AtomicArrays.jl

AtomicArrays.jl is a Julia library designed for simulating arrays of multi-level atoms, focusing on quantum optical effects and collective phenomena in structured atomic ensembles. It supports complex atomic structures, including two-level ($|g\rangle, ; |e \rangle$) and four-level ($|j = 0, m = 0 \rangle, ; |j=1, m = -1,0,+1 \rangle$) atoms, enabling analysis of collective quantum dynamics and light-matter interactions.

Features:

• Multi-level Atomic Models: Simulate two-level and four-level atoms.

• Hamiltonian Construction: Include dipole-dipole interaction, driving fields, Zeeman terms.

• Varied Time-Evolution Methods: Perform system dynamics simulations using:

•	Master equation

•	Meanfield approximation

•	Meanfield equations with correlation corrections

• Flexible Array Geometry: Model atomic arrays with customizable geometry.

Installation

Install AtomicArrays.jl directly from GitHub using Julia’s package manager:

using Pkg
Pkg.add(url="https://github.com/venichka/AtomicArrays.jl")

Getting Started

Here’s a practical example demonstrating the simulation of dynamics for a four-level atomic array with Zeeman terms and a driving field using the master equation:

using QuantumOptics
using AtomicArrays

a = 0.6  # lattice period
positions = AtomicArrays.geometry.rectangle(a, a; Nx=2, Ny=2)  # create 2x2 array
N = length(positions)

pols = AtomicArrays.polarizations_spherical(N)
gam = [AtomicArrays.gammas(0.25)[m] for m=1:3, j=1:N]
deltas = [0.0 for i = 1:N]  # detunings

coll = AtomicArrays.FourLevelAtomCollection(positions;
    deltas = deltas,
    polarizations = pols,
    gammas = gam
) #  create atomic collection

# Define a plane wave field in +z direction:
amplitude = 0.1
k_mod = 2π
angle_k = [0.0, 0.0]  # => +z direction
polarisation = [1.0, 1.0im, 0.0]
pos_0 = [0.0, 0.0, 0.0]

field = AtomicArrays.field.EMField(amplitude, k_mod, angle_k, polarisation; position_0=pos_0)
external_drive = AtomicArrays.field.rabi(field, AtomicArrays.field.plane, coll)

# Uniform magnetic field
B_f = 0.2  # projection of B onto z axis

# Build the Hamiltonian and jump operators
H = AtomicArrays.fourlevel_quantum.Hamiltonian(coll; magnetic_field=B_f,
                external_drive=external_drive,
                dipole_dipole=true)

Γ_fl, J_ops = AtomicArrays.fourlevel_quantum.JumpOperators(coll; flatten=true)

# Master equation time evolution
b = AtomicArrays.fourlevel_quantum.basis(coll)
# initial state => all ground |0,0>
ψ0 = basisstate(b, [(i == 1) ? AtomicArrays.fourlevel_quantum.idx_e_plus : 
AtomicArrays.fourlevel_quantum.idx_g for i = 1:N])
ρ0 = dm(ψ0)
tspan = [0.0:0.1:200.0;]
t, rho_t = timeevolution.master_h(tspan, ψ0, H, J_ops; rates=Γ_fl)

This example initializes a 2x2 array of four-level atoms including Zeeman interactions and a driving field, computes the Hamiltonian, and solves the master equation.

Documentation

Detailed documentation and function references are available within the docs/ directory. To build and view the documentation locally, use the Documenter.jl package and the following guide: https://documenter.juliadocs.org/stable/man/guide/

Examples and Tutorials

Explore provided examples and notebooks in the examples/ directory:

•	Superradiant and subradiant dynamics

•	Meanfield vs. correlation-enhanced simulations

•	Effects of Zeeman terms on collective emission

Contributing

Contributions are welcome! Please open an issue or submit a pull request with enhancements, bug reports, or suggestions.

License

AtomicArrays.jl is released under the MIT License. See the LICENSE file for more details.

Acknowledgments

AtomicArrays.jl is particularly inspired by packages such as QuantumOptics.jl and CollectiveSpins.jl.