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from pydantic import BaseModel

from braket.ir.ahs.physical_field import PhysicalField


class DrivingField(BaseModel):
    r"""Specifies the driving field, defined by the formula

    .. math::
        H_{drive} (t) := \frac{\Omega(t)}{2} e^{i \phi(t)} \left(
            \sum_k |g_k \rangle \langle r_k| + |r_k \rangle \langle g_k|
        \right) - \Delta(t) \sum_k{| r_k \rangle \langle r_k |}

    where

        :math:`\Omega(t)` is the global Rabi frequency in rad/s,

        :math:`\phi(t)` is the global phase in rad/s,

        :math:`\Delta(t)` is the global detuning in rad/s,

        :math:`|g_k \rangle` is the ground state of atom k,

        :math:`|r_k \rangle` is the Rydberg state of atom k.

    with the sum :math:`\sum_k` taken over all target atoms.

    Attributes:
        amplitude: PhysicalField(pattern=“uniform”)
        phase: PhysicalField(pattern=“uniform”)
        detuning: PhysicalField(pattern=“uniform”)
    """

    amplitude: PhysicalField
    phase: PhysicalField
    detuning: PhysicalField