) 253601; E. Lopaeva et al. , PRL 110, 153603 (2013) ] - Sub-Rayleigh quantum imaging [V. Giovannetti et al. , Phys. Rev. A 79, 013827 (2009)]. - Sub shot noise imaging [E. Brambilla et al. , PRA 77, 053807 (08); G. Brida, M. G. , I. Ruo Berchera, Nature Photonics 4 (10) 227] - Quantum enhanced differential interference contrast microscope [T. Ono, R. Okamoto, S. Takeuchi Nat. Commun. 4, 2426 (2013)] - Super resolution with subpoissonian light [Schwartz O and Oron D 2012 Phys. Rev. A 85 033812, Gatto Monticone D et al 2014 Phys. Rev. Lett. 113 143602, Thiel C et al 2007 Phys. Rev. Lett. 99 133603, Oppel S et al 2012 Phys. Rev. Lett. 109 233603, . . . ] - . . .

NOON States |N>|0> + |0> |N> Quantum Lithography Resolution λ/N ! A. N. Boto, et al. Phys. Rev. Lett. 85, 2733 (2000) M. D'Angelo, M. V. Chekhova, and Y. Shih Phys. Rev. Lett. 87, 013602 (2001) Zeilinger et al. (2004). "De Broglie wavelength of a non-local four-photon state". Nature. 429 (6988): 158 Quantum Interferometry • • S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, “Improvement of frequency standards with quantum entanglement, ” Phys. Rev. Lett. , 79, 3865 Steinberg et al. (2004). "Super-resolving phase measurements with a multiphoton entangled state". Nature. 429 (6988)

Photon number correlations and twin beams: a tool for quantum imaging metrology & sensing Photon number correlations represent a fundamental tool for Quantum imaging metrology & sensing "Real applications of quantum imaging", M. Genovese, Journal of Optics, 18 (2016) 073002 “Photon number correlation for quantum enhanced imaging and sensing» , A. Meda et al. J. Opt. 19 (2017) 094002

Squeezed Vacuum FAR FIELD Plane Wave Pump s) l( gna si x 1 q=0 idle r (i ) Two-Mode Entangled State (squeezed vacuum) -x 1 Photon number correlations in twin beams/ideal case 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) Relaxation of the phase matching condition uncertainty in the propagation directions of twin photons To detect quantum correlation, the detector size must be larger than the single spatial mode [Brambilla et al. Phys Rev A 69, 023802 (2004)].

Spatial entanglement in PDCNRF For quantifying the level of correlation we use the Noise Reduction Factor, defined as the fluctuation of the difference Ns-Ni normalized to the Shot Noise Level (Standard Quantum Limit). Beam splitter for coherent states for classical light (e. g. thermal) For PDC→sub shot noise regime η is the overall transmission of the optical channel SQL Agafonov, Chekhova, Leuchs, ar. Xiv: 0910. 4831; Bondani et al. , Phys. Rev. A 76, 013833(2007); O. Jedrkievicz et al. , Phys. Rev. Lett. 93, 243601 (2004); J. Blanchet el al. Phys Rev. Lett. 101, 233604 (2008), J. Perina et al. , Phys. Rev. A 85( 2012) 023816 G. Brida, L. Caspani, A. Gatti, M. G. , A. Meda, I. Ruo-Berchera, PRL 102, 213602 (09). 8

A first example : the ghost Imaging WHAT IS GHOST IMAGING?

ghost Imaging WHAT IS GHOST IMAGING?

ghost Imaging “Ghost imaging is a novel technique in which the object and the image system are on separate optical paths”

Ghost Imaging: theory Correlated photons Object Point-like or bucket detector D. N. Klyshko, Usp. Fiz. Nauk 154, 133 (1988) Spatial resolving detector intensity fluctuations correlation ”. . is equivalent to the following scenario: use a device that shoots two pebbles in random but exactly opposite directions. When one of the pebbles overshoots an object, it hits a bell. The other pebble instead hits a soft wall, where it remains glued to it. By shooting many pebbles and marking on the wall the pebble’s position every time we hear the bell ring, we will project the outline of the object on the wall. ”

Ghost Imaging: theory Twin beam Pittman et al. , Phys. Rev. A 52, 5 (1995). Thermal ligth beam It was successfully interpreted as a statistical correlation of intensity fluctuations of the classical correlated beams. Speckle –speckle correlation in pseudothermal beam Bennik et al. , PRL 89, 11 (2002), Gatti et al. , PRL 94, 183602 (2005), …

Ghost Imaging: applications Magentic domains [INRIM] Imaging through diffusive media…[R. Meyers et al. , M. Bondani et al…. ] Imaging through turbolent atmposphere [D. Shi et al. ]

Quantum imaging with undetected photons [GB Lemos, V Borish, GD Cole, S Ramelow, R Lapkiewicz, A Zeilinger Nature 512 (2014), 409] Quantum interference between the photons emitted by PDC in NL 1 and NL 2 allows imaging the object even if photons crossing it are never detected Entangled Images from Four-Wave Mixing [Boyer, Lett et al Science 321 (2008) 544] (A) Image of the probe seed in the far field. (B) Image of the output probe in the intermediate field. (C) Image of the conjugate in the far field.

Sub shot noise imaging Quantum sensing with twin beams 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 Sub shot noise microscope N. Samantaray, I. Ruo-Berchera, A. Meda, M, Genovese; Light: Science & Applications-Nature group (2017) 6, e 17005; (N= 10) (N=1 00)

Does quantum correlated light help in coupled interferometers? : Detecting the Holographic Noise 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) G. Hogan, Arxiv: 1204. 5948 G. Hogan, Phys. Rev. D 85, 064007 (2012) This new quantum uncertainty of space-time induces a slight random wandering of transverse position (called “holographic noise”)

d d • The random walk is bounded by a single light round trip Expected in the MHz region for meters C. Hogan, Arxiv: 1204. 5948; C. Hogan, PRD 85, 064007 (2012)

Holographic Noise and the Holometer Single Interferometer Holometer BS «Overlapping» spacetime volume BS M 2 M 1 BS «Separated» spacetime volume HOLOMETER: principles of operation • Evaluation of the cross-correlation between two equal Michelson interferometers occupying the same space-time volume • Reference measurement: HN correlation «turned off» by separating the space-time volumes of the two interferometers

HOLOMETER Even if the HN is hidden by the photon shot noise in one interferometer, it could emerge in the cross-correlation between two of them (waiting longer enough. . )

Quantum light in Coupled Interferometers I. Ruo Berchera, I. P. Degiovanni, S. Olivares, M. Genovese PRL 110, 213601 (2013); PRA 92, 053821 (2015) > 107 W Quantum Enhancement Uncertainty Fluctuations of the # of photons inside the interferometers arms induce phase fluctuations due to mirror recoil (Radiation Pressure Noise). photons momentum df. RP =

Experimental realisation Laser 1064 nm ST. Pradyumna, E. Losero, I. Ruo-Berchera, P. Traina, M. Zucco, C. S. Jacobsen, U. L. Andersen, I. P. Degiovanni, M. Genovese, T. Gehring ar. Xiv: 1810. 13386 M § Read-out AS port operated close to the dark fringe (LIGO, HOLOMETER) M § 2 -D Power recycling cavity 90% reflectivity (gain =10) M Alternatively: • Cross spectrum or cross correlation is measured • Twin beam like correlation are injected • The output difference is measured Isolator Two independent squeezing are injected PRM IFO 2 M BS Isolator • BS IFO 1 BS PRM I 1 - I 2 TWB Like I 1 -I 2

2 INDEPENDENT SQUEEZED INPUTS Uncorrelated White noise injected in both interf. s SNL+White Noise Single frequency noise injected in a one interf. SNL TWB+White Noise TWB