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Quantum Coherent Control with Non-classical Light Yaron Bromberg, Barak Dayan, Avi Pe’er, Itai Afek, Quantum Coherent Control with Non-classical Light Yaron Bromberg, Barak Dayan, Avi Pe’er, Itai Afek, Yaron Silberberg The Ultrafast Optics Group Department of Physics of Complex Systems The Weizmann Institute of Science Rehovot, Israel

THG images of biological specimen Femtosecond Pulse Shaping Phase, amplitude and polarization synthesizer Spectral THG images of biological specimen Femtosecond Pulse Shaping Phase, amplitude and polarization synthesizer Spectral SLM plane 10 fs pulses @ 800 nm ~130 nm FWHM

QCC with Non-classical Light Can we shape a single photon? … what does it QCC with Non-classical Light Can we shape a single photon? … what does it really mean? … and what is it good for?

Spontaneous Parametric Down-conversion a pump photon is spontaneously converted into two lower frequency photons Spontaneous Parametric Down-conversion a pump photon is spontaneously converted into two lower frequency photons non linear crystal pump signal idler energy conservation momentum conservation (phase matching)

Continuous Broadband Down-conversion: Time-Energy Entangled Photons The two-photon wavefunction SIGNAL (cw) PUMP (cw) (2) Continuous Broadband Down-conversion: Time-Energy Entangled Photons The two-photon wavefunction SIGNAL (cw) PUMP (cw) (2) IDLER (cw)

Time-Energy Entangled Photons signal (cw) non linear crystal Gate pump (cw) Sha per idler Time-Energy Entangled Photons signal (cw) non linear crystal Gate pump (cw) Sha per idler (cw) • The time DIFFERENCE between the photons behaves as a fs pulse … so lets shape the two-photon correlation function ! • But electronics limits temporal resolution to ~ns

How can we get fs resolution? 1. Hong-Ou-Mandel Interference 2. Instantaneous nonlinear interaction between How can we get fs resolution? 1. Hong-Ou-Mandel Interference 2. Instantaneous nonlinear interaction between photons

Two-Photon Coincidence Interference : Hong-Ou-Mandel Dip “Measurement of Subpicosecond Time Intervals between Two Photons Two-Photon Coincidence Interference : Hong-Ou-Mandel Dip “Measurement of Subpicosecond Time Intervals between Two Photons by Interference” C. K. Hong, Z. Y. Ou and L. Mandel, PRL 59 (1987) r pe a Sh SIGNAL PUMP (2) IDLER d

HOM in polarization 2 type-I crystals generate polarization entanglement and broad spectrum Fourier Plane HOM in polarization 2 type-I crystals generate polarization entanglement and broad spectrum Fourier Plane Computer 1 V Pump 364 nm φ SLM V H 2 PBS V Y X H A. V. Burlakov et. al. , PRA 64, (2001)

Experimental Setup Fourier Plane Computer 1 crystals Pump 364 nm SLM V H 2 Experimental Setup Fourier Plane Computer 1 crystals Pump 364 nm SLM V H 2 PBS Phase-and-polarization SLM Controls independently the ± 45° axes (X, Y)

Experimental Results B. Dayan, Y. Bromberg, I. Afek and Y. Silberberg, in preparation. Experimental Results B. Dayan, Y. Bromberg, I. Afek and Y. Silberberg, in preparation.

How can we get fs resolution? 1. Hong-Ou-Mandel Interference 2. nonlinear interaction between photons How can we get fs resolution? 1. Hong-Ou-Mandel Interference 2. nonlinear interaction between photons (instantaneous)

Coincidence detection through Sum-Frequency Generation (SFG) SIGNAL (CW) CW PUMP Delay (2) Delay IDLER Coincidence detection through Sum-Frequency Generation (SFG) SIGNAL (CW) CW PUMP Delay (2) Delay IDLER (CW) typical flux SFG efficiency SFG signal

How many ‘single photons’ can arrive in one second ? (How high can ‘low How many ‘single photons’ can arrive in one second ? (How high can ‘low light levels’ be ? ) The photon-pair arrives within 1/D A photon-pair per time-bin (n=1 photon per mode)

Quantum mechanical analysis of SFG entangled photons - photons per mode Quantum mechanical analysis of SFG entangled photons - photons per mode

1995: Kimble’s group measures a slope of 1. 3 at low photon numbers 1995: Kimble’s group measures a slope of 1. 3 at low photon numbers

SFG with Entangled Photons Computer Beam dump PP-KTP Down-converting crystal pump 532 nm 5 SFG with Entangled Photons Computer Beam dump PP-KTP Down-converting crystal pump 532 nm 5 W Dispersion compensation IR detector PP-KTP SFG crystal SPCM SFG 532 nm ~40, 000 s-1

Intensity Dependence of SFG with Entangled Photons 0 Intensity Dependence of SFG with Entangled Photons 0 "Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons", B. Dayan, A. Pe’er, A. A. Friesem and Y. Silberberg, Phys. Rev. Lett. 94, 043602 (2005)

Shaping of Entangeled Photons SLM Computer Beam dump IR detector Pump 532 nm Down-converting Shaping of Entangeled Photons SLM Computer Beam dump IR detector Pump 532 nm Down-converting crystal Fourier plane up-converting crystal SPCM

Temporal shaping of the two-photon wavefunction Temporal shaping of the two-photon wavefunction "Temporal Shaping of Entangled Photons", A. Pe’er, B. Dayan, A. A. Friesem and Y. Silberberg, Phys. Rev. Lett. 94, 073601 (2005)

We have seen… Pulse Shaping • Control of HOM interference • Shaping of two-photon We have seen… Pulse Shaping • Control of HOM interference • Shaping of two-photon correlation functions Nonlinear interactions • Linear SFG for low light levels • SFG as coincidence detection Pulse shaping offers a new tool for quantum information