| Complex conjugate of the preceding addend |
m
| Atomic mass |
,
| Complex polarization vectors for the Raman laser fields |
,
| Complex amplitudes of Raman laser fields |
,
| Time-dependent optical frequencies for lasers A and B
|
,
| Time-dependent laser phases
,
|
,
| Laser optical phases (not time-dependent):
,
|
ϕ
| Effective Rabi phase:
|
| Effective Rabi phase for the jth Raman pulse:
|
,
| Propagation vectors of lasers A and B
|
|
, vector difference of the laser propagation vectors |
,
| Complex Rabi frequencies associated with laser fields coupling the lower ground state level to the excited state and coupling the upper ground state level to the excited state:
,
|
q
| Elementary charge; the absolute value of the electric charge of a single electron |
| Energy of the excited state in frequency units |
| Combined Raman laser detuning:
|
| Combined Raman laser detuning for the jth Raman pulse:
|
Δ | Detuning of the mean laser frequency from the difference between the perturbed ground state energy and the excited state energy:
|
,
| AC Stark shifts of the hyperfine ground states:
,
|
| Differential AC Stark shift:
|
| Effective Rabi frequency of the Raman transition:
|
| Generalized effective Rabi frequency of the jth Raman pulse:
|
| State space mixing angle parameter of the jth Raman pulse:
,
|
| Raman pulse operator unit vector for the jth Raman pulse:
|
| Raman pulse operator for the jth Raman pulse:
|
|
|
|
|
σ
| Pauli spin matrix operator:
,
,
,
|
1
| Identity operator,
|
|
|
|
|
|
|
| Temporal midpoint of jth pulse:
|
| Total integrated phase between pulses j and
:
|
| Raman pulse evolution operator for the jth pulse:
|
| Midpulse value of the generalized effective Rabi rate for the jth pulse:
|