LABORATOIRE DE PHYSIQUE ET MODELISATION DES MILIEUX CONDENSES

Topological phases, both single-particle and many-body, are often formulated through momentum-space invariants, many of which rely on the presence of a spectral gap. However, disorder and gapless spectra can make these conventional approaches difficult to apply. The spectral localizer provides an alternative real-space framework for defining and characterizing topology in such settings. By combining the Hamiltonian with position operators, it constructs a pseudospectrum that can identify topologically protected states while simultaneously providing a measure of their spectral stability. The spectral localizer has been successfully applied to a variety of single-particle systems, including disordered and gapless systems. In this seminar, I will present recent work extending the spectral localizer to many-body systems. Our construction provides a general pseudospectral framework for identifying topologically protected states throughout the many-body spectrum. We have used this framework to identify candidates for quantum many-body scarring in both an interacting chiral bosonic chain and the PXP model, demonstrating that the approach is not tied to a particular microscopic mechanism for scarring. The many-body spectral localizer thus provides new insight into the structure and stability of these anomalous ETH-violating states, while offering a quantitative measure of their stability. Finally, I will discuss the implications of this framework for quantum error-correcting codes constructed from quantum many-body scar subspaces.

Geometric excitations provide a new way of probing the internal structure of fractional quantum Hall (FQH) states beyond their more familiar topological properties. In this talk, we will focus on a particular class of such excitations, known as graviton modes, and ask how their physics changes when we move from Landau levels to fractional Chern insulators (FCIs).

We will start with a brief introduction to the basic concepts and formalisms used to describe FQH states, with an emphasis on the guiding center degree of freedom and its connection to quantum geometry. This will provide the background for understanding the microscopic origin of graviton modes and how they can be identified in strongly correlated topological bands. We then turn to FCIs, where an intriguing contrast can be found. Despite the absence of continuous rotational symmetry in the underlying lattice, both the FCI ground state and the graviton mode exhibit an emergent guiding center rotational symmetry. The excitation continuum, however, does not share this symmetry. This mismatch allows the graviton mode to couple much more strongly to the continuum, giving it a much shorter lifetime than in Landau levels. We will introduce a simple microscopic model that helps explain why this happens.

Finally, we will discuss how the graviton mode may be enhanced and detected experimentally in moiré materials, and what kinds of tuning strategies could make it more visible. We will also briefly discuss how this picture can be generalized beyond spin-two graviton modes to geometric excitations with higher spins and what exciting physics can be expected there.

High-fidelity QND qubit measurements are a cornerstone of quantum error correction schemes. In state-of-the-art superconducting quantum processors, this is achieved by combining dispersive readout with low-noise microwave measurement chains based on parametric amplifiers. However, to protect the qubits from unwanted backaction, typical systems require multiple stages of bulky magnetic circulators, a major roadblock toward scaling this approach to thousands or millions of qubits. Here I will discuss various efforts toward building amplifiers which embed directionality, and their applications to qubit measurements. In particular, I will focus on the experimental demonstration of high-fidelity, multiplexed, QND qubit measurements with a circulator-free readout chain, achieving all the requirements for scalability.