dq.number

number(dim: int | None = None) -> Array

Returns the number operator of a bosonic mode.

It is defined by \(n = a^\dag a\), where \(a\) and \(a^\dag\) are the annihilation and creation operators, respectively.

Parameters

• dim –

  Dimension of the Hilbert space.

Returns

(array of shape (dim, dim)) Number operator.

Examples

>>> dq.number(4)
Array([[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 2.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 3.+0.j]], dtype=complex64)