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ℏω/2≈1.66×10−24 J≈10.3 μeV\hbar\omega/2 \approx 1.66\times10^{-24}\ \mathrm{J} \approx 10.3\ \mu\mathrm{eV}

Why this formula appears here

Putting numbers to the swing keeps it honest rather than decorative. Take ω\omega/2π\pi = 5\ GHz\mathrm{GHz} and g/2π\pi = 10\ MHz\mathrm{MHz} , both squarely inside the range of qubit and resonator frequencies and coupling strengths reported across circuit quantum electrodynamics architectures, which span a few gigahertz in frequency and from a fraction of a megahertz up to several hundred megahertz in coupling depending on the regime [ 12 ] . The swap time is t∗t^\ast = π\pi/(2g) = 1/(4×\times10\ MHz\mathrm{MHz}) = 25.0\ ns\mathrm{ns} , and the ledger’s swing at that instant is ℏ\hbarω\omega/2 ≈\approx 1.66×\times10^{-24}\ J\mathrm{J} ≈\approx 10.3\ μ\mueV\mathrm{eV} — an exact analytic evaluation under the stated…

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ω\omega

Symbol omega

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μ\mu

Symbol mu

mu is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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ℏω/2≈1.66×10−24 J≈10.3 μeV\hbar\omega/2 \approx 1.66\times10^{-24}\ \mathrm{J} \approx 10.3\ \mu\mathrm{eV}

Equation 105 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation gives an approximation: it relates the quantities while allowing an approximation.

Putting numbers to the swing keeps it honest rather than decorative. Take ω\omega/2π\pi = 5\ GHz\mathrm{GHz} and g/2π\pi = 10\ MHz\mathrm{MHz} , both squarely inside the range of qubit and resonator frequencies and coupling strengths reported across circuit quantum electrodynamics architectures, which span a few gigahertz in frequency and from a fraction of a megahertz up to several hundred megahertz in coupling depending on the regime [ 12 ] . The swap time is t∗t^\ast = π\pi/(2g) = 1/(4×\times10\ MHz\mathrm{MHz}) = 25.0\ ns\mathrm{ns} , and the ledger’s swing at that instant is ℏ\hbarω\omega/2 ≈\approx 1.66×\times10^{-24}\ J\mathrm{J} ≈\approx 10.3\ μ\mueV\mathrm{eV} — an exact analytic evaluation under the stated…

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