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sf.math.hermite_renormalized_1leftoverMode_reorderedAB

math.hermite_renormalized_1leftoverMode_reorderedAB(B, C, cutoffs)

Renormalized multidimensional Hermite polynomial given by the “exponential” Taylor series of \(exp(C + Bx - Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\). Note the minus sign in front of A.

Calculates all possible Fock representations of mode 0, where all other modes are PNR detected. This is done by applying the recursion relation in a selective manner.

Parameters:

  • A (ndarray) – The A matrix.

  • B (ndarray) – The B vector.

  • C (ndarray) – The C scalar.

  • cutoffs (Tuple[int]) – upper boundary of photon numbers in each mode

Return type:

ndarray

Returns:

The renormalized Hermite polynomial.

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