Active matter is matter composed of large numbers of active constituents, each of which consumes chemical energy in order to move or to exert mechanical forces.

This type of matter is commonly found in biology: swimming bacteria or migrating cells are both classic examples. In addition, a wide range of synthetic systems, such as active colloids or robotic swarms, can also fall into this umbrella.

Active matter has therefore been the focus of much research over the past decade, unveiling many surprising theoretical features and a suggesting a plethora of applications.

Perhaps most importantly, these systems’ ability to perform work leads to sustained non-equilibrium behaviour. This is distinctly different from that of relaxing equilibrium thermodynamic systems, commonly found in other areas of physics.

The concept of entropy production is often used to quantify this difference and to calculate how much useful work can be performed. If we want to harvest and utilise this work however, we need to understand the small-scale dynamics of the system. And it turns out this is rather complicated.

One way to calculate entropy production is through field theory, the workhorse of statistical mechanics. Traditional field theories simplify the system by smoothing out details, which works well for predicting densities and correlations. However, these approximations often ignore the individual particle nature, leading to incorrect results for entropy production.

The new paper details a substantial improvement on this method. By making use of Doi-Peliti field theory, they’re able to keep track of microscopic particle dynamics, including reactions and interactions.

The approach starts from the Fokker-Planck equation and provides a systematic way to calculate entropy production from first principles. It can be extended to include interactions between particles and produces general, compact formulas that work for a wide range of systems. These formulas are practical because they can be applied to both simulations and experiments.

The authors demonstrated their method with numerous examples, including systems of Active Brownian Particles, showing its broad usefulness. The big challenge going forward though is to extend their framework to non-Markovian systems, ones where future states depend on the present as well as past states.

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Topological quantum computing is a proposed approach to building quantum computers that aims to solve one of the biggest challenges in quantum technology: error correction.

In conventional quantum systems, qubits are extremely sensitive to their environment and even tiny disturbances can cause errors. Topological quantum computing addresses this by encoding information in the global properties of a system: the topology of certain quantum states.

These systems rely on the use of non-Abelian anyons, exotic quasiparticles that can exist in two-dimensional materials under special conditions.

The main challenge faced by this approach to quantum computing is the creation and control of these quasiparticles.

One possible source of non-Abelian anyons is the fractional quantum Hall state (FQH): an exotic state of matter which can exist at very low temperatures and high magnetic fields.

These states come in two forms: even-denominator and odd-denominator. Here, we’re interested in the even-denominator states – the more interesting but less well understood of the two.

In this latest work, researchers have observed this exotic state in gallium arsenide (GaAs) two-dimensional hole systems.

Typically, FQH states are isotropic, showing no preferred direction. Here, however, the team found states that are strongly anisotropic, suggesting that the system spontaneously breaks rotational symmetry.

This means that it forms a nematic phase – similar to liquid crystals – where molecules align along a direction without forming a rigid structure.

This spontaneous symmetry breaking adds complexity to the state and can influence how quasiparticles behave, interact, and move.

The observation of the existence of spontaneous nematicity in an even-denominator fractional quantum Hall state is the first of its kind.

Although there are many questions left to be answered, the properties of this system could be hugely important for topological quantum computers as well as other novel quantum technologies.

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Entanglement is a phenomenon where two or more particles become linked in such a way that a measurement on one of the particles instantly influences the state of the other, no matter how far apart they are. It is a defining property of quantum mechanics, which is key to all quantum technologies and remains a serious challenge to realize in large systems.

However, a team of researchers from Sweden and Spain has recently made a large step forward in the field of ultrafast entanglement. Here, pairs of extreme ultraviolet pulses are used to exert quantum control on the attosecond timescale (a few quintillionths of a second).

Specifically, they studied ultrafast photoionisation. In this process, a high-energy light pulse hits an atom, ejecting an electron and leaving behind an ion.

This process can create entanglement between the electron and the ion in a controlled way. However, the entanglement is fragile and can be disrupted or transferred as the system evolves.

For instance, as the newly-created ion emits a photon to release energy, the entanglement shifts from the electron – ion pair to the electron–photon pair. This transfer process takes a considerable amount of time, on the scale of 10s of nanoseconds. This means that the ion-electron pair is macroscopically separated, on the centimetre scale.

The team found that during this transition, all three particles – electron, ion, and photon – are entangled together in a multipartite state.

They did this by using a mathematical tool called von Neumann entropy to track how much information is shared between all three particles.

Although this work was purely theoretical, they also proposed an experimental method to study entanglement transfer. The setup would use two synchronised free-electron laser pulses, with attosecond precision, to measure the electron’s energy and to detect if a photon was emitted. By measuring both particles in coincidence, entanglement can be detected.

The results could be generalised to other scenarios and will help us understand how quantum information can move between different particles.  This brings us one small step closer to future technologies like quantum communication and computing.

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