Quantum Coherent ControlQuantum Coherent Controlwith Non-classical Lightwith Non-classical Light

Department of Physics of Complex SystemsDepartment of Physics of Complex SystemsThe Weizmann Institute of ScienceThe Weizmann Institute of Science

Rehovot, IsraelRehovot, Israel

Yaron Bromberg, Barak Dayan, Avi Pe’er, Itai Afek,

Yaron Silberberg

The Ultrafast Optics GroupThe Ultrafast Optics Group

10 fs pulses @ 800 nm ~130 nm FWHM

THG images of biological specimenTHG images of biological specimenFemtosecond Pulse ShapingFemtosecond Pulse Shaping

SLM

Phase, amplitude and polarization synthesizer

Spectral plane

QCC with Non-classical LightQCC with Non-classical Light

Can we shape a single photon?

… what does it really mean?

… and what is it good for?

Spontaneous Parametric Down-conversionSpontaneous Parametric Down-conversion

a pump photon is spontaneously converted into two lower frequency photons

ps

ienergy

conservation

momentum conservation

(phase matching)pk

sk

ik

non linear crystal

pumpsignal

idler

Continuous Broadband Down-conversion:Continuous Broadband Down-conversion:Time-Energy Entangled PhotonsTime-Energy Entangled Photons

5p MHz

THznm 1030

PUMP (cw)

)2(

SIGNAL (cw)

IDLER (cw)

, 0s i s s i it t E t E t

The two-photon wavefunction

1 0.2p s

is tt 21

is tt 1 100 fs

2/2/

1,1)(0)1(pp

gd

Gate

• The time DIFFERENCE between the photons behaves as a fs pulse

Time-Energy Entangled PhotonsTime-Energy Entangled Photons

non linear crystal

pump )cw(

signal )cw(

idler )cw(

… so lets shape the two-photon correlation function !

• But electronics limits temporal resolution to ~ns

Shaper

1. Hong-Ou-Mandel Interference

2. Instantaneous nonlinear interaction between photons

How can we get fs resolution?How can we get fs resolution?

c

~

“Measurement of Subpicosecond Time Intervals between Two Photons by Interference”

C.K. Hong, Z.Y. Ou and L. Mandel, PRL 59 (1987)

IDLER

SIGNAL

PUMP )2(

d

Two-Photon Coincidence Interference :Two-Photon Coincidence Interference : Hong-Ou-Mandel DipHong-Ou-Mandel Dip

Shaper

HOM in polarizationHOM in polarization

Pump364 nm

Computer

SLM

FourierPlane

PBS

V

1

2H

)(

V

φ

2 type-I crystals generatepolarization entanglementand broad spectrum

isis

isis

XYYX

VVHH

2

12

1

H

XV

Y

is

i

isVVeHH

2

1

A. V. Burlakov et. al. , PRA 64, (2001)

Experimental SetupExperimental Setup

Pump364 nm

Computer

crystalsSLM

FourierPlane

PBS

V

1

2H

)(

Phase-and-polarization SLMControls independently the ±45° axes (X,Y)

Experimental ResultsExperimental Results

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

1. Hong-Ou-Mandel Interference

2. nonlinear interaction between photons (instantaneous)

How can we get fs resolution?How can we get fs resolution?

Coincidence detection through Coincidence detection through Sum-Frequency Generation (SFG)Sum-Frequency Generation (SFG)

CW PUMP

)2(

SIGNAL )CW(

IDLER )CW(

)2(

910~ 1510~ s 1410 stypical flux SFG efficiency SFG signal

Delay

Delay

13 -1max 10 s 2 !!W

1

1

1

A photon-pair per time-bin

The photon-pair arrives within 1/

How many ‘single photons’ can arrive in one second ?How many ‘single photons’ can arrive in one second ?

(How high can ‘low light levels’ be ?)(How high can ‘low light levels’ be ?)

(n=1 photon per mode)

Quantum mechanical analysis of SFG

0

22

0

22

0nnnR SFGSFG

0n - photons per mode

2I Ientangled photons

1995: Kimble’s groupmeasures a slope of 1.3at low photon numbers

Down-convertingcrystal

SFGcrystal

pump 532nm5W

IR detector

SPCM

Beam dump

Dispersioncompensation

Computer

SFG with Entangled PhotonsSFG with Entangled Photons

PP-KTPPP-KTP

SFG 532nm~40,000 s-1

0

Intensity Dependence of SFG with Entangled Photons

0n 02

0 nn

"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)

Down-convertingcrystal

up-convertingcrystal

Pump 532nm

IR detector

SPCM

Beam dump

Computer

Shaping of Entangeled PhotonsShaping of Entangeled Photons

Fourierplane

SLM )(

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

Temporal shaping of the two-photon wavefunctionTemporal shaping of the two-photon wavefunction

We have seenWe have seen……

• Control of HOM interference

• Shaping of two-photon correlation functions

• Linear SFG for low light levels

• SFG as coincidence detection

Pulse shaping offers a new tool for quantum information

Pulse Shaping

Nonlinear interactions