arc.calculations_atom_single.OpticalLattice1D.BlochWavefunction#

OpticalLattice1D.BlochWavefunction(trapPotentialDepth, quasimomentum, blochBandIndex)[source]#

Bloch wavefunction as a function of 1D coordinate.

Paraeters:

trapPotentialDepth (float):: (in units of recoil energy OpticalLattice1D.getRecoilEnergy)
quasimomentum (float):: (in units of 2 pi / OpticalLattice1D.trapWavenegth; note that reciprocal lattice momentum in this units is 2, and that full range of quasimomentum is from -1 to +1)

Returns: Bloch wavefunction as a function of coordinate (see call example below)

Example

Returns Bloch wavefunction. Use as following:

trapPotentialDepth = 40  # units of recoil energy
quasimomentum = 0
blochBandIndex = 0  # Bloch band lowest in energy is 0
wf = lattice.BlochWavefunction(trapPotentialDepth,
                               quasimomentum,
                               blochBandIndex)
wf(x)  # returns complex number corresponding to value of Bloch
       # wavefunction at point x (cooridnate given in units of
       # 1/k where k = 2 \pi / trapWavenegth )
       # by default k=1, so one full wavelength is 2\pi