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QuantumCumulants

Generalized mean-field equations in open quantum systems

https://github.com/qojulia/quantumcumulants.jl

Science Score: 77.0%

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    Found 3 DOI reference(s) in README
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    Links to: arxiv.org
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    1 of 9 committers (11.1%) from academic institutions
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    Low similarity (11.6%) to scientific vocabulary

Keywords

cumulants julia quantum quantum-mechanics quantum-optics
Last synced: 6 months ago · JSON representation ·

Repository

Generalized mean-field equations in open quantum systems

Basic Info
Statistics
  • Stars: 85
  • Watchers: 6
  • Forks: 17
  • Open Issues: 22
  • Releases: 51
Topics
cumulants julia quantum quantum-mechanics quantum-optics
Created about 6 years ago · Last pushed 7 months ago
Metadata Files
Readme License Citation

README.md

QuantumCumulants.jl

QuantumCumulants.jl is a package for the symbolic derivation of mean-field equations for quantum mechanical operators in Julia. The equations are derived using fundamental commutation relations of operators. When averaging these equations they can be automatically expanded in terms of cumulants to an arbitrary order (generalized mean-field approximation). This results in a closed set of symbolic differential equations, which can also be solved numerically.

For the application of commutation relations QuantumCumulants.jl implements a simple noncommutative algebra, where any commutation relations are applied immediately. All other symbolic simplification and rewriting is done using the Symbolics.jl package.

To obtain a numerical solution, equations derived with QuantumCumulants.jl can be converted to ModelingToolkit.jl and subsequently solved with DifferentialEquations.jl. If you want to only depend on the second quantized algebra, you can use SecondQuantizedAlgebra.jl.

Development status

CI Codecov Documentation Documentation

Note that QuantumCumulants.jl is still at an early stage of development.

Installation

The package can be installed with

julia |pkg> add QuantumCumulants

Documentation

Please refer to the latest Documentation for more details and examples.

Short example

To briefly illustrate how QuantumCumulants.jl works, here's how you can implement a first-order mean-field model of a laser with a single atom as a gain medium:

```julia using QuantumCumulants

hcav = FockSpace(:cavity) hatom = NLevelSpace(:atom, (:g,:e)) h = tensor(hcav, hatom)

@cnumbers Δ g κ γ ν @qnumbers a::Destroy(h) σ::Transition(h)

H = Δa'a + g(a'σ(:g,:e) + a*σ(:e,:g)) J = [a,σ(:g,:e),σ(:e,:g)] rates = [κ,γ,ν]

eqs = meanfield([a,σ(:g,:e),σ(:e,:e)], H, J; rates=rates, order=1)

using ModelingToolkit, OrdinaryDiffEq @named sys = ODESystem(eqs) p0 = (Δ=>0, g=>1.5, κ=>1, γ=>0.25, ν=>4) u0 = ComplexF64[1e-2, 0, 0] prob = ODEProblem(sys,u0,(0.0,50.0),p0) sol = solve(prob,RK4())

using Plots n = abs2.(sol[a]) plot(sol.t, n, xlabel="t", label="n") ```

photon-number

The above code implements the Jaynes-Cummings Hamiltonian describing an optical cavity mode that couples to a two-level atom. Additionally, the decay processes are specified. Then, mean-field equations for the average values of the operators [a,σ(:g,:e),σ(:e,:e)] are derived and expanded to first order (average values of products are factorized). For the numerical solution an ODESystem (from ModelingToolkit.jl) is created and solved with the OrdinaryDiffEq.jl library. Finally, the time dynamics of the photon number n is plotted.

Citing

If you find QuantumCumulants.jl useful in your research, please consider citing this paper:

bib @article{plankensteiner2022quantumcumulants, doi = {10.22331/q-2022-01-04-617}, url = {https://doi.org/10.22331/q-2022-01-04-617}, title = {Quantum{C}umulants.jl: {A} {J}ulia framework for generalized mean-field equations in open quantum systems}, author = {Plankensteiner, David and Hotter, Christoph and Ritsch, Helmut}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {6}, pages = {617}, month = jan, year = {2022} }

Owner

  • Name: QuantumOptics.jl
  • Login: qojulia
  • Kind: organization

Umbrella organization for Quantum Optics related projects in Julia

Citation (CITATION.bib) 

@article{plankensteiner2022quantumcumulants,
  doi = {10.22331/q-2022-01-04-617},
  url = {https://doi.org/10.22331/q-2022-01-04-617},
  title = {Quantum{C}umulants.jl: {A} {J}ulia framework for generalized mean-field equations in open quantum systems},
  author = {Plankensteiner, David and Hotter, Christoph and Ritsch, Helmut},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {617},
  month = jan,
  year = {2022}
}

GitHub Events

Total
  • Create event: 14
  • Commit comment event: 3
  • Release event: 2
  • Issues event: 13
  • Watch event: 14
  • Delete event: 2
  • Issue comment event: 66
  • Push event: 80
  • Pull request review comment event: 8
  • Pull request review event: 14
  • Pull request event: 25
  • Fork event: 5
Last Year
  • Create event: 14
  • Commit comment event: 3
  • Release event: 2
  • Issues event: 13
  • Watch event: 14
  • Delete event: 2
  • Issue comment event: 66
  • Push event: 80
  • Pull request review comment event: 8
  • Pull request review event: 14
  • Pull request event: 25
  • Fork event: 5

Committers

Last synced: almost 3 years ago

All Time
  • Total Commits: 217
  • Total Committers: 9
  • Avg Commits per committer: 24.111
  • Development Distribution Score (DDS): 0.599
Top Committers
Name Email Commits
David Plankensteiner d****r@g****t 87
David Plankensteiner d****l@u****m 56
Christoph Hotter 5****r@u****m 49
j-moser 9****r@u****m 11
Christoph Hotter c****r@g****m 7
Christoph c****r@s****t 4
Ashish Panigrahi a****i@p****m 1
Andrew Keller 6****k@u****m 1
github-actions[bot] 4****]@u****m 1
Committer Domains (Top 20 + Academic)
student.uibk.ac.at: 1 gmx.at: 1

Issues and Pull Requests

Last synced: 6 months ago

All Time
  • Total issues: 47
  • Total pull requests: 145
  • Average time to close issues: 3 months
  • Average time to close pull requests: 29 days
  • Total issue authors: 29
  • Total pull request authors: 9
  • Average comments per issue: 3.7
  • Average comments per pull request: 1.05
  • Merged pull requests: 88
  • Bot issues: 0
  • Bot pull requests: 52
Past Year
  • Issues: 15
  • Pull requests: 30
  • Average time to close issues: about 2 months
  • Average time to close pull requests: 15 days
  • Issue authors: 9
  • Pull request authors: 5
  • Average comments per issue: 2.6
  • Average comments per pull request: 1.83
  • Merged pull requests: 17
  • Bot issues: 0
  • Bot pull requests: 8
View more stats
Top Authors
Issue Authors
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  • tnadolny (5)
  • eric940109 (2)
  • benneti (2)
  • andia89 (2)
  • Papageno2 (2)
  • leonbello (2)
  • StefanoGregorio (2)
  • david-pl (2)
  • yuezhuoqingluan (2)
  • lilbearx (1)
  • piperfw (1)
  • JuliaTagBot (1)
  • HumpyBlumpy (1)
  • jkosata (1)
Pull Request Authors
  • github-actions[bot] (65)
  • ChristophHotter (36)
  • oameye (28)
  • j-moser (25)
  • david-pl (23)
  • Nico0oblr (1)
  • kllrak (1)
  • benneti (1)
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Packages

  • Total packages: 1
  • Total downloads:
    • julia 48 total
  • Total dependent packages: 0
  • Total dependent repositories: 0
  • Total versions: 51
juliahub.com: QuantumCumulants

Generalized mean-field equations in open quantum systems

  • Versions: 51
  • Dependent Packages: 0
  • Dependent Repositories: 0
  • Downloads: 48 Total
Rankings
Dependent repos count: 9.9%
Stargazers count: 12.9%
Forks count: 16.2%
Average: 19.5%
Dependent packages count: 38.9%
Last synced: 6 months ago

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