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Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states Jones etc., arXiv:0811.4350v1 (2008) 22 Feb 2009 강병기

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Contents Magnetic field sensing Many spin-entangled state: Spin NOON state Trimethylphosphite(TMP) Sensing procedure & result Sensitivity & error Discussion

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Magnetic field sensing A single spin precess in magnetic field In rotating frame where = H ext phase shift external field Many spins entangled state can acquire phase at greater rate and enhance sensitivity to the applied field

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Spin-entangled state NOON State N-fold increase in phase: e iN t Spin-flips : MSSM( )state Ex. is one of five possible Lopsidedness l : l=|p-q| for l -fold increase in phase: e il t

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Trimethylphosphite( (CH 3 O) 3 P ) Star topology distinguishable A, indistinguishable N Bs in NMR 1 central 31 P spin, 9 identical surrounding 1 H spin lopsidedness l for different gyromagnetic ratios for For 1 H nucleus, 9.4-fold phase-enhancement

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Sensing (N+1) spin-NOON state Fr0m ground state Applying Hadamard gate to A Applying C-NOT gate to B controlled by A : NOON state After some period T wait Applying C-NOT gate again

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31 P NMR spectrum of TMP red: initial 31 P NMR NOON, MSSM are generated blue: 31 P NMR after evolving for time For 400 s, ~ change for NOON state ~0.107 phase shift ~3.13 T magnetic field detuning For MSSM state MSSM ~ N C M Lopsidedness l =|9.4-2S| red: initial 31 P NMR NOON, MSSM are generated blue: 31 P NMR after evolving for time For 400 s, ~ change for NOON state ~0.107 phase shift ~3.13 T magnetic field detuning For MSSM state MSSM ~ N C M Lopsidedness l =|9.4-2S|

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31 P NMR spectrum of TMP Fourier transform with respect to T wait Freq., linewidth <1 Accuracy increase with l

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Sensitivity Comparison with optical NOON state Error: photon loss vs field noise in individual spin N dependent sensitivity limit For Standard Quantum limit: ~N 1/2 For Heisenberg limit: ~N Spin NOON limit: ~N 3/4

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Improvements by DNP or algorithmic cooling Application for Spin amplification to detect single spin discussion

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1:1 degassed solution of TMP and aceton-d 6 20 ˚C, /2 pulse length 30 s for 31 P/ 1 H Spin-spin coupling J PH : 10.5Hz 31 P: T1=5.6s, T2=2.2s 1 H: T1=12.5s, T2=2.3s C-NOT gate: 1 H /2 - spin echo length of 1/2J - 1 H /2 condition & gate operation

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