A new approach has been developed to calculate transition rates, fundamental to quantum optics and chemistry, by first defining the possible range of responses over various interactions rather than specifying one upfront. This reverses conventional calculations; it determines if desired control is achievable given specific parameters before calculating rate changes. Applying this approach to energy transfer demonstrates continuous reversal of response for fixed interactions by tuning cavity frequency.

Researchers have devised a new method for predicting how easily physical processes, such as energy transfer or chemical reactions, can be influenced by first considering all *possible* outcomes rather than predefining specific conditions; this approach determines if desired control is achievable before detailed calculations begin. This reverses conventional methods which require specifying interactions upfront and instead establishes boundaries for potential rate changes given certain parameters.

Researchers have developed a new method for predicting how easily physical processes, such as energy transfer or chemical reactions, can be influenced by first considering all *possible* outcomes rather than predefining specific conditions; this approach determines if desired control is achievable before detailed calculations begin.

This reverses conventional methods which require specifying interactions upfront and instead establishes boundaries for potential rate changes given certain parameters. Traditionally, calculating these rates, using what’s known as Fermi’s Golden Rule, is like following a recipe: you need to know every ingredient (interaction) beforehand to predict the outcome. However, understanding the full ‘interaction space’, akin to adjusting knobs on a machine representing all possible influences, reveals limits of predictability. The team demonstrated that tuning cavity detuning, similar to fine-tuning a radio signal, can continuously reverse energy transfer responses even with fixed interactions.

Reversible Energy Transfer Governed by Interaction Strength and Cavity Detuning

Continuous reversal of energy transfer rates, switching from enhancement to suppression, was demonstrated for fixed interactions, exceeding previous limitations where single interactions yielded static responses. Framing Fermi’s Golden Rule calculations as quadratic forms dependent on interactions allowed researchers to derive rigorous boundaries for rate modulation within an ‘interaction space,’ representing all possible influencing factors simultaneously. These bounds reveal that both interaction strength *and* external parameters like cavity detuning jointly determine whether rate control is achievable, offering unprecedented insight into manipulating quantum processes beyond pre-defined conditions and establishing limits to predictability in weakly coupled transitions.

Enhancement and suppression were observed at every tested cavity frequency; specifically, modulation ranged from -15.7% to +23.0% across the examined detuning intervals using an operator basis encompassing linear and nonlinear coordinate dependencies. At a normalised cavity frequency of 0.8, modulations between −8.4% and +16.6% occurred, shifting to −12.1% to +12.8% at 1.0, and finally reaching −15.2% to +13.7% at 1.2, demonstrating that even fixed interactions can switch behaviour with changing conditions.

Predicting Quantum Transition Rates With Incomplete System Information

Predicting how easily quantum processes occur is important across physics and chemistry, governing everything from light emission to chemical reactions; this work highlights a persistent challenge: conventional calculations using established methods like Fermi’s golden rule demand complete knowledge before you begin. The traditional approach feels akin to building with Lego bricks only after meticulously cataloguing every single piece, it works well when knowing the desired outcome but struggles with open exploration. Acknowledging fully predicting quantum behaviour remains computationally intensive, requiring detailed prior knowledge which limits exploratory work, the research offers a valuable alternative.

The University of Tokyo scientists established predictable boundaries for controlling quantum processes by shifting focus from specifying interactions to defining achievable responses within a given parameter range, a fundamental change in approach compared with traditional calculations reliant on complete prior knowledge. Formulating transition rates as mathematical expressions dependent on interactions, similar to quadratic forms, allowed derivation of rigorous limits on how much these rates can be altered without upfront knowledge of all influencing factors.

This method demonstrated continuous control over energy transfer via cavity tuning even when individual interactions remained fixed, surpassing limitations where static responses were previously observed.

This research established boundaries for controlling quantum transition rates, processes like energy and charge transfer, without needing complete knowledge of all influencing factors. The scientists formulated these rates using mathematical expressions that allowed them to predict how much rate modulation is possible within defined parameters, offering an alternative to calculations requiring fully specified interactions.

Applying their method to energy transfer between molecules and vibrations coupled with an optical cavity revealed continuous control over enhancement or suppression of the process through adjustments in cavity detuning; one interaction shifted from +7.38% enhancement to -7.48% suppression at specific frequencies. This approach may be applicable to a range of other golden-rule processes as well.

👉 More information
🗞 Bounds on Attainable Rate Modulation in Fermi’s Golden Rule
✍️ Kaisei Ohata, Jun-Yu Dong, Yasutaka Kitahama, Akihito Ishizaki and Keisuke Goda (The University of Tokyo)
🧠 ArXiv: https://arxiv.org/abs/2610.29404

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