AtomicDensityMatrix`
AtomicDensityMatrix`

# BranchingRatio

BranchingRatio[label]

is a parameter for AtomicState that specifies the branching ratio for radiative decay to the state with label label.

BranchingRatio[label][state]

returns the branching ratio for the AtomicState state to the state with label label, or BranchingRatio[StateLabel[state],label] if it is not specified.

# Details and Options

• The branching ratio refers to the fraction atoms that spontaneously decay from a particular -state into another -state. This parameter is used by the OpticalRepopulation function to calculate transfer rates due to spontaneous decay. The fraction of atoms transferred to various hyperfine and Zeeman sublevels is automatically taken into account by OpticalRepopulation.
• If the NaturalWidth of state is zero, any branching ratio from that state is taken to be zero.
• The branching ratio from a state to itself is taken to be zero.
• BranchingRatio can also be called with an AtomicState as its first argument: BranchingRatio[state2][state1]. This gives the same result as BranchingRatio[StateLabel[state2]][state1] unless the branching ratio from state2 to state1 has been defined to be nonzero or if state1 and state2 have the same parity, in which case the branching ratio is taken to be zero.

# Examples

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## Basic Examples(1)

Define an atomic system with a branching ratio from state 2 to state 1:

The branching ratio of each state in the system to state 1:

## Applications(1)

Define an atomic system with three states:

The repopulation matrix for spontaneous decay:

## Properties & Relations(2)

Here, the branching ratio of state 1 to the state with label 2 is undefined:

If the natural width of state 1 is defined to be zero, all branching ratios from that state are taken to be zero:

Call BranchingRatio with state specifications for the initial and final states:

If the branching ratio from state 2 to state 1 is specified to be nonzero, then the branching ratio from state 1 to state 2 is taken to be zero:

Likewise, if the two states are specified to have the same parity, the branching ratio is taken to be zero: