Jonathan P. Dowling

Quantum Optical Metrology, Imaging, and

Computing

quantum.phys.lsu.edu

Hearne Institute for Theoretical PhysicsQuantum Science and Technologies Group

Louisiana State UniversityBaton Rouge, Louisiana USA

QONMIV, 26 JAN 2011, CSRC, Beijing

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Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008).

Jian Dow-Ling 建道灵“Spiritual Alliance”

Photo: 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.DaSilvaTop Inset: P.M.Anisimov, B.R.Bardhan, A.Chiruvelli, L.Florescu, M.Florescu, Y.Gao,

K.Jiang, K.T.Kapale, T.W.Lee, S.B.McCracken, C.J.Min, S.J.Olsen, R.Singh, K.P.Seshadreesan, S.Thanvanthri, G.Veronis.

Bottom Inset C. Brignac, R.Cross, B.Gard, D.J.Lum, Keith Motes, G.M.Raterman, C.Sabottke,

Hearne Institute for Theoretical PhysicsQuantum Science & Technologies Group

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Outline

1.1. Nonlinear Optics vs. Projective Nonlinear Optics vs. Projective

MeasurementsMeasurements

2.2. Quantum Imaging vs. Precision Quantum Imaging vs. Precision

MeasurementsMeasurements

3.3. Showdown at High N00N!Showdown at High N00N!

6. Super Resolution with Classical Light6. Super Resolution with Classical Light

7. Super-Duper Sensitivity Beats 7. Super-Duper Sensitivity Beats

Heisenberg! Heisenberg!

8. A Parody on Parity8. A Parody on Parity

Optical Quantum Computing:Two-Photon CNOT with Kerr

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

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).

R is a /2 polarization rotation,followed by a polarization dependentphase shift .

(3)

Rpol

PBS

z

|0= |H Polarization|1= |V Qubits

Two Roads to Optical Quantum

Computing

Cavity QED

I. Enhance Nonlinear Interaction with a Cavity or EIT — Kimble, Walther, Lukin, et al.II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Nemoto, et al.

Photon-PhotonXOR Gate

Photon-PhotonNonlinearity

Kerr Material

Cavity QEDEIT

ProjectiveMeasurement

  LOQC  KLM

WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?

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

KLM CSIGN: Self Kerr Franson CNOT: Cross Kerr

NON-Unitary Gates Effective Nonlinear Gates

A Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature! 

Projective Measurement Yields Effective Nonlinearity!

Strategies to improve sensitivity:1. Increase — sequential (multi-round) protocol.2. Probes in entangled N-party state and one trial

To make as large as possible —> N00N!

Theorem: Quantum Cramer-Rao bound

optimal POVM, optimal statistical estimator

Phase Estimation

S. L. Braunstein, C. M. Caves, and G. J. Milburn, Annals of Physics 247, page 135 (1996)V. Giovannetti, S. Lloyd, and L. Maccone, PRL 96 010401 (2006)

independent trials/shot-noise limit

ΔH

+NA0BeiNϕ0ANB

1 + cos N ϕ

2

1 + cos ϕ

2

ABϕ|N⟩A |0⟩B N Photons

N-PhotonDetector

ϕ = kxΔϕ: 1/√N →1/ΝuncorrelatedcorrelatedOscillates N times as fast!N-XOR GatesN-XOR Gatesmagic BSMACH-ZEHNDER INTERFEROMETERApply the Quantum Rosetta Stone!

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

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.

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Low N00N

2 0 + ei2ϕ 0 2

SNL

HL

N Photons

N-PhotonDetectorϕ = kx+NA0BeiNϕ0ANB

1 + cos N ϕ

2

1 + cos ϕ

2

uncorrelatedcorrelatedOscillates in REAL Space!N-XOR Gatesmagic BSFROM QUANTUM INTERFEROMETRYTO QUANTUM LITHOGRAPHY

Mirror

N

2 A

N

2 B

LithographicResist

ϕ →Νϕ λ →λ/Ν

ψ a†

a†

aa ψa† N a N

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

Super-Resolution

Sub-Rayleigh

Quantum Lithography Experiment

|20>+|02>

|10>+|01>

Low N00N

2 0 + ei2ϕ 0 2

Showdown at High-N00N!

|N,0 + |0,NHow do we make High-N00N!?

*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).

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

This is not practical! — need k =  but k = 10–22 !

|1

|N

|0

|0|N,0 + |0,N

FIRST LINEAR-OPTICS BASED HIGH-N00N GENERATOR

Success probability approximately 5% for 4-photon output.

e.g. component

oflight from an

optical parametric oscillator

Scheme conditions on the detection of one photon at each detector

mode a

mode b

H. Lee, P. Kok, N. J. Cerf and J. P. Dowling, PRA 65, 030101 (2002).J.C.F.Matthews, A.Politi, Damien Bonneau, J.L.O'Brien, arXiv:1005.5119

Towards A Realistic Quantum Sensor

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

Try other detection scheme and states!

M&M Visibility€

ψM&M

GeneratorDetector

Lost photons

Lost photons

La

Lb

€

ψ =( m,m' + m',m ) 2M&M state:

€

ψ =( 20,10 + 10,20 ) 2

€

ψ =(10,0 + 0,10 ) 2

€

ϕ

N00N Visibility

N00N: V=0.05

M&M: V=0.3

M&M’ Adds Decoy Photons

恶魔

MZI with Coherent Light

I. Coherent state inputII. Beam splitter is adjusted to balance any possible loss

? ψ

AB=αeiϕ / 2

Aα / 2

B

There’s N00N in Them There Hills —

Partner!

How can we make coherent state interferometry super-

resolving? – Gao, Anisimov, …, Dowling, JOSA B 27, A170 (2010)

Quantum Inspired Detection: 0NN0-N00N!

K.J. Resch, …, A.G. White, Physical Review Letters 98, 223601 (2007)

1 2 3 4 5 6

- 0.0002

- 0.0001

0.0001

0.0002Visibility is Very,

Very Low!

0 1 2 3 4 5 6

1

2

3

4

5

1 2 3 4 5 60

1

2

3

4

5

?

1n

Sensitivity is Much Worse Than Shot Noise!

Quantum Inspired Detection: 0NN0-N00N!

Quantum Inspired Detection: Sum O’ NooNs!

- 2 - 1 0 1 2 3

- 0.003

- 0.002

- 0.001

0.001

0.002

0.003Visibility is Very Low!

Quantum Inspired Detection: Sum O’ M&Ms!

Signal: Sensitivity:

Sub-Rayleigh & Visibility is

One!

We Hit Shot-Noise Limit!

SNL

Every Photon is Precious!

λ / n

Recall single mode phase measurement by projection synthesis discussed in – Barnett&Pegg, PRL 76, 4148 (1996).

We Have Re-Invented the Barnett & Pegg Phase Operator!

The Barnett & Pegg Phase Operator Transforms into the Parity Operator!

Parity OpB&P Op

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>.

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SNL HLTMSV& QCRB

HofL

SNL ≡1/ n       HL≡1/ n       TMSV ≡1/ n n + 2       HoϕL≡1/ n2

|TMSV>

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Parity detection in quantum optical metrologywithout number-resolving detectors

New Journal of Physics 12 (2010) 113025, 1367-2630/10/113025+12$30.00

William N Plick, Petr M Anisimov, JPD, Hwang Lee, and Girish S Agarwal

Abstract. We present a method for directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light and parity detection may be practically implemented for an arbitrary photon flux.

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Outline1.1. Nonlinear Optics vs. Projective Nonlinear Optics vs. Projective

MeasurementsMeasurements

2.2. Quantum Imaging vs. Precision Quantum Imaging vs. Precision

MeasurementsMeasurements

3.3. Showdown at High N00N!Showdown at High N00N!

6. Super Resolution with Classical Light6. Super Resolution with Classical Light

7. Super-Duper Sensitivity Beats 7. Super-Duper Sensitivity Beats

Heisenberg! Heisenberg!

8. A Parody on Parity8. A Parody on Parity

非常感谢你！