QUINTO project

Fractional quantum Hall states in atom arrays

Our second approach to create a topological order in atom arrays is to focus on a different kind of topological order: fractional quantum Hall (FQH) states. These were first discovered in condensed matter. It is possible to confine electrons to move in two-dimensions only (such as in the 2D material graphene or in so-called metal-oxide-semiconductor transistors) and then put them in a strong perpendicular magnetic fields. The electrons then move in circles (so-called “cyclotron motion”), but since they are quantum objects, only some values of radius are allowed. Thus, the energy can only take certain fixed values (we call them “Landau levels”). There are however different possibilities of an electron having the same energy, because the center of the orbit can be located in different places – we say that Landau levels are “degenerate”. And when there is degeneracy, the interaction between electrons becomes very important. Without interactions, there are many possible ways of arranging electrons within a Landau level, all with the same energy. In the presence of interactions, some arrangements become preferred – and it turns out those correspond to topological orders known as the FQH states. Such systems host anyons which look like fractions of an electron – like somehow the electron split into several parts.

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#Physics #science #TopologicalOrder #Quantum #QuantumOptics #CondensedMatter #CondMat #cond_mat #QuantumHall

Mar 31, 2025 at 5:41pmWeb
Show threadQUINTO projectMar 31, 2025

Magnetic field acts completely differently on atom arrays than on electrons, as photons, unlike electrons, don’t have electric charge. But it turns out that in some circumstances (atoms with two excited states instead of one, responding to the light that is circularly polarized, i.e its electric field vector traces out a circle instead of oscillating along a line), they give rise to something similar to a Landau level – a topological energy band, a range of allowed energies which also corresponds to cyclotron motion. If this range is sufficiently narrow (a “nearly-flat band”), there is an approximate degeneracy and FQH states may occur.

We are currently working on a draft of article showing that for small enough number of atoms and excitations, the topological band becomes sufficiently flat that it can host FQH states of few excitations. For a minimal case of two excitations, we propose how these states can be created and measured. We plan to build on these ideas to increase the system size and the number of particles, to build a genuinely many-body quantum-optical version of the fractional quantum Hall effect.
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