Open Quantum Systems Driven by Chirped Pulses: Quantized versus Semiclassical Fields and the Validity of the Rotating-Wave Approximation

Abstract: Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D$_2$ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.

• The paper analyzes chirped RAP in open quantum systems, comparing quantized and semiclassical field treatments while rigorously testing the limits of the RWA.
• It employs a time-dependent variational approach with the multiple-Davydov D2 ansatz to capture quantum correlations and environmental dissipation.
• Results reveal robust inversion plateaus and provide experimental criteria for high-fidelity state preparation in photonic and solid-state quantum setups.

Analysis of Population Transfer in Open Quantum Systems Driven by Chirped Pulses

Introduction

This work investigates the population transfer induced by chirped rapid adiabatic passage (RAP) in open quantum systems by systematically comparing quantized and semiclassical field descriptions, with and without the rotating-wave approximation (RWA). Using a time-dependent variational approach (multiple-Davydov D$_2$ ansatz), the study benchmarks the Jaynes–Cummings (JC) and Rabi models in both open-system and field-quantized regimes, elucidating their domains of validity and the impact of field quantization, counter-rotating terms, phonon dissipation, and pulse parameters.

Theoretical Framework and Methodology

The study employs four models, derived from the Hamiltonians of open Rabi and JC systems, in both quantized and semiclassical frameworks. The Hamiltonians incorporate dissipative coupling to a phonon bath and driving by a time-dependent chirped Gaussian pulse. Field quantization is systematically controlled via the initial mean photon number $|\alpha|$ in the coherent state, allowing interpolation between strictly semiclassical ($|\alpha| \gg 1$) and fully quantum ($|\alpha| \sim 1$) regimes.

The explicit time-dependent variational algorithm, using the multiple Davydov D$_2$ ansatz, is deployed to solve the non-Markovian dynamics. This choice captures quantum correlations and environmental effects beyond the limitations of master equations or perturbative approaches. The chirp parameter $\varphi$ encodes the frequency sweep of the driving pulse, and pulse area $\Theta$ determines overall excitation strength.

Results: Validity of Semiclassical Approximations and RWA

Semiclassical vs. Quantized Field Description

• Convergence in High Photon Number Limit: For large $|\alpha|$ and small $\Theta$, dynamics from all four models converge, validating the semiclassical approximation in the weak-coupling, high-intensity limit. In this regime, population transfer is robust and insensitive to microscopic bath details.
• Breakdown at Low Photon Numbers: With small $|\alpha|$, the semiclassical approximation fails; quantum fluctuations and field quantization play an essential role. Numerical results confirm strong discrepancies in transient and final population probabilities between quantized and semiclassical treatments in this regime.

Rotating-Wave Approximation

• RWA Validity Boundaries: For both quantized and semiclassical cases, RWA is accurate at low pulse area or weak spin–photon coupling. As $|\alpha|$0 increases (i.e., strong coupling at the pulse center), marked deviations occur between JC and full Rabi models. This is due to the activation of excitation-number non-conserving processes, inaccessible to RWA but enabled by counter-rotating terms in the Rabi Hamiltonian.
• Transient vs. Final State Discrepancy: Despite RWA and non-RWA models yielding similar final populations for some parameter sets, the time-dependent population $|\alpha|$1 can exhibit substantial differences, especially in the presence of sizable counter-rotating interactions.

Chirp Control and Robustness of Population Transfer

Pulse Parameters and Adiabaticity

• Pulse Area and Chirp Parameter: In the low coupling regime, RAP achieves near-complete population transfer at odd-integer multiples of $|\alpha|$2 pulse area, consistent with analytic Landau-Zener predictions. Increasing the negative chirp parameter $|\alpha|$3 reduces the frequency sweep rate, enabling higher adiabatic fidelity and transition probability.
• Plateau of Robust Population Inversion: With sufficiently strong negative chirp ($|\alpha|$4), both QRM and QJC models predict a plateau of near-unity population transfer $|\alpha|$5, largely independent of pulse area, spin–phonon coupling, or detuning. This robust inversion persists even in the presence of dissipation.

Role of Phonon Dissipation and Environmental Coupling

• Insensitivity to Environmental Coupling: In the robust regime, population transfer exhibits substantial immunity to variations in spin–phonon coupling $|\alpha|$6 and detuning, confirming resilience against environmental noise and moderate parameter fluctuations.

Parametric Regimes for Experimental Realization

• System–Bath Hierarchies: The study directly maps dimensionless energy gap $|\alpha|$7 to experimental regimes, clarifying when RWA and semiclassical models remain valid (e.g., optically driven quantum dots, trapped ions, circuit QED).
• Distinguishing Experimental Outcomes: The models provide quantitative benchmarks for interpreting chirped-pulse experiments, especially in the context of solid-state emitters, vacuum Rabi experiments, and quantum simulation platforms.

Theoretical and Practical Implications

• Limits of Semiclassical and RWA Descriptions: The work rigorously delineates parameter regimes where these commonly used approximations fail, particularly at low photon numbers, strong coupling, and for time-dependent control protocols.
• Criteria for High-Fidelity State Preparation: The results establish criteria for chirp and pulse area that guarantee robust, high-fidelity population transfer, potentially simplifying calibration and error mitigation in quantum technologies.
• Benchmarks for Quantum Simulators: The models and predictions are amenable to direct experimental scrutiny in modern quantum simulators (trapped ions, superconducting circuits) due to tunability of key parameters (detuning, coupling, pulse chirp).

Future Directions

• Multimode Fields and Finite Temperature Effects: Extending the framework to genuine multimode photon fields with Gaussian spectra represents a natural progression. Incorporating finite temperature phonon baths would also render the theory quantitatively predictive for realistic solid-state and molecular platforms.
• Time-resolved and Two-Dimensional Spectroscopies: The findings prompt further exploration of RAP protocols in nonlinear and multidimensional spectroscopies of open quantum aggregates and organic semiconductors.
• Non-Equilibrium and Strong Excitation Regimes: The variational methodology could be instrumental in studying dynamical processes beyond adiabatic rapid passage, such as nonadiabatic transitions and photoinduced phase transformations.

Conclusion

This study offers a comprehensive variational analysis of chirped RAP in open quantum systems under quantized and semiclassical electromagnetic driving, establishing precise bounds for the validity of RWA and semiclassical field treatments. The rigorous comparison elucidates when quantum fluctuations and counter-rotating terms critically shape both transient and asymptotic dynamics. The identification of chirp-controlled inversion plateaus, insensitive to dissipation and drive imperfections, has significant implications for robust quantum control, state engineering in noisy environments, and interpretation of RAP-driven population dynamics in advanced quantum platforms. The results provide clear theoretical criteria and experimental benchmarks for future developments in quantum optics, quantum information processing, and condensed-matter quantum technologies.

[See (2607.00583) for full details.]