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Jonathan P. Dowling

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Quantum Optical Metrology, Imaging, and Computing

Jonathan P. Dowling

Hearne Institute for Theoretical Physics

Quantum Science and Technologies Group

Louisiana State University

Baton Rouge, Louisiana USA

quantum.phys.lsu.edu

Frontiers of Nonlinear Physics, 19 July 2010

On The «Georgy Zhukov» Between Valaam and St. Petersburg, Russia

Not to be confused with:

Quantum Meteorology!

Dowling JP, “Quantum Metrology,”

Contemporary Physics 49 (2): 125-143 (2008)

Hearne Institute for Theoretical Physics

QuantumScience & Technologies Group

H.Cable,C.Wildfeuer,H.Lee, S.D.Huver, W.N.Plick, G.Deng, R.Glasser, S.Vinjanampathy, K.Jacobs,D.Uskov,J.P.Dowling,P.Lougovski,N.M.VanMeter, M.Wilde, G.Selvaraj, A.DaSilva

Not Shown: P.M.Anisimov,B.R.Bardhan,A.Chiruvelli, R.Cross,G.A.Durkin, M.Florescu, Y.Gao, B.Gard, K.Jiang,K.T.Kapale,T.W.Lee,D.J.Lum,S.B.McCracken, C.J.Min, S.J.Olsen, G.M.Raterman,C.Sabottke,R.Singh,K.P.Seshadreesan,S.Thanvanthri, G.Veronis

Nonlinear Optics vs. Projective Measurements

Quantum Imaging vs. Precision Measurements

Showdown at High N00N!

Mitigating Photon Loss

6. Super Resolution with Classical Light

7. Super-Duper Sensitivity Beats Heisenberg!

(3)

PBS

Rpol

z

Unfortunately, the interaction (3)is extremely weak*:

10-22 at the single photon level —This is not practical!

*R.W. Boyd, J. Mod. Opt.46, 367 (1999).

Optical Quantum Computing:

Two-Photon CNOT with Kerr Nonlinearity

The Controlled-NOT can be implemented using a Kerr medium:

|0= |H Polarization

|1= |V Qubits

R is a /2 polarization rotation,

followed by a polarization dependent

phase shift .

Cavity QED

Two Roads to

Optical Quantum Computing

I. Enhance Nonlinear Interaction with a Cavity or EIT — Kimble, Walther, Lukin, et al.

II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Franson, et al.

Linear Optical Quantum Computing

Linear Optics can be Used to Construct 2 X CSIGN = CNOT Gate and a Quantum Computer:

Milburn

Franson JD, Donegan MM, Fitch MJ, et al.

PRL 89 (13): Art. No. 137901 SEP 23 2002

Knill E, Laflamme R, Milburn GJ

NATURE 409 (6816): 46-52 JAN 4 2001

WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?

Photon-Photon

XOR Gate

LOQC

KLM

Cavity QED

EIT

Photon-Photon

Nonlinearity

???

Kerr Material

Projective

Measurement

Projective Measurement Yields Effective Nonlinearity!

G. G. Lapaire, P. Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314

A Revolution in Nonlinear Optics at the Few Photon Level:

No Longer Limited by the Nonlinearities We Find in Nature!

NON-Unitary Gates Effective Nonlinear Gates

Franson CNOT: Cross Kerr

KLM CSIGN: Self Kerr

H.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325

Quantum Metrology

Shot noise

Heisenberg

Sub-Shot-Noise Interferometric Measurements

With Two-Photon N00N States

A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500.

SNL

HL

AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733

a† N a N

Super-Resolution

Sub-Rayleigh

New York Times

Discovery Could Mean Faster Computer Chips

Quantum Lithography Experiment

|20>+|02>

|10>+|01>

Quantum Imaging: Super-Resolution

N=1 (classical)

N=5 (N00N)

Quantum Metrology: Super-Sensitivity

N=1 (classical)

N=5 (N00N)

dPN/d

Shotnoise

Limit:

1 = 1/√N

Heisenberg

Limit:

N = 1/N

dP1/d

Showdown at High-N00N!

How do we make High-N00N!?

|N,0 + |0,N

With a large cross-Kerr nonlinearity!* H = a†a b†b

|1

|0

|N

|N,0 + |0,N

|0

This is not practical! —

need = p but = 10–22 !

*C Gerry, and RA Campos, Phys. Rev. A64, 063814 (2001).

FIRST LINEAR-OPTICS BASED HIGH-N00N GENERATOR PROPOSAL

Success probability approximately 5% for 4-photon output.

Scheme conditions on the detection

of one photon at each detector

mode a

e.g.

component of

light from an

optical

parametric

oscillator

mode b

H. Lee, P. Kok, N. J. Cerf and J. P. Dowling, PRA 65, 030101 (2002).

Implemented in Experiments!

Mitchell,…,Steinberg

Nature (13 MAY)

Toronto

Walther,…,Zeilinger

Nature (13 MAY)Vienna

2004

3, 4-photon

Super-

resolution

only

Nagata,…,Takeuchi,

Science (04 MAY)

Hokkaido & Bristol

2007

4-photon

Super-sensitivity

&

Super-resolution

1990’s

2-photon

N00N State Experiments

Rarity, (1990)

Ou, et al. (1990)

Shih (1990)

Kuzmich (1998)

Shih (2001)

6-photon

Super-resolution

Only!

Resch,…,White

PRL (2007)

Queensland

Noise

Target

Nonclassical

Light

Source

Delay

Line

Detection

Quantum LIDAR

“DARPA Eyes Quantum Mechanics for Sensor Applications”

— Jane’s Defence Weekly

Winning

LSU Proposal

INPUT

inverse problem solver

“find

min( )“

forward problem solver

N: photon

number

loss A

loss B

FEEDBACK LOOP:

Genetic Algorithm

OUTPUT

Loss in Quantum Sensors

SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008

Lost photons

La

N00N

Detector

Lb

Lost photons

Generator

Visibility:

Sensitivity:

N00N 3dB Loss ---

N00N No

Loss —

SNL---

HL—

11/27/2014

22

Super-Lossitivity

Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008

N=1 (classical)

N=5 (N00N)

3dB Loss, Visibility & Slope — Super Beer’s Law!

Loss in Quantum Sensors

S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008

Lost photons

La

N00N

Detector

Lb

Lost photons

Generator

A

B

Gremlin

Q: Why do N00N States Do Poorly in the Presence of Loss?

A: Single Photon Loss = Complete “Which Path” Information!

Towards A Realistic Quantum Sensor

S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008

Lost photons

La

M&M

Detector

Lb

Lost photons

Generator

Try other detection scheme and states!

M&M state:

N00N Visibility

M&M Visibility

M&M’ Adds Decoy Photons

0.3

0.05

Towards A Realistic Quantum Sensor

S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008

Lost photons

La

M&M

Detector

Lb

Lost photons

Generator

M&M state:

N00N State ---

M&M State —

A Few

Photons

Lost

Does Not

Give

Complete

“Which Path”

N00N SNL ---

M&M SNL ---

M&M HL —

M&M HL —

Optimization of Quantum Interferometric Metrological Sensors In the

Presence of Photon Loss

PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009

Tae-Woo Lee, Sean D. Huver, Hwang Lee, Lev Kaplan, Steven B. McCracken, Changjun Min, Dmitry B. Uskov, Christoph F. Wildfeuer, Georgios Veronis, Jonathan P. Dowling

We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number.

Lossy State Comparison

PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009

Here we take the optimal state, outputted by the code, at each loss level and project it on to one of three know states, NOON,M&M, and “Spin” Coherent.

The conclusion from this plot is that the optimal states found by the computer code are N00N states for very low loss, M&M states for intermediate loss, and “spin” coherent states for high loss.

Super-Resolution at the Shot-Noise Limit with Coherent States

and Photon-Number-Resolving Detectors

J. Opt. Soc. Am. B/Vol. 27, No. 6/June 2010

Y. Gao, C.F. Wildfeuer, P.M. Anisimov, H. Lee, J.P. Dowling

We show that coherent light coupled with photon number resolving detectors — implementing parity detection — produces super-resolution much below the Rayleigh diffraction limit, with sensitivity at the shot-noise limit.

Quantum

Classical

Parity

Detector!

Quantum Metrology with Two-Mode Squeezed Vacuum:

Parity Detection Beats the Heisenberg Limit

PRL 104, 103602 (2010)

PM Anisimov, GM Raterman, A Chiruvelli, WN Plick, SD Huver, H Lee, JP Dowling

We show that super-resolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves <n> times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/<n>.

SNL

HL

TMSV

& QCRB

HofL

Nonlinear Optics vs. Projective Measurements

Quantum Imaging vs. Precision Measurements

Showdown at High N00N!

Mitigating Photon Loss

6. Super Resolution with Classical Light

7. Super-Duper Sensitivity Beats Heisenberg!