Week 2: Project Pivots, Repository Decisions, and Exploring the Rabi Model

Week 2 has been all about making crucial project decisions and expanding our understanding of quantum models. From timeline adjustments to repository strategies, plus a deep dive into the Rabi model and its relationship to the Jaynes-Cummings model, this week laid important groundwork for the path ahead.

Key Project Decisions (June 12th Meeting)

Our Thursday meeting with Eric, Alex, Neill, and myself covered several pivotal decisions that will shape the project’s trajectory:

Timeline Extension Request

One of the most significant developments was the decision to request a timeline extension from 12 to 16 weeks. Alex will be reaching out to NumFOCUS to make this request official. This extension is particularly valuable given that I have summer schools scheduled for June 15-20 and August 18-September 5, which will impact my availability during those periods.

The extra 4 weeks will allow for:

• More thorough development and testing of the quantum systems library
• Better integration with QuTiP core
• Comprehensive documentation and examples
• Buffer time for unexpected challenges (like the JSON serialization complexities we discussed)

JSON Format: Parking the Complexity

After extensive discussion, the team decided to park the agnostic format (JSON) requirement for now. As noted in the meeting, “not everyone is convinced of the value for this” and “it is not necessary to get started.” This is actually a relief, it allows us to focus on building solid, functional quantum systems first, and we can always add serialization capabilities later if there’s demand.

This decision simplifies the immediate development path significantly and lets us concentrate on the core physics and software architecture.

Repository Strategy: Staying in QuTiP Core

Eric raised an important concern about separate repositories potentially not being maintained long term. The solution? We’ll develop directly in QuTiP core, within a new quantum_systems folder. Eric will create a development branch called dev.qsystem, and I’ll be pushing commits and PRs to this branch for testing and review.

This approach has several advantages:

• Ensures long term maintenance and integration
• Makes collaboration with the QuTiP team seamless
• Provides immediate access to QuTiP’s existing infrastructure
• Facilitates testing with the broader QuTiP ecosystem

Design Philosophy: Functions Creating Objects

The architectural direction became clearer this week. The main module will contain functions that create structured objects for quantum systems. I’ll be sharing a Jaynes-Cummings example for team review, which will serve as the template for other quantum models.

This function based approach strikes a nice balance between usability and structure, users get simple function calls, but the underlying system maintains proper object-oriented design for extensibility.

Exploring the Rabi Model: Beyond the Rotating Wave Approximation

While working on the Jaynes-Cummings implementation, I’ve been diving deep into the Rabi model, which provides fascinating insights into the fundamental atom-field interaction without approximations.

The Physics Connection

The Rabi model is essentially the “parent” of the Jaynes-Cummings model. Where JCM uses the rotating wave approximation to simplify the math, the Rabi model keeps all terms in the interaction:

Rabi Model Hamiltonian: H_{Rabi} = \omega_c a^\dagger a + \frac{\omega_a}{2} \sigma_z + g(a^\dagger + a)(\sigma_+ + \sigma_-)

Jaynes-Cummings Model (with RWA): H_{JC} = \omega_c a^\dagger a + \frac{\omega_a}{2} \sigma_z + g(a^\dagger \sigma_- + a \sigma_+)

The key difference is that the Rabi model includes the “counter-rotating” terms a^\dagger \sigma_+ and a \sigma_-, which represent processes that don’t conserve energy (creating a photon while exciting the atom, or destroying a photon while de-exciting the atom).

When Does the Difference Matter?

The rotating wave approximation is valid when g \ll \omega_c, \omega_a, meaning the coupling is much weaker than the characteristic frequencies. But in several important scenarios, the Rabi model becomes essential:

1. Strong Coupling Regime: When g approaches \omega_c or \omega_a
2. Circuit QED: Superconducting qubits in microwave cavities often reach strong coupling
3. Ultrastrong Coupling: Some systems achieve g/\omega > 0.1, where the RWA completely breaks down

Collapse Operators for the Rabi Model

For the complete open system description, the Rabi model uses the same dissipation mechanisms as JCM:

• Cavity decay: C_1 = \sqrt{\kappa (1 + n)} a
• Atomic decay: C_2 = \sqrt{\gamma} \sigma_-
• Atomic dephasing: C_3 = \sqrt{\gamma_\phi} \sigma_z

The master equation structure remains the same, but the Hamiltonian evolution includes the additional oscillating terms that can lead to richer dynamics.

Implementation Considerations

Including both Rabi and Jaynes-Cummings models in our library provides users with:

• JCM: Fast, well understood dynamics for weak coupling
• Rabi: Accurate physics for strong coupling regimes
• Educational value: Direct comparison of approximations vs exact models
• Research flexibility: Users can easily switch between models

The parameter sets are nearly identical, making it easy to implement both and let users choose based on their specific regime of interest.

Development Progress and Next Steps

This week’s practical work included:

• Setting up the development environment for working with QuTiP core
• Beginning the Jaynes-Cummings implementation that will serve as our template
• Researching the Rabi model as our second quantum system

Week 3: I am in Paris for a summer school so will not be working actively on the project.

Week 4 Goals

The coming week will focus on:

• Getting the development branch set up and testing the workflow
• Finalizing the Jaynes-Cummings implementation
• Starting the Rabi model implementation
• Creating clear documentation and examples
• Testing integration with QuTiP’s existing functionality

Reflections

This week felt like a turning point where the project crystallized from abstract planning into concrete development. The decision to park JSON serialization removes a major complexity, while the timeline extension provides breathing room for quality implementation.

The repository decision to stay within QuTiP core is particularly exciting, it means our work will have immediate access to the full QuTiP ecosystem and a clear path to long term maintenance.

Diving into the Rabi model has also been intellectually rewarding. Understanding how it relates to the Jaynes-Cummings model provides a perfect example of why having a comprehensive quantum systems library matters, researchers need easy access to both approximate and exact models depending on their specific use case.

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Next week: Branch setup, first PR submissions, and implementing the Rabi model alongside our JCM template.