Quantum Interferometric Sensors 22 APR 09, NIST, Gaithersburg 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 High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008).
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QuantumInterferometric Sensors
22 APR 09, NIST, Gaithersburg
Jonathan P. Dowling
Quantum Science & Technologies Group Hearne Institute for Theoretical Physics
Department of Physics & AstronomyLouisiana State University, Baton Rouge
http://quantum.phys.lsu.edu/
JP Dowling, “Quantum Optical Metrology — The Lowdown On High-N00NStates,” Contemporary Physics 49 (2): 125-143 (2008).
Quantum Science & Technologies GroupHearne Institute for Theoretical Physics
Sanders, PRA 40, 2417 (1989).Boto,…,Dowling, PRL 85, 2733 (2000).Lee,…,Dowling, JMO 49, 2325 (2002).
The Abstract Phase-Estimation ProblemEstimate , e.g. path-length, field strength, etc. withmaximum sensitivity given samplings with a total ofN probe particles.
Phase Estimation
Prepare correlationsbetween probes
Probe-systeminteraction DetectorN single
particles
Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811
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
!H
Optical N00N states in modes a and b ,Unknown phase shift on mode b so .
Cramer-Rao bound “Heisenberg Limit!”.
Phase Estimation
mode a
mode b phaseshift
paritymeasurement
Super-sensitivity: beating the shotnoise limit.
Deposition rate:
Classical input :
N00N input :
Quantum Interferometric Lithography
source of two-modecorrelated
light
mirror
N-photonabsorbingsubstrate
phase difference along substrate
Boto, Kok, Abrams, Braunstein, Williams, and Dowling PRL 85, 2733 (2000)
Super-resolution, beating the classical diffraction limit.
!N"( ) = a
†+ e
# i"b†( )
N
a + e+ i"b( )
N
!N"( ) = cos2N " / 2( )
!N"( ) = cos2 N" / 2( )
NOONGenerator
a
b
Super-Resolution á la N00N
N=1 (classical)N=5 (N00N)
!
! /N
Super-Sensitivity!" =
!P
d P / d"
N=1 (classical)N=5 (N00N)
dP1/d!
dPN/d!
For Many SensorApplications —
LIGO, Gyro, etc., —We Don’t CARE
Which Fringe We’reOn!
The Question forUs is IF any Given
Fringe Moves, WithWhat Resolution
Can We Tell This!?
Outline
Overview — N00N states, properties,applications and experiments.