# Analog Hamiltonian Simulation

Braket.AtomArrangementItemMethod
AtomArrangementItem(coord::Tuple{Number, Number}, site_type::SiteType=filled)

Create a coordinate with filling site_type (either vacant or filled). Default filling is filled.

Braket.TimeSeriesType
TimeSeries
TimeSeries()

Struct representing a series of values in a neutral atom simulation.

Braket.ShiftingFieldType
ShiftingField <: Hamiltonian
ShiftingField(magnitude::Union{Field, TimeSeries}) -> ShiftingField

Represents a shifting field in a Hamiltonian which changes the energy of the Rydberg level in an AnalogHamiltonianSimulation.

$$$H_{sf}(t) = - \Delta(t) \sum_k h_k \left| r_k \right\rangle\left\langle r_k \right|$$$

Where $\left| r_k \right\rangle$ is the Rydberg state of atom $k$, and $h_k$ is the local pattern of unitless real numbers between 0 and 1.

The argument magnitude represents the global magnitude time series $\Delta(t)$, where time is in units of seconds and values are in units of radians / second.

Braket.DrivingFieldType
DrivingField <: Hamiltonian
DrivingField(amplitude::Union{Field, TimeSeries}, phase::Union{Field, TimeSeries}, detuning::Union{Field, TimeSeries}) -> DrivingField

Represents a driving field in a Hamiltonian which coherently transfers atoms from the ground state to the Rydberg state in an AnalogHamiltonianSimulation.

$$$H_{df}(t) = \frac{1}{2} \Omega(t)\exp(i \phi(t)) \sum_k \left( | g_k \rangle\langle r_k | + h.c.\right) - \Delta(t) \sum_k| r_k \rangle\langle r_k |$$$

Where $\left| g_k \right\rangle$ is the ground state of atom $k$ and $\left| r_k \right\rangle$ is the Rydberg state of atom $k$.

Arguments

• amplitude represents the global amplitude $\Omega(t)$. The time is in units of seconds, and the value is in radians/second.
• phase represents the global phase $\phi(t)$. The time is in units of seconds, and the value is in radians/second.
• detuning represents the global detuning $\Delta(t)$. The time is in units of seconds, and the value is in radians/second.