quantum metrology gets real - maynooth university · quantum metrology konrad banaszek. faculty of...
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Quantum metrology
Konrad BanaszekFaculty of Physics, University of Warsaw, Poland
gets real
All-Ireland Conferenceon Quantum Technologies
Maynooth UniversityI June 2016
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Phase measurement
N photons
photons
photons
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Estimation procedure
Actual value
Measurement result
Estimate
Example: around operating point:
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Fisher information
Cramér-Rao bound:for unbiased estimators
Shot noise limit: for independently used photons
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Two-photon interferometry
&
Coincidence between ports:
Double count on one port:
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Two photons sent one-by-one(shot noise limit):
ExperimentJ. G. Rarity et al., Phys. Rev. Lett. 65, 1348 (1990)
Two-photon interference:
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General picture
Dete
ctio
n
For any measurement
where Quantum Fisher information reads
Prep
arat
ion
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Heisenberg limit
– photon number uncertainty in the sensing arm– precision of phase estimation
0 N
N photons
Maximum possibledefines the Heisenberg limit:
N independently usedphotons (shot noise limit):
J. J. Bollinger et al., Phys. Rev. A 54, R4649(R) (1996)J. P. Dowling, Phys. Rev. A 57, 4736 (1998)
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N00N state
Prep
arat
ion
One photon lost:
More photons…
No photon lost:
M.A. Rubin and S. Kaushik, Phys. Rev. A 75, 053805 (2007)G. Gilbert, M. Hamrick, and Y.S. Weinstein, J. Opt. Soc. Am. B 25, 1336 (2008)
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Numerical optimisationOne-arm losses Two-arm losses
Optimal
Chopped n00n
N00N state
U. Dorner, R. Demkowicz-Dobrzański et al.,Phys. Rev. Lett. 102, 040403 (2009)
R. Demkowicz-Dobrzański, U. Dorner et al.,Phys. Rev. A 80, 013825 (2009)
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Two-photon experiment
Component weights
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Phase uncertainty
Optimal 2-NOON Shot noise
M. Kacprowicz et al., Nature Photon. 4, 357 (2010)
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Scaling
Phas
e un
cert
aint
ySample transmission
100% •
shot noise
ultimate quantum limit
K.Banaszek, R. Demkowicz-Dobrzański, and I. Walmsley,Nature Photon. 3, 673 (2009)
80% •60% • 90% •
Number of photons (probes) N
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General picture
Actual value
R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, Nature Commun. 3, 1063 (2012)
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Two-arm losses
Prep
arat
ion
For a quantum state with average photon number
*Assuming no external phase reference is available:M. Jarzyna and R. Demkowicz-Dobrzański, Phys. Rev. A 85, 011801(R) (2012)
Shot noise limit Ultimate quantum limit
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Shot noise revisited
–
Stro
ngla
ser
beam
sph
oton
s
C. M. Caves, Phys. Rev. D 23, 1693 (1981)
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Gravitational wave detectionJ. Abadie et al. (The LIGO Scientific Collaboration), Nature Phys. 7, 962 (2011)
GEO600
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Noise analysisR. Demkowicz-Dobrzański, K. Banaszek, and R. Schnabel, Phys. Rev. A 88, 041802(R) (2013)
Shot noiselimit
10dB squeezing(implemented)
16dB squeezingand ultimatebound
When most power comesfrom the laser beam
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Optimality of squeezed statesR. Demkowicz-Dobrzański, K. Banaszek, and R. Schnabel, Phys. Rev. A 88, 041802(R) (2013)
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Operating point
1
1
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Partial spectral distinguishability
shot noise limit
Fisher information
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One- and two-photon interference
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Transverse displacement
Fisher information
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Partial transverse overlap
Fisher information
Coherent superposition
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Coherent superposition
No postselection or any attempt to resolve the spectral degree of freedom inducing !!!!!
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Optimal measurement
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Projection basis
Spatial modesOptimal two-photonprojections
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Enhancement
Relative uncertainty
No spatialdisplacement
Spatial overlap optimizedfor individual operating
point
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Shot-by-shot imaging
R. Chrapkiewicz, W. Wasilewski, and K.Banaszek, Opt. Lett. 39, 5090 (2014)
M. Jachura and R. Chrapkiewicz,Opt. Lett. 40, 1540 (2015)
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Imaging experiment
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Coincidence events
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Transverse displacement
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Coincidence eventsM. Jachura et al., Nature Commun. 7, 11411 (2016)
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locallyoptimized
Relative uncertainty
spatial displacement
M. Jachura et al., Nature Commun. 7, 11411 (2016)
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2 + 1 photonsM. Jachura et al., Nature Commun. 7, 11411 (2016)
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Conclusions
• Benefit analysis of quantum metrology needsto take into account noise and imperfections
• Even in noisy scenarios quantum enhancementis possible – and worthwhile!
• (Nearly) optimal operation can be achieved with (relatively) modest means
• Applications where fixed-scale enhancementis useful / critical
• Qubits live in a vast physical space – explore!
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Acknowledgements
Uwe DornerBrian Smith
Jeff LundeenIan A. WalmsleyUniversity of Oxford
Mădălin GuţăUniversity of Nottingham
Roman SchnabelUniversität Hannover
Radosław ChrapkiewiczRafał Demkowicz-DobrzańskiMichał JachuraMarcin JarzynaJan KołodyńskiWojciech WasilewskiUniwersytet Warszawski
Marcin KacprowiczUniwersytet Mikołaja Kopernikaw Toruniu