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arXiv:2512.07045

From Quantum Chaos to Classical Chaos via Gain-Induced Measurement Dynamics in a Photon Gas

Violetta Sharoglazova, Marius Puplauskis, Lotte Hof, Jan Klaers

quant-phSubmitted Dec 7, 2025• Announced Dec 9, 2025• 0 citations
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Abstract

How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical link is provided by measurement processes. In this work, we identify gain competition in a chaotic photon gas as an operational quantum measurement that selects single motional modes from an initial superposition through stochastic, nonlinear amplification. We show that this mechanism naturally gives rise to classical chaotic behavior, most notably sensitivity to initial conditions. Our results provide a concrete physical mechanism for the quantum-classical transition in a chaotic system and demonstrate that essential aspects of quantum measurement-state projection, Born-rule-like selection, and irreversibility-can naturally emerge from intrinsic gain dynamics.

Comments
7 pages, 4 figures

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How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical link is provided by measurement processes. In this work, we identify gain competition in a chaotic photon gas as an operational quantum measurement that selects single motional modes from an initial superposition through stochastic, nonlinear amplification. We show that this mechanism naturally gives rise to classical chaotic behavior, most notably sensitivity to initial conditions. Our results provide a concrete physical mechanism for the quantum-classical transition in a chaotic system and demonstrate that essential aspects of quantum measurement-state projection, Born-rule-like selection, and irreversibility-can naturally emerge from intrinsic gain dynamics.
Quantum mechanics is the most fundamental theory describing nature, and according to the correspondence principle, classical mechanics should emerge from it. However, in areas like chaotic motion, the connection between classical and quantum descriptions is not straightforward. A key challenge is understanding how classical chaotic behaviour, especially sensitivity to initial conditions, arises from quantum mechanics. Measurement processes are expected to drive such transitions, yet they raise many unresolved questions, known collectively as the measurement problem—including whether wavefunction collapse is a real physical process. Here, we experimentally study the quantum-to-classical transition in a two-dimensional billiard system. Position-dependent gain in this system acts similarly to a measurement, reducing quantum superpositions to eigenstates. By varying the gain position, we observe sensitivity to initial conditions via mode jumps. Our experiment offers a concrete example of how measurement-like processes can yield classical chaotic behaviour in a quantum system. Unlike idealized axiomatic measurements, our process is a tangible physical phenomenon, offering new insight into the nature of quantum measurements.
Quantum mechanics is considered the most fundamental theory for describing nature. Classical mechanics is thought to arise from quantum mechanics in the limit of high quantum numbers. Unlike quantum mechanics, classical mechanics allows for chaotic motion, characterized by sensitivity to initial conditions, a feature ambiguous for translation to quantum systems. Here, we investigate the onset of classical chaos in a non-Hermitian quantum system. We study photons in a microcavity, treated as two-dimensional quantum particles moving in the plane of the resonator. By nanostructuring the resonator's mirrors, we can confine the photons in arbitrary potential landscapes, particularly billiard-like potentials. Non-resonant optical pumping inside of these potentials creates gain in the optical medium. We anticipate that introducing latter will amplify modes with maximum overlap with the gain region, introducing sensitivity to initial conditions, specifically to the pumping spot position. This investigation is expected to shed light on the quantum-to-classical transition in a chaotic system.
Using the key properties of chaos, i.e. ergodicity and exponential instability, as a resource to control classical dynamics has a long and considerable history. However, in the context of controlling "chaotic" quantum unitary dynamics, the situation is far more tenuous. The classical concepts of exponential sensitivity to trajectory initial conditions and ergodicity do not directly translate into quantum unitary evolution. Nevertheless properties inherent to quantum chaos can take on those roles: i) the dynamical sensitivity to weak perturbations, measured by the fidelity decay, serves a similar purpose as the classical sensitivity to initial conditions; and ii) paired with the fact that quantum chaotic systems are conjectured to be statistically described by random matrix theory, implies a method to translate the ergodic feature into the control of quantum dynamics. With those two properties, it can be argued that quantum chaotic dynamical systems, in principle, allow for full controllability beyond a characteristic time that scales only logarithmically with system size and ℏ−1\hbar^{-1}ℏ−1. In the spirit of classical targeting, it implies that it is possible to fine tune the immense quantum interference with weak perturbations and steer the system from any initial state into any desired target state, subject to constraints imposed by conserved quantities. In contrast, integrable dynamics possess neither ergodicity nor exponential instability, and thus the weak perturbations apparently must break the integrability for control purposes. The main ideas are illustrated with the quantum kicked rotor. The production of revivals, cat-like entangled states, and the transition from any random state to any other random state is possible as demonstrated.
This thesis makes a unique contribution to the field of quantum chaos by theoretically demonstrating the effect that measurement has on the emergence of chaos from the quantum world and demonstrating a means to control the onset of chaos in the quantum system using adaptive measurements. Here we investigate how the choice of the continuous measurement strategy for an open quantum system affects the emergence of chaos in the transition from the quantum limit to the classical limit when the system is dissipative. We consider two models in our research. The Duffing oscillator is classically chaotic and also dissipative( ie. an open quantum system), whereas the driven top is classically a closed system; adding dissipation via continuous measurement therefore changes the behaviour in from the classical limit. The first half of this thesis presents the investigation of a dissipative system whose classical limit is chaotic. We explore the emergence of chaos from the open quantum system that is continuously monitored and investigate the dependence on the choice of monitoring by changing a single parameter in a homodyne measurement scheme, effectively changing the information gained by the measurement. We show that the emergence of chaos in the regime where quantum effects are still present can be determined solely by changing the measurement parameter. This is a result of the interplay between the quantum interference effects induced by the nonlinear dynamics and the localisation and decoherence that occurs due to the measurement. We also investigate the case where the classical limit is regular for the Duffing oscillator, and demonstrate the semiclassical effect of chaos induced by the measurement back-action. A certain choice of measurement leads to a noise which drives the system to large spread in the dimensionless position enabling a non-classical transition mechanism that is classically forbidden, inducing chaos in the system. These results are verified by the numerical calculation of the maximal Lyapunov exponent in the quantum regime. The second part of this thesis investigates the possibility of controlling the degree of chaos with quantum control. We design an effective control scheme to control the degree of chaos using the measurement dependency of the state. We propose an adaptive measurement scheme which changes the homodyne measurement angle in real time depending on the direction of the state's interference fringes in phase space. This is done using the knowledge gained by the measurement signal. We show that this control scheme can enhance or suppress chaos. By enhancing the degree of chaos we are also able to push the onset of chaos further into the quantum regime than was possible before. By suppressing chaos we generate highly non-classical states and regular motion. The feasibility of experimentally realising this control technique is discussed in detail. The final section of this thesis considers a chaotic system that is not dissipative in the classical limit: the driven top. We investigate the effect that opening the quantum system to decoherence has on the degree of chaos when we continuously measure the system. We demonstrate that the presence of decoherence suppresses the chaos and alters the dynamics of the quantum system. This is seen to worsen as the strength of the measurement is increased unless a particular measurement is chosen that perfectly cancels out the decoherence resulting in the Hamiltonian evolution in addition to noise from the measurement. These results are verified by the separation time between classical and quantum dynamics.
How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics, driven by unitary evolution, is linear. The question that still remains is - what are the footprints of classical chaos in the quantum world? One can understand the quantum signatures of classical chaos by studying a quantum system whose classical analogue is chaotic. In this thesis, we use the quantum kicked top model of few qubits in the deep quantum regime to investigate signatures that can be considered as a precursor to chaos in the classical limit. In particular, we study out-of-time-ordered correlators (OTOCs) and Loschmidt echo, the two well-known dynamical diagnostics of chaos. We find vestiges of classical chaos even in such a deep quantum regime. Another arena where one can study the effects of chaos and randomness is quantum state tomography. We study quantum tomography from a continuous measurement record obtained by measuring expectation values of a set of Hermitian operators generated by a unitary evolution of an initial observable. The rate of information gain and reconstruction fidelity shows vestiges of chaos. As another contribution of this thesis, we have harnessed the power of randomness inherent in the maximally mixed state to give an efficient quantum algorithm to measure OTOCs. The protocol achieves an exponential speedup over the best known classical algorithm, provided the OTOC operator to be estimated admits an efficient gate decomposition. This protocol also helps benchmark unitary gates, which is important from the quantum computation and control perspective.
This paper proposes a novel approach to quantum measurement based on the principles of chaos theory. It leverages the sensitive dependence on initial conditions inherent in chaotic systems to predict the evolution of quantum states during measurement. The core mechanism involves mapping the quantum measurement process onto a chaotic system, analyzing the resulting probability distributions, and subsequently predicting the outcome of the quantum measurement. This method, termed "pre-reading," aims to anticipate the state of a quantum system before the actual measurement is performed. The theoretical framework presented here offers a fundamentally new perspective on quantum information processing, bridging the gap between deterministic chaos and the probabilistic nature of quantum mechanics. This work explores the potential for enhanced quantum control and information manipulation through the exploitation of chaotic dynamics. We demonstrate a conceptual framework with mathematical formulations outlining the key steps involved in this predictive quantum measurement process.