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arXiv:2602.21896

Prodiabatic Elimination: Higher Order Elimination of Fast Variables with Quantum Noise

Jan Neuser, Marcelo Janovitch, Matteo Brunelli, Patrick P. Potts

quant-phSubmitted Feb 25, 2026• Announced Feb 26, 2026• 0 citations• Revised Mar 2, 2026 (v2)
v1 · Feb 25, 2026v2 · Mar 2, 2026
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Abstract

We introduce the prodiabatic elimination, a powerful approximation technique that systematically extends the adiabatic elimination of fast degrees of freedom in light-matter coupled systems. Through a controlled expansion of operators, the prodiabatic elimination incorporates higher-order corrections and consistently includes noise contributions, leading to a significantly improved performance compared to standard adiabatic elimination. Importantly, it retains the simplicity and computational efficiency of the adiabatic elimination, making it convenient for practical applications. We demonstrate the approach on two setups: a driven dissipative Jaynes-Cummings model and a three-level system in a two-mode cavity that performs stimulated Raman adiabatic passage (STIRAP). These examples establish the prodiabatic elimination as a robust and broadly applicable tool for analyzing open quantum systems.

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We introduce the prodiabatic elimination, a powerful approximation technique that systematically extends the adiabatic elimination of fast degrees of freedom in light-matter coupled systems. Through a controlled expansion of operators, the prodiabatic elimination incorporates higher-order corrections and consistently includes noise contributions, leading to a significantly improved performance compared to standard adiabatic elimination. Importantly, it retains the simplicity and computational efficiency of the adiabatic elimination, making it convenient for practical applications. We demonstrate the approach on two setups: a driven dissipative Jaynes-Cummings model and a three-level system in a two-mode cavity that performs stimulated Raman adiabatic passage (STIRAP). These examples establish the prodiabatic elimination as a robust and broadly applicable tool for analyzing open quantum systems.
Abstract Spin-squeezed states are metrologically useful quantum states where entanglement allows for enhanced sensing with respect to the standard quantum limit. Key challenges include the efficient preparation of spin-squeezed states and the scalability of estimation precision with the number N of probes. Recently, in the context of the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity, it was shown that increasing the atom-cavity coupling can be detrimental to spin squeezing generation, an effect that is not captured by the standard second-order adiabatic cavity removal approximation. We describe adiabatic elimination techniques to derive an effective Lindblad master equation up to third order for the atomic degrees of freedom. Numerical simulations show that the spin squeezing scalability loss is correctly reproduced by the reduced open system dynamics, highlighting the role of higher-order contributions. Furthermore, we conjecture an extension beyond leading order of the adiabatic elimination technique to the case of conditional dynamics under quantum non-demolition continuous measurement and fast cavity loss, whose reliability is again confirmed by numerical simulation of the dynamics and the corresponding behavior of spin squeezing as a function of N .
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
Adiabatic elimination methods allow the reduction of the space dimension needed to describe systems whose dynamics exhibit separation of timescale. For open quantum systems, it consists in eliminating the fast part assuming it has almost instantaneously reached its steady state and obtaining an approximation of the evolution of the slow part. These methods can be applied to eliminate a linear subspace within the system Hilbert space or, alternatively, to eliminate a fast subsystem in a bipartite quantum system. In this work, we extend an adiabatic elimination method used for removing fast degrees of freedom within a system [Phys. Rev. A 101, 042102 (2020)] to eliminate a subsystem from an open bipartite quantum system. As an illustration, we apply our technique to a dispersively coupled two-qubit system and in the case of the open Rabi model.
Efficient initialization and manipulation of quantum states is important for numerous applications and it usually requires the ability to perform high fidelity and robust swapping of the populations of quantum states. Stimulated Raman adiabatic passage (STIRAP) has been known to perform efficient and robust inversion of the ground states populations of a three-level system. However, its performance is sensitive to the initial state of the system. In this contribution we demonstrate that a slight modification of STIRAP, where we introduce a non-zero single-photon detuning, allows for efficient and robust population swapping for any initial state. The results of our work could be useful for efficient and robust state preparation, dynamical decoupling and design of quantum gates in ground state qubits via two-photon interactions.
The so-called “adiabatic elimination” of fast decaying degrees of freedom in open quantum systems can be performed with a series expansion in the timescale separation. The associated computations are significantly more difficult when the remaining degrees of freedom (center manifold) follow fast unitary dynamics instead of just being slow. This paper highlights how a formulation with Sylvester’s equation and with adjoint dynamics leads to systematic, explicit expressions at high orders for settings of physical interest.
Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non-trace-preserving character of the evolution. We illustrate our results with two different systems, one where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture of the correction to the trace of the density matrix as a detailed balance equation.