Table 1 Fidelities for Protocols I and II.

From: Protocol designs for NOON states

 

FI

FII

Pθ = π/2

 
 

r = 0

r = M

 

tμ

tν

tm

Set 1

0.986

0.997

0.974

0.0024 s

0.0065 s

6.1639 s

Set 2

0.964

0.991

0.920

0.0026 s

0.0072 s

2.8913 s

  1. Numerical calculations of the fidelities FI and FII and related times tm, tμ, and tν concerning to the parameters of Set 1 and Set 2 for M = 4 and P = 11. As the values remain almost constant for Pθ ∈ [0, π], varying less than 1%, we displayed here only the values corresponding to the phase Pθ = π/2, for fixed tν and tμ. Set 1: U/ℏ = 104.846 Hz, J/ℏ = 71.62 Hz, μ/ℏ = 30.02 Hz, and tm ~ 6.16 s. Set 2: U/ℏ = 105.60 Hz, J/ℏ = 104.95 Hz, μ/ℏ = 27.42 Hz, and tm ~ 2.89 s. The required times tm,  2tm to produce the NOON states are comparable with typical lifetimes of optical lattice traps, which can be as large as a few minutes48.
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