[Paper Review] Macroscopic Singlet, Triplet, and Colour-Charged States of Coherent Photons

Shinichi Saito|arXiv (Cornell University)|Mar 30, 2023

Cold Atom Physics and Bose-Einstein Condensates63 references4 citations

TL;DR

This paper demonstrates that coherent photons from a laser can be engineered into macroscopic quantum states using standard optical components, realizing SU(3) and SU(4) representations through superpositions of polarization and orbital angular momentum. The key result is the experimental realization of singlet, triplet, and topologically charged states via controlled phase and amplitude manipulation, confirmed by projection measurements on the Poincaré sphere and Gell-Mann hypersphere.

ABSTRACT

A ray of photons, emitted from a laser source, is in a coherent state, where macroscopic number of photons are degenerate in the same quantum state. The coherent state has degrees of freedom for spin and orbital angular momentum, which allow an arbitrary superposition state among orthogonal states with varying their amplitudes and phases, described by a representation theory of Lie algebra and Lie group. Here, we experimentally demonstrate that we can construct generators of rotations for the quantum states of coherent photons, simply by combining widely available optical components, such as half- and quarter-wave plates and vortex lenses. We have found that a superposition state between vortexed and no-vortex states is characterised by the motion of the topological charge upon the rotation in the SU(3) states. We also realised singlet and triplet states by combining rays of photons with orthogonal polarisation states and vortexed states. This corresponds to realise an effective SU(4) state and we have confirmed the projection to an SU(2)$ imes$SU(2) state upon passing through a polariser.

Motivation & Objective

• To explore macroscopic quantum coherence in coherent photons beyond the standard SU(2) polarization model.
• To extend the quantum description of photons to include orbital angular momentum and construct higher-rank SU(N) symmetries.
• To experimentally realize and verify SU(3) and SU(4) states using accessible optical components.
• To demonstrate the projection of SU(4) states into SU(2) × SU(2) upon polarization filtering, mimicking symmetry breaking.
• To provide a tabletop platform for studying topological and collective quantum states in a classically accessible system.

Proposed method

• Utilized standard optical components—half-wave plates, quarter-wave plates, and vortex lenses—to manipulate the polarization and orbital angular momentum of a laser beam.
• Engineered superposition states between Gaussian (no-vortex) and vortex modes to realize continuous motion of topological charge in SU(3) states.
• Mapped the photonic state onto the Gell-Mann hypersphere in SO(8) using expectation values of the su(3) Lie algebra generators.
• Combined orthogonal polarization and vortex states to construct SU(4) states, with singlet and triplet configurations verified via projection through a polarizer.
• Projected the SU(4) state into SU(2) × SU(2) by selecting a single polarization, enabling independent control of spin and orbital angular momentum.
• Used CMOS imaging to observe and confirm the predicted spatial intensity patterns of the projected states, validating theoretical expectations.

Experimental results

Research questions

• RQ1 Can coherent photons be used to realize macroscopic SU(3) and SU(4) quantum states through superposition of polarization and orbital angular momentum?
• RQ2 How does the topological charge evolve under continuous phase and amplitude modulation of vortex and Gaussian modes?
• RQ3 Can singlet and triplet states be experimentally realized and distinguished via polarization projection?
• RQ4 What is the behavior of the system when SU(4) states are projected into SU(2) × SU(2) via a polarizer?
• RQ5 To what extent can standard optical components simulate complex quantum group representations in a macroscopic photonic system?

Key findings

• The authors successfully demonstrated continuous control over the topological charge of coherent photons by adjusting the amplitude and phase of superpositions between vortex and Gaussian modes.
• A superposition state between vortex and non-vortex modes exhibited continuous motion of the topological charge upon rotation, confirming its characterization in SU(3) space.
• Singlet and triplet states were experimentally realized by combining orthogonal polarization and vortex states, with observed intensity patterns matching theoretical predictions.
• After passing through a polarizer, the SU(4) state projected into an SU(2) × SU(2) state, with the spin and orbital angular momentum degrees of freedom independently controllable.
• The direction of rotation in the Poincaré sphere for orbital angular momentum was found to be opposite between rotated singlet and triplet states, confirming SU(4) symmetry behavior.
• The system served as a viable experimental platform to observe the projection from SU(4) to SU(2) × SU(2), and potentially from SU(6) to SU(2) × SU(3), via simple optical setups.