Conservation laws govern the behavior of physical systems across both classical and quantum scales. However, experimental verification of these conservation laws at the quantum level, particularly for complex properties such as orbital angular momentum, has remained limited until recently. This gap has raised important questions about whether the same symmetry-driven classical symmetry-based constraints also hold in the inherently probabilistic and non-deterministic domain of quantum mechanics.
Image Credit: ezphoto/Shutterstock.com
A recent study by researchers from Tampere University, in collaboration with teams from India and Germany, provides the first experimental confirmation of orbital angular momentum conservation in single-photon interactions, extending the validity of conservation laws to fundamental quantum scales. The study was published in Physical Review Letters on 20 May 2025.1
Why Conservation Laws Matter
Conservation laws represent invariant quantities arising from fundamental symmetries in physical systems, as formalized by Noether’s theorem (linking continuous symmetries to conserved quantities).
In classical physics, where observables possess definite values at all times, these laws apply deterministically to individual events, enabling precise predictions of system behavior. For instance, the conservation of angular momentum in a closed system reflects its rotational symmetry and remains constant across interactions, ensuring dynamic consistency throughout the system’s evolution.
In quantum physics, conservation laws operate within a probabilistic framework, where physical observables remain indeterminate until a measurement collapses the system into a defined state.
Although such laws are typically expressed through expectation values across ensembles, their strict enforcement becomes evident in individual measurement events. For example, in a singlet state comprising two spin-½ particles with zero total spin, the spin components along any axis are undefined before observation. However, once measured, the outcomes always yield equal and opposite values, thereby confirming the conservation of angular momentum in each instance.
Violation of these laws at the quantum level would challenge the foundational symmetries of quantum field theory, leading to inconsistencies in quantum state predictions. This could disrupt technologies relying on quantum coherence, such as quantum computing and quantum communication, necessitating a fundamental reevaluation of the theoretical frameworks governing quantum interactions and information dynamics.2,3
Overview of the Study
The study published in Physical Review Letters experimentally investigated the conservation of orbital angular momentum (OAM) at the single-photon level using a cascaded spontaneous parametric down-conversion (SPDC) setup. This setup generated single photons with well-defined OAM using a nonlinear crystal, which subsequently served as inputs for a second nonlinear interaction that produced photon pairs. This enabled tracking of OAM transfer and its conservation through successive quantum processes.
The theoretical framework supporting the experiment is based on a time-dependent Hamiltonian that incorporates the second-order nonlinear susceptibility χ(2)(z) and quantized electric field operators.
This Hamiltonian describes the interaction between the pump, signal, and idler photons within the nonlinear medium, with each field represented by Laguerre-Gaussian modes characterized by radial (p) and azimuthal (l) indices.
The azimuthal index corresponds to the quantized orbital angular momentum carried by the photons, and the interaction strength depends on the spatial overlap integral Λ{p_j}{l_j} of these modes. This overlap enforces the selection rule lp=ls+li, ensuring that the total orbital angular momentum is conserved during the spontaneous parametric down-conversion process. This selection rule emerges from the cylindrical rotational symmetry inherent in the nonlinear optical medium, which dictates that the total orbital angular momentum before and after the interaction must remain invariant. Consequently, the conservation of orbital angular momentum is not merely an empirical observation but a direct consequence of the fundamental symmetries encoded in the system’s Hamiltonian.
The researchers validated this theoretical prediction by measuring the OAM correlations of photon pairs with spatial light modulators and single-photon detectors, thereby demonstrating conservation of OAM in each photon-pair generation at the single-photon quantum level. 4
Key Findings and Implications
The study confirmed OAM conservation with high precision across various experimental configurations. When pump photons carried zero OAM, the resulting photon pairs exhibited complementary OAM values summing to zero. For pump photons with ℓ = −1, the generated pairs displayed combinations of ℓ = 0 and ℓ = −1, or ℓ = −1 and ℓ = 0. Similarly, pump photons with ℓ = +2 produced photon pairs with ℓ = +1 values, consistently preserving total OAM.
In addition, no significant differences were observed between experiments using single-photon pumps and classical laser sources, with correlation coefficients exceeding 99%, demonstrating that conservation laws apply equivalently whether the driving field contains individual photons or many photons.
These findings reinforce quantum field theory by confirming that fundamental conservation laws hold in single-photon nonlinear interactions, thus supporting the underlying symmetry principles at the quantum scale. This confirmation is significant for quantum computing and communication, as the ability to control entangled photons carrying conserved OAM enables high-dimensional quantum encoding, which increases information capacity, enhances security in quantum key distribution, and allows for more complex quantum logic operations.
Furthermore, this novel experimental approach facilitates the scalable generation of multipartite entangled states in spatial modes, advancing the development of quantum networks and precision quantum sensing technologies.4
Methodological Insights
The researchers employed superconducting nanowire single-photon detectors with an efficiency of 80% and dark count rates below 100 Hz, which enabled the detection of extremely rare photon conversion events. Since only one in every billion pump photons underwent successful down-conversion, measurement times extended up to 168 hours to acquire complete correlation matrices.
In addition, spatial light modulators were used to impose precise OAM states on photons through phase-only modulation with spiral phase patterns, maximizing transmission efficiency while maintaining mode purity.
The researchers ensured the reliability of this method by a heralded photon detection scheme that confirmed the presence of a single photon before initiating subsequent nonlinear processes, effectively filtering out false detections and isolating genuine quantum events. In addition, the combination of highly efficient, low-noise detectors and lossless OAM state control provided accurate tracking of angular momentum conservation at the single-photon level.4
Future Directions
The study has resolved longstanding uncertainties concerning the conservation of OAM in quantum optical processes under single-photon excitation. Previous investigations have mainly utilized classical or weak coherent light sources, where conservation laws hold statistically rather than deterministically due to photon-number fluctuations. In addition, some SPDC experiments occasionally indicated potential violations of OAM conservation, raising questions about angular momentum behavior at the quantum scale.
This study eliminates such ambiguity by demonstrating that OAM conservation holds strictly even when a single photon is used as the pump, thereby closing a critical gap in experimental quantum optics and reinforcing the symmetry principles underlying quantum field theory.
This is expected to drive significant progress in quantum information science and photonic quantum technologies. For example, the controlled generation of entangled photon pairs with conserved OAM can facilitate high-dimensional quantum states, increasing information density in quantum communication and enhancing photonic quantum computing. Furthermore, the cascaded SPDC approach offers a practical route for generating multipartite entanglement across spatial degrees of freedom, enabling scalable quantum network architectures.
Despite these advancements, the researchers acknowledge several limitations in their current setup, including low photon conversion rates associated with bulk nonlinear crystals and imperfections in the heralded photon source due to super-Poissonian statistics.
To overcome these challenges, researchers plan to focus on employing higher-nonlinearity materials, improving photon detection efficiency, and integrating advanced mode-sorting techniques to enhance OAM resolution. These refinements will expand the accessible state space and support more complex quantum experiments involving higher-order spatial modes and multiple entangled degrees of freedom.1,4
References and Further Reading
- Fickler, R. (2025). Researchers confirm fundamental conservation laws at the quantum level. Tampere Universities. https://www.tuni.fi/en/news/researchers-confirm-fundamental-conservation-laws-quantum-level
- Aharonov, Y., Popescu, S., & Rohrlich, D. (2023). Conservation laws and the foundations of quantum mechanics. Proceedings of the National Academy of Sciences, 120(41), e2220810120. https://doi.org/10.1073/pnas.2220810120
- Paul, H. (2010). Conservation laws - Introduction to Quantum Theory. Cambridge University Press EBooks, 124–129. https://doi.org/10.1017/cbo9780511755644.008
- Kopf, L., Barros, R., Prabhakar, S., Giese, E., & Fickler, R. (2025). Conservation of Angular Momentum on a Single-Photon Level. Physical Review Letters, 134(20). https://doi.org/10.1103/physrevlett.134.203601
Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.