Download PPT - LSU Physics & Astronomy

Quantum
Interferometric Sensors
Jonathan P. Dowling
Quantum Science & Technologies Group
Hearne Institute for Theoretical Physics
Department of Physics & Astronomy
Louisiana State University, Baton Rouge
http://quantum.phys.lsu.edu/
JP Dowling, “Quantum Optical Metrology — The Lowdown On HighN00N States,” Contemporary Physics 49 (2): 125-143 (2008).
22 APR 09, NIST, Gaithersburg
Quantum Science & Technologies Group
Hearne Institute for Theoretical Physics
K.Jacobs
H.Lee
T.Lee
G.Veronis
P.Anisimov
H.Cable
G.Durkin
M.Florescu
L.Florescu
A.Guillaume
P.Lougovski
K.Kapale
S.Thanvanthri
D.Uskov
A.Chiruvelli
A.DaSilva
Z.Deng
Y.Gao
R.Glasser
M.Han
S.Huver
B.McCracken
S.Olson
W.Plick
G.Selvaraj
S.Vinjamanpathy
Z.Wu
Quantum Control Theory
Quantum Metrology
Quantum
Imaging
Quantum
Sensing
Quantum Computing
You Are Here!
Predictions are Hard to Make —
Especially About the Future!
$
You Are Here!
$Quantum$
$Metrology$
$Quantum$
$Computing$
1995
2000
2005
2010
2015
2020 …
Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs and
Ultrastable Gyroscopes
Properties of N00N states
 Path-entangled state
. High-N00N state if N > 2.
 Super-Sensitivity – improving SNR for detecting small phase
(path-length) shifts . Attains Heisenberg limit
.
 Super-Resolution – effective photon wavelength = /N.
Schrödinger cat
defined by relative
photon number
N00N
state
Sanders, PRA 40, 2417 (1989).
Boto,…,Dowling, PRL 85, 2733 (2000).
Lee,…,Dowling, JMO 49, 2325 (2002).
Schrödinger cat
defined by relative
optical phase
Phase Estimation
The Abstract Phase-Estimation Problem
Estimate , e.g. path-length, field strength, etc. with
maximum sensitivity given samplings with a total of
N probe particles.
N single
particles
Prepare
correlations
between
probes
Probe-system
interaction
Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811
Detector
Phase Estimation
Theorem: Quantum Cramer-Rao bound
optimal POVM, optimal statistical estimator
independent trials/shot-noise limit
Strategies to improve sensitivity:
1. Increase
— sequential (multi-round) protocol.
2. Probes in entangled N-party state and one trial
To make Ĥ as large as possible —> N00N!
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)
Phase Estimation
Optical N00N states in modes a and b
Unknown phase shift
on mode b so
Cramer-Rao bound
mode b
.
“Heisenberg Limit!”.
phase
shift
mode a
Super-sensitivity:
beating the shotnoise limit.
parity
measurement
,
Quantum Interferometric Lithography
mirror
source of
two-mode
correlated
light
a
N-photon
NOON
Generator
absorbing
substrate
b
phase difference along substrate
Deposition rate:    
N
â
†
i
 e b̂
†
 â  e b̂
N
i
N
Classical input :  N    cos2 N  / 2 
N00N input :
 N    cos 2 N / 2 
Super-resolution, beating the classical diffraction limit.
Boto, Kok, Abrams, Braunstein, Williams, and Dowling PRL 85, 2733 (2000)
Super-Resolution á la N00N
 /N

N=1 (classical)
N=5 (N00N)

 
P̂
d P̂ / d

dP1 /d
Super-Sensitivity
N=1 (classical)
N=5 (N00N)
dPN /d
For Many Sensor
Applications —
LIGO, Gyro, etc., —
We Don’t CARE
Which Fringe We’re
On!
The Question for
Us is IF any Given
Fringe Moves, With
What Resolution
Can We Tell This!?
Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs and
Ultrastable Gyroscopes
Road to
EntangledParticle
Interferometry:
Early Example of
Remote
Entanglement
Generation by
Erasure of
Which-Path
Information
Followed by
Detection!
N00N & Linear Optical Quantum Computing
For proposals* to exploit a non-linear photon-photon interaction
e.g. cross-Kerr interaction Ĥ   â †âb̂ †b̂ ,
the required optical non-linearity not readily accessible.
Nature 409,
page 46,
(2001).
*C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001).
WHEN IS A KERR NONLINEARITY LIKE
A PROJECTIVE MEASUREMENT?
Linear Opt
KLM/Franson
Photon-Photon
XOR Gate
Cavity QED
Kimble
Photon-Photon
Nonlinearity
Projective
Measurement
Kerr Material
Projective Measurement
Yields Effective Kerr!
G. G. Lapaire, Pieter Kok,
JPD, J. E. Sipe, PRA 68
(2003) 042314
We are no longer limited by the nonlinearities we find in Nature!
NON-Unitary Gates 
KLM CSIGN Hamiltonian
Effective Unitary Gates
Franson CNOT Hamiltonian
High NOON States
How do we make: |N,0
+ |0,N
With a large Kerr non-linearity*:
|1
|0
|N
|0
But this is not practical…need  = 1!
*C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001).
Measurement-Induced Nonlinearities
G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314
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!
SuperQuantumPhaseRealisticallyExtractedálaPhotons!
1990
2-photon
Rarity, (1990)
Ou, et al. (1990)
Shih, Alley (1990)
….
6-photon
Super-Resolution
Resch,…,White
PRL (2007)
Queensland
Mitchell,…,Steinberg
Nature (13 MAY)
Toronto
2004
3, 4-photon
Superresolution
2007
4-photon
Super-sensitivity
&
Super-resolution
Walther,…,Zeilinger
Nature (13 MAY)
Vienna
Nagata,…,Takeuchi,
Science (04 MAY)
Hokkaido & Bristol
Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs With Orbital
Angular Momentum Beams of Light
N00N
Yes, Jeff and
Anton, N00N
States Are Really
Entangled!
Physical Review A 76, 063808 (2007)




2
2
2
0
0.03
( 50  05 )
2
U
1
0



Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs With Orbital
Angular Momentum Beams of Light
Who in Their Right Mind Would Think Quantum
States Could be Used in Remote Sensing!?
“DARPA Eyes Quantum
Mechanics for Sensor
Applications”
— Jane’s Defence Weekly
Winning
LSU Proposal
Loss
Target
Entangled
Light
Source
Delay
Line
Detection
Loss in Quantum Sensors
SD Huver, CF Wildfeuer, JP Dowling, PRA 063828 (2008).
La

N00N

Detector
Generator

Lb
Visibility:
  ( 10,0  0,10 )
Lost
photons
2

Lost
photons
Sensitivity:   ( 10,0  0,10 )
2
N00N 3dB
Loss ---


N00N No
Loss —
SNL--5/24/2017
34
HL—
Super-Lossitivity
 
P̂
d P̂ / d
dPN /d
Gilbert, Hamrick, Weinstein,
JOSA B, 25 (8): 1336-1340
AUG 2008

e
L
e
NL
N=1 (classical)
N=5 (N00N)
dP1 /d
3dB Loss, Visibility & Slope — Super Beer’s Law!
Loss in Quantum Sensors
S. Huver, C. F. Wildfeuer, J.P. Dowling, PRA 063828 (2008).
A
N00N

Lost
photons
La

Detector
B
Generator
Lb

Lost
photons

Gremlin
Q: Why do N00N States “Suck” in the Presence of Loss?
A: Single Photon Loss = Complete “Which Path” Information!
N
A
0
B
e
iN
0
A
N
B
0
A
N 1 B
Towards A Realistic Quantum Sensor
Try other detection scheme and states!
M&M
La


Detector
Generator
M&M state:
  ( m,m'  m',m )
M&M Visibility
  ( 20,10  10,20 )

Lb
Lost
photons
2
N00N Visibility
  ( 10,0  0,10 )
2

0.3
Lost
photons

0.05
2
M&M’ Adds Decoy Photons
Mitigating Loss in Quantum Sensors
Try other detection scheme and states!
M&M
La


Detector
Generator
M&M state:

  ( m,m'  m',m )

Lost
photons
Lb
2
Lost
photons
N00N State --M&M State —
N00N SNL --M&M SNL --M&M HL —
M&M HL —
A Few
Photons
Lost
Does Not
Give
Complete
“Which Path”
Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs and
Ultrastable Gyroscopes
Sagnac Effect in Gyroscopy
Sagnac effect is used to measure rotation rates using interference
Atom interferometers are in principle more sensitive that light-based ones.
A
Sagnac  4
v
mc 2 /  ~ 1010
Orbital Angular Momentum of Light
1. Wavefront contains
azimuthal
phase singularities.
l
2. Each photon carries
l
of orbital angular momentum.
i
a
l

e
a l





[1] K.T. Kapale and J.P. Dowling, PRL 95, 173601 (2005).
[2] N. Gonzalez et. al, Opt. Exp. 14, 9093 (2006)
2
STIRAP* Makes BEC Vortex Superpositions
   il ikz
  ( ,  , z,t )  a  0 (t )   e e ; c (t )   0 (t )
 w
14 2 43
LG l ( ,  )
0
|l |
Counterintuitive
c
pulse sequence
*Stimulated Rapid Adiabatic
Passage



Mexican Hat Trap with
Thomas-Fermi Wave function
General state of the BEC at time ‘t’
r (t)  (t)g (r )  (t) (r )   (t) (r )
g (r )  LG00 (,);  (r )  LG02 (,  )
Measure of vortex transfer

F(t) |  (t) |2  |  (t) |2  |  (t) |2


[3] S. Thanvanthri, K. T. Kapale and J.P. Dowling, PRA 77, 053825 (2008)
Sagnac effect in vortex BEC superpositions
For a vortex superposition rotating at angular velocity
the vortex interference pattern rotates by an angle
iSagnac
r (t, )  (e
 Sagnac
r
r
iSagnac
  (r )  e
  (r )) / 2

4 R m 
 N(t)

h
2
Sagnac
,
Detection using Phase Contrast Imaging
Advantage: Non destructive detection, increased
phase accumulation with time.
SNR  Sagnac / noise
noise  1 / Nsc
Sensitivity
min ~ 1.25  105 rads–1Hz –1/2
State of the art
min ~ 1010 rads–1 Hz –1/2
Stability?
Noise from Atomic drift:
4  2 m
Sagnac (,t)  N(t)

h
  1.5 R
 R
  0.5 R



  Sagnac(1.5 R ,t)  Sagnac(0.5 R ,t)

Over 8 hours accumulation   0.2 deg/ hr
Current atom gyros, over 4 hours,
  68 deg/ hr
D. S. Durfee, Y. K. Shaham
 and M. A. Kasevich, PRL 97, 240801 (2006).
• An ultra-stable, compact atom
gyroscope.
• Better imaging techniques directly
improve sensitivity.
• Atom drift can further be controlled
using trap geometry.
“Quantum Metrology has Rejuvenated My Career!”
— Carlton M. Caves (Oct 07)
You Are Here!
Outline
 Overview — N00N states, properties,
applications and experiments.
 Fully scalable N00N-state generators — from
linear-optical quantum computing.
 Characterizing and engineering N00N states
 What’s New with N00N?
 Coherent Manipulation of BECs and
Ultrastable Gyroscopes