Equation 79 · Part 1 · The Entry a Relabeling Cannot Write

Symbol H_SB

H_{SB} = \hbar g\big(\sigma_+^S \sigma_-^B + \sigma_-^S \sigma_+^B\big).

H_{SB}

What this part means

$H_S$ B is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$H_S$ B is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol H_SBArticle meaning

The passage around this formula

…of freedom — with bare Hamiltonians $H_S$ = ( $\hbar$ $\omega$ /2) $\sigma_z^S$ and $H_B$ = ( $\hbar$ $\omega$ /2) $\sigma_z^B$ tuned to the same frequency $\omega$ , coupled by an excitation-conserving exchange term, $H_{SB} = \hbar g\big(\sigma_+^S \sigma_-^B + \sigma_-^S \sigma_+^B\big)$ . Because $H_{SB}$ conserves total excitation number, the dynamics starting from a single excitation stays confined to the two-dimensional subspace spanned by |e,g $\rangle$ (system excited, bath in its ground state) and |g,e $\rangle$ (the reverse). On resonance, both basis states carry the same bare energy,…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[12] Circuit Quantum Electrodynamics ↗

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