Towards Single-Photon Nonlinearities using Cavity EIT Z. Burkley, C. Kupchak, B. Jordaan, P. Nguyen, C. Cheung, S. Rind, C. Noelleke, and E. Figueroa Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA

Z. Burkley, B. Jordaan, C. Cheung, C.

Future Perspectives

Optical Quantum States at Rb Resonance

Motivation • Quantum logic gates are the key ingredient for constructing a quantum processor.

• Promising logic gate realizations can be achieved through the interaction of single photon qubits.

• Two photon interaction requires strong nonlinearities at the single photon level.

Introduction

Quantum Gate Implementation

Current Status:• Nonlinear crystal characterization √• Construction of OPA bow tie cavity √• Generate narrow linewidth blue light√• Pound Drever Hall Cavity Locking √• SHG Cavity implementation.• Simultaneous transmission for two frequencies (locking/quantum state).• Production of quantum states of light tuned to rubidium.

1) Quantum Light Source Single Photons at Rubidium Resonance 2) Interface Quantum Technology with Atoms (Quantum Memory) 3) Characterization of the Gate Quantum Tomography

A way to create nonlinearities is through the use of electromagnetically-induced transparency (EIT).

Quantum Tomography of Few Photon Level Pulses

<n>=2.4

Experimental Results

EIT Measurements

Quantum Process Tomography of Quantum Gates

function

controlfield 1

probephoton

signalphoton

MirrorNPBS

SPDC

MOT

LO

HDcontrolfield 2

Wignerreconstruction

Implementation of Single Photon XPM in Rubidium

However, EIT is not enough. We need to engineer N & M Type Schemes to create Giant Kerr effects, also known as cross phase modulation (XPM). Mo-reover, the use of optical cavities might help us achieve XPM with single photons.

M1 M2

2 1 0 1 2 3

1.0

1.0

2.0

Re(χ )(1)Im(χ )(1)

ω /probe γ

3

12

Ωc, ωcωp

γ2

∆2∆1

−5 −4 −3 −2 −1 0 1 2 3 4 50

20

40

60

80

100

∆/κ1

Rela

tive

tran

smis

sion

<b+b>=0

<b+b>=1

1

2

4

Crystal Mount

M1 M2

M4 M3

0 0.5 1 1.5 2 2.5 3x 10-5

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Time(s)

Inte

nsity

(a.u

.)

Incoming pulseRetrieved pulse IMControl field switching IMRetrieved pulseControl field switching

Experimental Requirements for a Quantum Gate

5 2S1/2

5 2P1/2

5 2P3/2

F=1

F=2

F=1

F=2

F=1

F=0

F=2

F=3

795 nm 377 THz

780 nm 384 THz

72 MHz

157 MHz

267 MHz

2.56 GHz

4.27 GHz

306 MHz

510 MHz

ΩP

ΩC1

ΩS

ΩC2

−13.5 0 +11.60.4

0.5

0.6

0.7

0.8

0.9

1

One-Photon Detuning (MHz)

Tran

smis

sion

(%)

0 0.5 1 1.5 2 2.50.04

0.05

0.06

0.07

0.08

0.09

0.1

Time (ms)

Phot

odio

de V

olta

ge (a

.u.)

Off resonanceOne-photon resonance

Two-photon resonanceBackground

EITPeak

Current Status:• Achieve EIT in a Rb MOT √• Eliminate spurious magnetic fields in experiment.

87

0 20 40 60 80 100

0.015

0.02

0.025

Time (µs)Ph

otod

iode

Vol

tage

(a.u

.)

Probe PulseN−Type ModifiedPulseEIT SlowdownPulse

Current Status:• Slowdown of few microsecond pulses √ • Characterization of cavities.• N-Type scheme modification of pulses √ • Simultaneous slowdown of pulses.• Construction of cavities √ • Few photon level nonlinearity.

Engineering Lambda, N, & M type schemes in Rubidium 87.

4FS

R p

has

e lo

ck

Single Photon

Mixer

8MHz200 mV

Function Generator

Input

Output

Pie

zoServo Controller

PPKTP

BBO

Error Signal Generation

ΩP

ΩLO

PBS

NPBS

Magneto-Optically

Trapped 87Rb

Dual Cavities

To Homodyne Detector

Dual Cavities

ΩP

ΩS

ΩC1 To Homo

Detect

ΩΩS

Ω C2

2

1. Rev. Mod. Phys. 77, 633 (2005) 2. Eur. Phys. J. D 40, 281 (2006)

Homodynedetector

Probefield

Quantum processLocaloscillator

ρin ρout

controlfield 1

signalfield

Mirror

MOT

Quantum Impedance MatchingReferences:

0 200 400 600 800 1000 12000

0.02

0.04

0.06

0.08

Piezo

Time ( µs)

EIT measurementPulse train

Slowdown pulseTransmitted pulse

Phot

odio

de v

olta

ge (a

. u.)

0 5 10 15 20−30

−20

−10

0

10

20

30

Local Oscillator phase (a. u.)

=πTransmitted pulses (<n>=600)Slowdown pulses (∆ /60)

Qua

drat

ue v

alue

s

0 5 10 15 20 25

−1

0

1

2

3

4

5

6

Slowdown pulses

Transmitted pulses

Pulsed Tomography Reconstruction

X quadrature

Y qu

adra

ture

Preliminary Data