Department of Physics • University of Cologne

As first noted in [1], single-component fermionic polar molecules confined to two dimensions at sufficiently low temperatures form a topologically non-trivial px +ipy superfluid. For NaK, the critical temperature is theoretically predicted to be at around 15% of the Fermi temperature [2] and in our lab at MPQ we can currently reach temperatures as cold as 25%. It has been proposed in [3] to use blue-detuned tweezers to potentially braid Majoranas hosted at vortex cores in the px + ipy superfluid phase and also a topological qubit read-out scheme was suggested specific for ultracold molecules. Using these techniques it becomes feasible to build a prototype of a topological qubit, apply a gate operation by braiding Majoranas and measure the state of the qubit afterwards. This would directly show the non-Abelian character of the exchange of two vortices and thus provide a clear signature for the existence of Majoranas at their cores. Within this talk I will provide a detailed description of the experimental techniques necessary for such a prototypical topological qubit and outline its significance, but also the shortcomings mainly due to the finite lifetime of the superfluid making it unfortunately not immediately suitable for a full topological quantum computer. [1] N. R. Cooper and G. V. Shlyapnikov, “Stable topological superfluid phase of ultracold polar fermionic molecules,” vol. 103, no. 15, p. 155302. [2] F. Deng, X.-Y. Chen, X.-Y. Luo, W. Zhang, S. Yi, and T. Shi, “Effective potential and superfluidity of microwave-shielded polar molecules,” vol. 130, no. 18, p. 183001. [3] S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and majorana zero modes of a p x + i p y superfluid of fermionic cold atoms,” vol. 98, no. 1, p. 010506.

In physics, we are used to describing the world around us in terms of particles, or quasiparticles, with defined properties and interactions. Even when the particles have substructure, this description remains useful, for as long as the particles remain intact. Living matter consists of very complex “particles”, with internal states that are often hidden to the observer. Inferring the quantitative properties and interactions of these biological particles from targeted experiments is an exciting endeavor for physicists. I will try to demonstrate this for the case where the particles are micron-sized bacterial cells, using examples from our own and other groups work.

For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. This talk will present the state-of-the-art in pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of m-particle pseudofermion vertices. We will discuss the achievements of PFFRG in successfully predicting the spectroscopic signatures of candidate quantum spin liquid materials based on complex three-dimensional geometries with intricate Hamiltonians. These include the recently studied bi-trillium lattice S=1 K2Ni2(SO4)3 and the hyperhyperkagome lattice S=1/2 PbCuTe2O6 compounds. We also present the success of PMFRG in treating finite-temperature properties of three-dimensional systems by describing phase transitions and the associated critical exponents.

Electronic transport measurements guide the discovery and characterization of quantum materials. The Biot-Savart law dictates that the motion of electrons generates a stray magnetic field during such a transport experiment. I will show how imaging these magnetic fields with a scanning SQUID microscope allows us the determine the path that current takes through our devices. I will then discuss the application of this approach to the quantum anomalous Hall regime in magnetically doped topological insulators. Using local information about the current distribution, I will show how bulk conduction processes give rise to a quantized Hall effect. I will then describe our efforts to visualize the breakdown of the quantum anomalous Hall effect under the application of large bias currents.

Surface codes, leading candidates for quantum error correction (QEC) – and entanglement phases – a key notion for many-body quantum dynamics - have heretofore been unrelated. Here, we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (bit flips or uniaxial rotations) to (1+1)D free-fermion quantum circuits via Ising models. We show that the error-correcting phase implies a topologically nontrivial area law for the circuit's 1D long-time state |ψ∞>. Above the error threshold, we find a topologically trivial area law for incoherent errors and logarithmic entanglement in the coherent case. In establishing our results, we formulate 1D parent Hamiltonians for |ψ∞> via linking Ising models and 2D scattering networks, the latter displaying respective insulating and metallic phases and setting the 1D fermion gap and topology via their localization length and topological invariant. We expect our results to generalize to a duality between the error-correcting phase of (d+1)D topological codes and d-dimensional area laws; this can facilitate assessing code performance under various errors. The approach of combining Ising models, scattering networks, and parent Hamiltonians can be generalized to other fermionic circuits and may be of independent interest.

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