Q-Demonstrator
Multi-mode spin-boson simulation · ²⁵Mg⁺/²⁶Mg⁺ hybrid Coulomb crystal
Configure a mixed ²⁵Mg⁺/²⁶Mg⁺ Coulomb crystal, add voltage noise on the control electrodes, choose two spin initial states, and watch the trace-distance trajectories evolve. The normal modes of the crystal are computed from first principles (Coulomb + trap potential). The noise spectral profile shapes the effective bath structure seen by the spin.
0 Presets
1 Method
2 Crystal
1 ²⁵Mg⁺ (qubit) + N ²⁶Mg⁺ (bath ions) in linear Paul trap. Axial normal modes computed from Coulomb + harmonic potential.
Lorentzian noise on electrodes: S(ω) = S₀ (Γ/2)² / ((ω−ω_c)² + (Γ/2)²). Broadband noise tends toward a more Markovian effective bath; structured narrowband spectra can introduce memory effects.
Bloch vector (b_x, b_y, b_z). A must start farther from RSS than B. Transverse components required for crossing.
STATE A · farther
STATE B · closer
3 Run
Press Run to see trace-distance trajectories.
Bloch components
Spin purity
Effective spectral density J(ω)
4 Download
Run a simulation first.
Method
Crystal solver: Equilibrium positions via damped Newton's method on the Coulomb + harmonic axial potential. Normal modes from the mass-weighted Hessian eigenvalue problem (Jacobi algorithm). Each mode's Lamb-Dicke parameter η_k is computed from the qubit ion's participation in the eigenvector.
Noise model: Lorentzian voltage noise spectral density S_V(ω) centred at ω_c with bandwidth Γ. Each normal mode k receives a damping rate γ_k = γ_base + S₀ · S_V(ω_k). Broadband noise tends toward a more Markovian effective description (modes damped roughly equally). Structured narrowband spectra selectively damp modes near ω_c and can enhance memory effects, but whether the resulting dynamics are rigorously non-Markovian depends on coupling regime and requires a proper witness (not currently computed).
Quantum trajectories: State vector |ψ⟩ in the full spin ⊗ modes Hilbert space. RK4 propagation under H, with a simplified stochastic phonon jump process (not a full MCWF unravelling — see engine comments). Multiple trajectories averaged. Active mode filtering reduces dimension automatically. Adequate for weak damping; inaccurate at strong dissipation.
Effective-J HEOM: Reduced spin-only hierarchy model with simplified one-term-per-mode decomposition. The multi-mode spectral density J_eff(ω) is constructed from the crystal modes and noise profile. Currently exploratory rather than benchmarked against established HEOM implementations.
Backend comparison caveat: The trajectory backend prepares pure spin states (Bloch vector direction, ignoring length for ‖b‖ < 1). The HEOM backend uses the full mixed-state density matrix ρ = (I + b·σ)/2. For pure initial states (‖b‖ = 1), both backends are equivalent. For mixed states, results should not be compared quantitatively between backends.
Source: js/mpemba-engine.js. All parameters covered by SHA-256 provenance hash.