Storage and retrieval of optical skyrmions with topological characteristics

This paper reports the first experimental demonstration of storing and retrieving optical skyrmions in a cold $^{87}$Rb vapor using dual-path electromagnetically induced transparency, confirming that their topological skyrmion number remains robust against perturbations and imbalanced loss for several microseconds.

The Gist

The Big Idea: Storing "Knots" of Light

Imagine you have a piece of string. If you tie a simple knot in it, that knot has a specific "identity." No matter how much you shake the string, stretch it, or twist it slightly, the knot remains a knot. You can't untie it just by pulling on the ends; you have to cut the string to destroy the knot. In physics, this is called topology.

Now, imagine light isn't just a straight beam, but a swirling, twisting ribbon with a similar "knot" in its structure. Scientists call these optical skyrmions. They are like tiny, invisible tornadoes of light where the direction of the light waves (polarization) twists in a specific, complex pattern.

The big question this paper answers is: Can we put these "knots of light" into a storage box (a memory), wait a little while, and take them out without the knot unraveling?

The Problem: The "Jittery" Storage Box

Usually, storing light in atoms (like cold Rubidium gas) is tricky. Think of the storage process like trying to park two cars in a garage at the same time.

• Car A is a small compact car.
• Car B is a giant truck.

Because they are different sizes, they don't fit the garage perfectly. One might get parked easily, while the other gets stuck or takes longer. In the world of light, this means one part of the "knot" gets stored efficiently, while the other part gets lost or delayed.

In the past, if you tried to store complex light patterns like this, the "garage" (the memory) would mess up the balance. The light would come out looking scrambled, like a tangled headphone cord. The information would be lost to "noise" and "decoherence" (the scientific way of saying things getting messy and fuzzy).

The Experiment: The "Magic" Cold Atoms

The researchers built a special storage system using cold Rubidium atoms (imagine a cloud of atoms cooled down until they are almost frozen in time). They used a technique called EIT (Electromagnetically Induced Transparency).

Think of EIT as a "magic switch."

1. The Switch: Normally, the atoms are opaque (you can't see through them). But when you shine a specific "control laser" on them, they suddenly become transparent, letting the "signal laser" (the skyrmion) pass through and get trapped inside the atoms.
2. The Storage: The light stops moving and turns into a "spin wave" (a vibration of the atoms). It sits there, frozen in time.
3. The Retrieval: When they turn the control laser back on, the atoms release the light, and it flies out again.

The Breakthrough: The Knot Survives

The team created optical skyrmions with different "knot strengths" (called skyrmion numbers: 1, 2, or 3). They sent these through their cold-atom storage system.

Here is the magic part:
Even though the two parts of the light beam were treated differently (one part got stored better than the other, and the timing was slightly off), the knot didn't unravel.

• The Analogy: Imagine you have a complex origami crane made of two different colored papers glued together. You put it in a box, shake the box violently, and maybe the glue gets a little sticky or the paper gets a bit crumpled. When you take it out, the paper is crumpled, but the shape of the crane is still there. You can still tell it's a crane.
• The Result: The researchers stored the light for several microseconds (a millionth of a second). When they took it out, the "knot number" (the skyrmion number) was exactly the same as when they put it in.

They even tested what happens if they changed the power of the "control laser" (the magic switch) by more than 100%. The light got a bit distorted, but the fundamental knot structure remained intact.

Why Does This Matter?

This is a huge step forward for Quantum Computing and Secure Communication.

1. Super-Stable Memory: Current quantum memories are very fragile. If there is a little bit of noise or a slight error in the equipment, the information is lost. This research shows that if you encode information into these "knots of light," the information is naturally protected. The knot cannot accidentally turn into a flat piece of string (a trivial state) just because of a little bit of noise.
2. Future Tech: This suggests we can build "topologically protected" devices. Just like a knot is hard to untie, these light structures are hard to destroy. This could lead to quantum computers that don't crash as easily and communication systems that are immune to interference.

Summary

The researchers successfully proved that you can store complex, twisted structures of light in a cloud of cold atoms and retrieve them later without losing their special "knot" shape. Even when the storage process is imperfect and the light gets a little jostled, the topological "knot" survives. It's like proving that a complex knot in a rope can survive being thrown into a washing machine and still come out tied the same way. This opens the door to building much more robust and reliable quantum technologies.

Technical Summary

1. Problem Statement

Optical skyrmions are topological structures of light characterized by a robust "skyrmion number" ($N_{sky}$), which is theoretically resistant to perturbations. This makes them ideal candidates for quantum information storage, where resilience against decoherence is critical. However, a significant gap exists in the field: the preservation of these topological characteristics during coherent storage has not been experimentally demonstrated.

Current methods for storing polarization-encoded information (such as vector beams or polarization qubits) in atomic ensembles typically rely on dual-path interferometric configurations. These methods face severe limitations:

• They require highly balanced efficiency and phase stability between the two paths.
• Any imbalance in storage efficiency or phase errors (arising from different mode profiles or dispersion) severely degrades the output fidelity.
• Conventional encoding schemes (like Orbital Angular Momentum or standard polarization) lack the inherent topological protection to survive these realistic imperfections.

2. Methodology

The authors employed a dual-path Electromagnetically Induced Transparency (EIT) memory scheme using a cold $^{87}$Rb atomic vapor.

• State Preparation:

  • Optical skyrmions were generated as vectorial light fields defined by a superposition of Laguerre-Gaussian (LG) modes with different azimuthal indices ($l$) and circular polarizations ($\sigma_+$, $\sigma_-$).
  • The state $|\Psi_l\rangle = \frac{1}{\sqrt{2}} (|LG^0_0\rangle|\sigma_+\rangle + |LG^l_0\rangle|\sigma_-\rangle)$ was converted into a spatial mode and path-correlated state: $|\Psi_l\rangle = \frac{1}{\sqrt{2}} (|LG^0_0\rangle|ch1\rangle + |LG^l_0\rangle|ch2\rangle)\sigma_+$.
  • This conversion allowed the two spatial modes to be stored independently in separate paths while maintaining the entanglement in the path degree of freedom.

• Storage Mechanism:

  • The system utilized a $\Lambda$-type atomic system in cold $^{87}$Rb atoms (prepared in the $|F=1, m_F=+1\rangle$ state).
  • Probe Beam: The two spatial modes ($LG^0_0$ and $LG^l_0$) drove the $|1\rangle \to |3\rangle$ transition in their respective paths.
  • Control Beam: A single shared control beam drove the $|2\rangle \to |3\rangle$ transition in both paths simultaneously.
  • The probe pulse (0.5 $\mu$s Gaussian duration) was stored by adiabatically switching off the control beam, mapping the optical state into a collective atomic spin wave.
  • Retrieval was achieved by switching the control beam back on.

• Experimental Conditions:

  • The experiment intentionally introduced asymmetries to test robustness:
    1. Imbalanced Storage Efficiency: Due to different beam waists of the LG modes (scaling as $\sqrt{l+1}$), the optical depth (OD) and light-atom interaction strength differed between paths.
    2. Phase Differences: Caused by dispersion accumulation along the two paths.
    3. Control Beam Perturbations: The power of the control beam was varied significantly (up to 53 mW, a >100% change) to alter the medium's refractive response.

3. Key Contributions

• First Experimental Demonstration: This is the first report of storing and retrieving optical skyrmions in a quantum memory while preserving their topological characteristics.
• Topological Invariance under Non-Unitary Transformations: The study demonstrates that the skyrmion number ($N_{sky}$) remains invariant even when the storage process involves non-unitary transformations (specifically, asymmetric efficiency and phase errors) that would destroy conventional polarization or OAM encoding.
• Robustness Against Decoherence: The work proves that the topological protection of skyrmions can survive realistic memory imperfections, including spin-wave decoherence and efficiency imbalances.

4. Experimental Results

• Conservation of Skyrmion Number:

  • The team measured the topological textures of input and retrieved skyrmions for $N_{sky} = 1, 2, \text{and } 3$.
  • Despite storage times of up to 2.5 $\mu$s and significant efficiency imbalances between the two paths, the calculated $N_{sky}$ of the retrieved signal remained consistent with the input values (within experimental error margins).
  • Minor deviations were attributed to imaging system noise and atomic fluorescence, but the global topological invariant was preserved.

• Resilience to Control Beam Power Variations:

  • When the control beam power was increased by over 100%, the local ellipticity and polarization rotation of the retrieved skyrmion changed.
  • However, the topological texture remained clear and intact, and the skyrmion number remained quantized. The structure did not degenerate into a trivial configuration.

• Comparison with Vector Beams:

  • The results contrast sharply with the behavior of standard vector beams, where similar perturbations lead to a rapid decay of concurrence (a measure of entanglement/quality). The skyrmion number proved superior in maintaining information integrity.

• No Gouy Phase Accumulation:

  • Because the optical state is mapped to a stationary atomic spin wave during storage, there is no free-space propagation. Consequently, relative Gouy phase accumulation (which usually alters topological structures during propagation) is avoided, further aiding preservation.

5. Significance and Future Outlook

• Topologically Protected Photonic Technologies: This work validates that topological invariants can serve as a resource for protecting quantum information against the complex light-matter interactions and decoherence inherent in quantum memories.
• New Encoding Paradigm: It establishes that a fixed skyrmion number defines a topologically protected subspace. Quantum information can be encoded within this subspace (e.g., using superpositions of different azimuthal or radial indices while keeping the total skyrmion number fixed) to ensure robustness.
• Pathway to Quantum Networks: By combining topological photonics with quantum memory, this research paves the way for robust quantum communication networks and photonic quantum computing that are inherently resistant to noise and mode distortion.
• Future Directions: The authors suggest future work could focus on optimizing memory performance, investigating stability limits at high-power levels, and exploring superpositions of distinct skyrmion numbers for advanced qubit encoding.