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Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states

Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states. Jones etc., arXiv:0811.4350v1 (2008). 22 Feb 2009 강병기. Contents. Magnetic field sensing Many spin-entangled state: Spin NOON state Trimethylphosphite (TMP) S ensing procedure & result Sensitivity & error

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Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states

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

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

  3. Magnetic field sensing • A single spin precess in magnetic field • In rotating frame • whered=gHext • phase shift  external field • Many spins entangled state can acquire phase at greater rate and enhance sensitivity to the applied field

  4. Spin-entangled state • NOON State • N-fold increase in phase: eiNdt • Spin-flips : MSSM( )state • Ex. is one of five possible • Lopsidedness l: l=|p-q| for • l-fold increase in phase: eildt

  5. Trimethylphosphite((CH3O)3P) • Star topology • distinguishable A, indistinguishable N Bs in NMR • 1 central 31P spin, 9 identical surrounding 1H spin • lopsidedness lg for different gyromagnetic ratios for • For 1H nucleus, 9.4-fold phase-enhancement

  6. 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 Twait • Applying C-NOT gate again

  7. 31P NMR spectrum of TMP • red: initial 31P NMR • NOON, MSSM are generated • blue: 31P NMR after evolving for time • For 400ms, ~p change for NOON state • ~0.107 p phase shift • ~3.13mT magnetic field detuning • For MSSM state • rMSSM~ NCM • Lopsidedness lg=|9.4-2S| • red: initial 31P NMR • NOON, MSSM are generated • blue: 31P NMR after evolving for time • For 400ms, ~p change for NOON state • ~0.107 p phase shift • ~3.13mT magnetic field detuning • For MSSM state • rMSSM~ NCM • Lopsidedness lg=|9.4-2S|

  8. 31P NMR spectrum of TMP • Fourier transform with respect to Twait • Freq. , linewidtha<1 • Accuracy increase with lg

  9. Sensitivity • Comparison with optical NOON state • Error: photon loss vs field noise in individual spin • N dependent sensitivity limit • For Standard Quantum limit: ~N1/2 • For Heisenberg limit: ~N • Spin NOON limit: ~N3/4

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

  11. condition & gate operation • 1:1 degassed solution of TMP and aceton-d6 • 20 ˚C, p/2 pulse length 30ms for 31P/ 1H • Spin-spin coupling JPH: 10.5Hz • 31P: T1=5.6s, T2=2.2s • 1H: T1=12.5s, T2=2.3s • C-NOT gate: • 1H p/2 - spin echo length of 1/2J - 1H p/2

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