Spin-2 BEC wavefunction#
The spin-2 BEC wavefunction class contains the wavefunction arrays plus an assortment of useful functions for manipulating and using the wavefunction.
Constructing the Wavefunction object is done through the constructor
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Represents the spin-2 BEC wavefunction. |
Here, the parameter grid is a Grid object defined prior to instantiating the Wavefunction class.
Wavefunction methods#
Initial state#
Below are the methods associated with the initial state.
Sets the components of the wavefunction according to the ground state we wish to be in. |
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Sets the wavefunction components to the specified arrays. |
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Adds noise to the specified wavefunction components using a normal distribution. |
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Applies a phase to specified components. |
The set_ground_state method is used to set the initial state to a specified ground state of the spin-2 system. It is typically the way we start shaping the condensate. The supported ground states are listed below
Ground state |
Wavefunction |
Description |
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“UN” |
\(\psi=(0, 0, 1, 0, 0)^T\) |
Uniaxial-nematic ground state. |
“BN” |
\(\psi=(1, 0, 0, 0, 1)^T/\sqrt{2}\) |
Biaxial-nematic ground state. |
“F2p” |
\(\psi=(1, 0, 0, 0, 0)^T\) |
Ferromagnetic ground state with total spin 2, pointing up. |
“F2m” |
\(\psi=(0, 0, 0, 0, 1)^T\) |
Ferromagnetic ground state with total spin 2, pointing down. |
“F1p” |
\(\psi=(0, 1, 0, 0, 0)^T\) |
Ferromagnetic ground state with total spin 1, pointing up. |
“F1m” |
\(\psi=(0, 0, 0, 1, 0)^T\) |
Ferromagnetic ground state with total spin 1, pointing down. |
“cyclic” |
\(\psi=(\sqrt{(1 + f_z) / 3}, 0, 0, \sqrt{(2 - f_z) / 3}, 0)^T\) |
Cyclic ground state where \(f_z=p+q/c_2n\). |
If more flexibility is required, the set_wavefunction method allows us to set specific components to specified arrays. The add_noise method adds noise to each grid point of the wavefunction for the specified components. The noise is drawn from a uniform distribution with the mean and standard deviation specified in the function signature. Finally, apply_phase applies a user-defined phase to the specified wavefunction components as \(\psi_m\rightarrow\psi_m e^{i\phi}\) for phase \(\phi\) and component \(m \in \{2, 1, 0 , -1, -2\}\).
Other methods#
The methods below fall under the miscellaneous category and are self-explanatory.
Fourier transforms real-space components and updates Fourier-space components. |
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Inverse Fourier transforms Fourier-space components and updates real-space components. |
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Returns an array of the total condensate density. |
Attributes#
See SpinTwoWavefunction for list of class attributes (variables).