Transcript PPT - Louisiana State University

QUANTUM SENSORS:
WHAT’S NEW WITH N00N STATES?
Jonathan P. Dowling
Hearne Institute for Theoretical Physics
Louisiana State University
Baton Rouge, Louisiana
quantum.phys.lsu.edu
SPIE F&N 23 May 2007
Statue Antiche di Firenze
(Ancient Statues of Florence)
Mother with Children
Scully with Projector
Hearne Institute for Theoretical Physics
Quantum Science & Technologies Group
H.Cable, C.Wildfeuer, H.Lee, S.Huver, W.Plick, G.Deng, R.Glasser, S.Vinjanampathy,
K.Jacobs, D.Uskov, JP.Dowling, P.Lougovski, N.VanMeter, M.Wilde, G.Selvaraj, A.DaSilva
Not Shown: R.Beaird, M.A. Can, A.Chiruvelli, GA.Durkin, M.Erickson, L. Florescu,
M.Florescu, M.Han, KT.Kapale, SJ. Olsen, S.Thanvanthri, Z.Wu, J.Zuo
Outline
1. Quantum Computing & Projective
Measurements
2. Quantum Imaging, Metrology, & Sensing
3. Showdown at High N00N!
4. Efficient N00N-State Generating Schemes
The objective of the DARPA Quantum
Sensor Program is to develop practical
sensors operating outside of a controlled
laboratory environment that exploit nonclassical photon states (e.g. entangled,
squeezed, or cat) to surpass classical sensor
resolution.
Two Roads to Optical CNOT
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.
Cavity QED
WHY IS A KERR NONLINEARITY LIKE
A PROJECTIVE MEASUREMENT?
LOQC
KLM
Photon-Photon
XOR Gate
Cavity QED
EIT
Photon-Photon
Nonlinearity
Projective
Measurement
Kerr Material
Projective Measurement
Yields Effective “Kerr”!
GG Lapaire, P Kok,
JPD, JE 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 
KLM CSIGN Hamiltonian
Effective Unitary Gates
Franson CNOT Hamiltonian
Single-Photon Quantum
Non-Demolition
You want to know if there is a single photon in mode b,
without destroying it.
Cross-Kerr Hamiltonian: HKerr =
|in b
|1 a
 a †a b †b
Kerr medium
|1
D2
D1
“1”
Again, with  = 10–22, this is impossible.
*N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).
Linear Single-Photon
Quantum Non-Demolition
The success probability is less
than 1 (namely 1/8).
D0
|1
The input state is constrained
to be a superposition of 0, 1,
and 2 photons only.
Conditioned on a detector
coincidence in D1 and D2.
D1
D2
 /2
|1
 /2
Effective  = 1/8
 21 Orders of
Magnitude
Improvement!
|0
|in =
2
cn |n

n=0
|1
P Kok, H Lee, and JPD, PRA 66 (2003) 063814
Quantum Metrology with N00N States
H Lee, P Kok, JPD,
J Mod Opt 49,
(2002) 2325.
Shotnoise to
Heisenberg Limit
Supersensitivity!
AN Boto, DS
Abrams, CP
Williams, JPD, PRL
85 (2000) 2733
a† N a N
Superresolution!
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
|0
This is not practical! —
need  =  but  = 10–22 !
N00N States
In Chapter 11
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
Solution: Replace the Kerr with
Projective Measurements!
single photon detection
at each detector
a’
a
OPO
3a3
b
b’
b
6
4
2
0
a
a
a
a
0
2
4
6
b
b
3a1b
b
1a3b
4
a'
0
b'
0
a'
4
b'
b
Probability of success:
3
64
Best we found:
3 Cascading
16 Not
Efficient!
H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).
|10::01>
|10::01>
|20::02>
|20::02>
|30::03>
|40::04>
|30::03>
Local and Global Distinguishability
in Quantum Interferometry
GA Durkin & JPD, quant-ph/0607088
A statistical distinguishability based on relative entropy characterizes the
fitness of quantum states for phase estimation. This criterion is used to
interpolate between two regimes, of local and global phase
distinguishability.
The analysis demonstrates that, in a passive MZI, the Heisenberg limit
is the true upper limit for local phase sensitivity — and Only N00N
States Reach It!
N00N
NOON-States Violate Bell’s Inequalities
CF Wildfeuer, AP Lund and JP Dowling, quant-ph/0610180
Probabilities of correlated clicks and independent clicks
Pab (,),Pa (),Pb ()
Building a Clauser-Horne Bell inequality from the expectation
values Pab (,),Pa (),Pb ()

1 Pab (,)  Pab (,)  Pab (,)  Pab (,)  Pa ()  Pb ()  0


Shared Local Oscillator Acts
As Common Reference
Frame!
Bell
Violation!
Efficient Schemes for
Generating N00N States!
|N>|0>
Constrained
|N0::0N>
Desired
|1,1,1>
Number
Resolving
Detectors
Question: Do there exist operators “U” that produce “N00N” States Efficiently?
Answer: YES!
H Cable, R Glasser, & JPD, quant-ph/0704.0678. Linear!
N VanMeter, P Lougovski, D Uskov, JPD, quant-ph/0612154. Linear!
KT Kapale & JPD, quant-ph/0612196. (Nonlinear.)
Quantum P00Per Scooper!
H Cable, R Glasser, & JPD, quant-ph/0704.0678.
2-mode
squeezing process
Old Scheme
linear
optical
processing
χ
OPO
beam
splitter
New Scheme
How to eliminate
the “POOP”?
U(50:50)|4>|4>
0.3
|amplitude|^2
0.25
0.2
0.15
0.1
0.05
0
|0>|8>
|2>|6>
|4>|4>
Fock basis state
|6>|2>
|8>|0>
quant-ph/0608170
G. S. Agarwal, K. W. Chan,
R. W. Boyd, H. Cable
and JPD
Quantum P00Per Scoopers!
H Cable, R Glasser, & JPD, quant-ph/0704.0678.
“Pizza
Pie”
Phase
Shifter
Spinning glass wheel. Each segment a
different thickness.
N00N is in Decoherence-Free Subspace!
Feed Forward based circuit
Generates and manipulates special
cat states for conversion to N00N
states.
First theoretical scheme scalable to
many particle experiments!
Linear-Optical Quantum-State
Generation: A N00N-State Example
N VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/0612154




2
2
2
0
0.03
2
U
1
0



( 50  05 )
This counter example disproves
the N00N Conjecture: That N
Modes Required for N00N.
The upper bound on the resources scales quadratically!
Upper bound theorem:
The maximal size of a N00N
state generated in m modes via
single photon detection in m–2
modes is O(m2).
Conclusions
1. Quantum Computing & Projective
Measurements
2. Quantum Imaging & Metrology
3. Showdown at High N00N!
4. Efficient N00N-State Generating Schemes