The speed of light is the cosmic speed limit, according to physicists’ best understanding: No information can be carried at a greater rate, no matter what method is used. But an analogous speed limit seems to exist within materials, where the interactions between particles are typically very short-range and motion is far slower than light-speed. A new set of experiments and simulations by Marc Cheneau and colleagues have identified this maximum velocity, which has implications for quantum entanglement and quantum computations.
In non-relativistic systems, where particle speeds are much less than the speed of light, interactions still occur very quickly, and they often involve lots of particles. As a result, measuring the speed of interactions within materials has been difficult. The theoretical speed limit is set by the Lieb-Robinson bound, which describes how a change in one part of a system propagates through the rest of the material. In this new study, the Lieb-Robinson bound was quantified experimentally for the first time, using a real quantum gas.
Within a lattice (such as a crystalline solid), a particle primarily interacts with its nearest neighbors. For example, the spin of an electron in a magnetically susceptible material depends mainly on the orientation of the spins of its neighbors on each side. Flipping one electron’s spin will affect the electrons nearest to it.
But the effect also propagates throughout the rest of the material — other spins may themselves flip, or experience a change in energy resulting from the original electron’s behavior. These longer-range interactions can be swamped out by extraneous effects, like lattice vibrations. But it’s possible to register them in very cold systems, as lattice vibrations die out near absolute zero.
In the experiment described in Nature, the researchers begin with a simple one-dimensional quantum gas consisting of atoms in an optical lattice. This type of trap is made by crossing laser beams so that they interfere and create a standing-wave pattern; by adjusting the power output of the lasers, the trap can be made deeper or shallower. Optical lattices are much simpler than crystal lattices, as the atoms are not involved in chemical bonding.
By rapidly increasing the depth of the optical lattice, the researchers create what is known as aquenched system. You can think of this as analogous to plunging a hot forged piece of metal into water to cool it quickly. Before the change, the atoms are in equilibrium; after the change, they are highly excited.
As in many other strongly interacting systems, these excitations take the form of quasiparticles that can travel through the lattice. Neighboring quasiparticles begin with their quantum states entangled, but propagate rapidly in opposite directions down the lattice. As in all entangled systems, the states of the quasiparticles remain correlated even as the separation between them grows. By measuring the distance between the excitations as a function of time, the real velocity of the quasiparticles’ propagation can be measured. As measured, it is more than twice the speed of sound in the system.
The specific lattice strengths used in the experiment make it difficult to do direct comparisons to theory, so the researchers were only able to use a first-principles numerical model (as opposed to a detailed theoretical calculation). To phrase it another way, the velocity they measured cannot currently be derived directly from fundamental quantum physics.
It’s difficult to generalize these results as well. Systems with other physical properties will have different maximum speeds, just as light moves at different speeds depending on the medium; the researchers found things changed even within a simple one-dimensional lattice whenever they varied the interaction strength between the atoms.
However, showing that excitations must have a consistent maximum speed is a groundbreaking result. As with relativity, this speed limit creates a type of “light cone” that separates regions where interactions can occur and where they are forbidden. This has profound implications for the study of quantum entanglement, and thus most forms of quantum computing.

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