OSCAR Reports

an SFB/TR 185 magazine

Second Funding Period, Issue 3

Author: Prof. Dr. James Anglin

**Deterministic spin-photon entanglement from a trapped ion in a fiber Fabry–Perot cavity**

Pascal Kobel, Moritz Breyer and Michael Köhl

Quantum Information **7**, 6 (2021)

Quantum computers in the modern sense were first conceived in the age of the Internet, and so it has been a goal from the beginning of quantum information science not only to process quantum information locally, but to distribute it coherently between spatially separated processing centers. Achieving this goal seems likely to require two kinds of carriers for quantum information: atoms, with their nonlinear interactions, for local processing, and photons, with their speed and coherence, for transmission between nodes. Since the whole advantage of quantum information rests on quantum entanglement, the first challenge in developing quantum network nodes is learning to entangle photons and atomic degrees of freedom, such as spin, in a reliable way. Our OSCAR colleagues in Project A2 have recently recorded a significant advance.

An effective quantum network node would let light traveling through an optical fibre interact strongly with an atom trapped in an optical cavity. The simple realization of this setup in Project A2 is to hollow out the ends of two optical fibres and coat them to make them reflective, so that the cavity is literally just the space between the ends of the fibres. Simple quantum nodes of this kind have been built before, but our OSCAR colleagues are the first to demonstrate entanglement of matter and light in this kind of node. The polarisation of a photon emitted into the fibre has been entangled with the spin of a trapped Ytterbium ion, and the entanglement verified, with a fidelity around 90%.

The procedure is to excite the Ytterbium atom with a laser and then let the decisive step of producing entanglement be performed by spontaneous emission. The spin-1 Ytterbium ion has degenerate ground states distinguished by spin; angular momentum conservation ensures that the result of decay is a superposition of anti-correlated ion spin and photon circular polarisation — an entangled state. The emitted photon is allowed to fly 1.5 meters down the fibre before its polarisation is measured (destructively) by detecting the photon as it exits on one side or the other of a beam-splitter. Since spontaneous emission is a random process which may also emit photons in modes that do not couple into the fibre, often no photons are there to detect; but then one can simply re-excite the ion and try again. If a photon is detected, however, the ion’s spin can be measured to high accuracy within a fraction of a millisecond by applying a laser pulse to transfer one of the two spin states into a flourescent bright state and seeing whether the ion is glowing or not.

On any one run, this procedure measures only correlation between spin and polarisation. Precisely which superpositions of spin and polarisation states are distinguished, however, can be controlled by rotating either or both before measuring. Measuring with different rotations allows tomographic determination of the precise quantum state, confirming entanglement with high fidelity.

**Competing magnetic orders in a bilayer Hubbard model with ultracold atoms**

Marcell Gall, Nicola Wurz, Jens Samland, Chun Fai Chan and Michael Köhl

Nature **589**, 40 (2021)

The long-promised power of quantum simulation to reveal the mysteries of quantum many-body physics is beginning to be realized at last. Ultracold fermions in optical lattices have been shown to exhibit non-trivial phase transitions predicted for condensed matter systems in two dimensions. Our OSCAR colleagues in Project B4 have now taken the first step into three dimensions, by realizing a “sandwich” of two two-dimensional lattices directly on top of each other, so that fermions in both lattices interact with each other.

Adding just one more layer does not really approach three-dimensional physics, but it significantly expands the range of two-dimensional effects to be seen. In particular, where different kinds of magnetic-like ordering have been seen in single layer lattices, with the bilayer two qualitatively different kinds of magnetic ordering can be seen to compete. The competition can be examined in detail by tuning the system to favor either form of ordering over the other to any degree.

The ultracold Fermi gas in a deep enough optical lattice potential realizes the theoretical Hubbard model, which is often used as a starting point for understanding non-Fermi-liquid behavior such as high-temperature superconductivity. In the single-band Hubbard limit the fermions occupy only the ground states of each individual potential well in the lattice, and travel between sites by tunneling. By tuning the optical lattices, the tunneling rates can be tuned; in the bilayer system the in-plane and between-plane tunneling rates can be different.

Stronger in-plane or between-plane tunneling makes the system more like a pair of planes, or more like a plane of pairs. These different dynamical regimes favor different forms of ordering both within and between the two layers. In the pair-of-planes limit one can see antiferromagnetic Mott insulators in each plane, with interactions between the planes turning on as between-plane tunneling grows. In the plane-of-pairs limit, in contrast, one effectively has one two-dimensional lattice with two bands, because each lattice site has two internal states. If strong enough tunneling between each pair of sites opens a large energy gap between these two states, a band insulator can form, displacing the antiferromagnetic ordering of the pair-of-planes limit. Phenomena like these were once only accessible to theoretical speculation, but they can now be explored experimentally with high resolution. Quantum many-body simulators are here!

**Observation of a Charge-2 Photonic Weyl Point in the Infrared**

Sachin Vaidya, Jiho Noh, Alexander Cerjan, Christina Jörg, Georg von Freymann and Mikael C. Rechtsman

Physical Review Letters **125**, 253902 (2020).

Whether they are electron wave functions or electromagnetic waves, waves in spatially modulated media have non-trivial dispersion relations. Band gaps may open in the frequency spectrum — ranges of frequencies in which no normal modes exist. In three dimensions, however, a dispersion relation in a periodic medium is a set of surfaces in three-dimensional wave-vector space, stretching through the periodic Brillouin zone. If the periodic structure of the medium has — or lacks — certain discrete symmetries, frequency surfaces of different bands may intersect at special points in k-space.

As long as the essential symmetry conditions are preserved, the existence of such special intersection points can be topological, so that perturbations and distortions of the medium can only shift them around in k-space and but not separate the bands and eliminate them. Excitations near such intersection points are topologically protected: they will adiabatically adapt to irregularities in the medium, following the nearby intersection points as they shift, but not scatter and disperse into many other modes.

An kind of intersection point which is especially simple — but not easy to realize! — is the Weyl point, near which the dispersion relation resembles that of the kind of massless two-spinor field that was once considered to represent neutrinoes. An even more elusive kind of intersection is a double Weyl point, possessing twice the topological charge of a simple one. Until recently this kind of topological intersection point for electromagnetic waves, and the topologically protected modes with wave vectors near it, had only been generated at microwave frequencies, using intricate macroscopic waveguide structures. Our OSCAR colleagues in Project B6 have managed to produce a microscopically engineered photonic crystal with charge-2 Weyl points for infrared light.

These designer electromagnetic media consist of stacks of rods thinner than one micron. Unlike the tightly confining metallic waveguides available for microwaves, the material in these rods only has a refractive index of 1.52, providing only modest contrast in index from air, and thus making the periodic modulation of the medium quite weak. The important advance achieved here has been to show that topological phenomena like double Weyl points can still be seen even with such modest index contrast. This means that topologically non-trivial media can be realized for a wider range of frequencies. And it is a fine example of interplay between the topological physics of OSCAR Area C and the broad application of open-system control in OSCAR as a whole.