There is a close theoretical connection between topological Floquet physics and cavity QED, yet this connection has not been realized experimentally due to complicated cavity QED models that often arise. We propose a simple, experimentally viable protocol to realize non-adiabatic topological photon pumping mediated by a single qubit, which we dub the anomalous Floquet photon pump. For both quantized photons and external drive, the system exhibits a non-trivial topological phase across a broad range of parameter space. Transitions out of the topological phase result from frequency-space delocalization. Finally, we argue that the protocol can be implemented in existing experiments via driven qubit non-linearities, with topological pumping witnessed in measurements of the cavity Wigner distribution functions.
There is a close theoretical connection between topological Floquet physics and cavity QED, yet this connection has not been realized experimentally due to complicated cavity QED models that often arise. We propose a simple, experimentally viable protocol to realize non-adiabatic topological photon pumping mediated by a single qubit, which we dub the anomalous Floquet photon pump. For both quantized photons and external drive, the system exhibits a non-trivial topological phase across a broad range of parameter space. Transitions out of the topological phase result from frequency-space delocalization. Finally, we argue that the protocol can be implemented in existing experiments via driven qubit non-linearities, with topological pumping witnessed in measurements of the cavity Wigner distribution functions.
Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics of Floquet engineering in its semi-classical limit. However, the mapping between these two widely different scenarios remains mysterious in many aspects. We discuss the emergence of anomalous topological phases in cavity-QED materials, and link topological phase transitions in the many-body spectrum with those in the 0- and π-gaps of Floquet quasienergies. Our results allow to establish the microscopic origin of an emergent discrete time-translation symmetry in the matter sector, and link the physics of isolated many-body systems with that of periodically driven ones. Finally, the relation between many-body and Floquet topological invariants is discussed, as well as the bulk-edge correspondence.
Topology has emerged as a central concept for classifying phases of matter. The situation is especially rich in periodically driven systems, where anomalous Floquet topological phases break the usual bulk-boundary correspondence between Chern number and edges modes of two-dimensional systems. These phases were so far realized by periodic modulation of the tunneling elements at frequencies near-resonant with respect to the system's bandwidth, a regime where Floquet heating plays a significant role in interacting systems. Here we show that such anomalous Floquet topological phases can also be realized by means of an adiabatic protocol, where the system is always in the instantaneous ground state of the cyclic path in parameter space, like in a Thouless charge pump. We experimentally realize such a state using ultracold atoms in a hexagonal lattice where we adiabatically modulate the lattice geometry, including the sublattice offset. To infer the topology, we use the micromotion area in real-space, which was recently identified as a proxy for the winding number. This way of realizing anomalous phases avoids resonant Floquet heating and imperfect loading into the target state. We demonstrate the robustness of the adiabatic construction by observing the anomalous phase even in the presence of mean-field interactions of magnitude comparable to all other energy scales. These findings are promising for engineering novel topological states in a more robust way.
Topological Floquet energy pumps, which use periodic driving to create a topologically protected quantized energy current, have been proposed and studied theoretically, but have never been observed directly. Previous work [D. M. Long et al., Phys. Rev. Lett. 128, 183602 (2022)] proposed that such a pump could be realized with a strongly driven superconducting qubit coupled to a cavity. Here, we experimentally demonstrate that the proposed hierarchy of energy scales and drive frequencies can be realized using a transmon qubit. We develop an experimental toolkit to realize the adiabatic driving field required for energy pumping using coordinated frequency modulation of the transmon and amplitude modulation of an applied resonant microwave drive. With this toolkit, we measure adiabatic evolution of the qubit under the applied field for times comparable to T1, which far exceed the bare qubit dephasing time. This result paves the way for direct experimental observation of topological energy pumping.
Periodic driving is a ubiquitous tool for controlling experimental quantum systems. When the drive fields are of comparable, incommensurate frequencies, new theoretical tools are required to treat the resulting quasiperiodic time dependence. Similarly, new and surprising phenomena of topological origin may emerge in this regime, including the quantized pumping of energy from one drive field to another. This dissertation will describe how to exploit this energy pumping to coherently translate––or boost––quantum states of a cavity in the Fock basis. This protocol enables the preparation of highly excited Fock states for use in quantum metrology––one need only boost low occupation Fock states. Energy pumping, and hence boosting, may be achieved nonadiabatically as a robust edge effect associated to an anomalous localized topological phase (ALTP) of fermions on a wire, called the quasiperiodic Floquet-Thouless energy pump (QP pump). We present a simple coupled-layer model for the QP pump, and describe the broader topological classification which characterizes its robust properties. Finally, we argue that energy pumping by the edge modes is robust to the introduction of weak interactions between fermions, making the QP pump a stable, interacting, non-equilibrium phase of matter.
The concept of multi-gap topology has recently been shown to give rise to uncharted phases beyond conventional single-gap classifications. These phases relate to band nodes with non-Abelian quaternion charges and momentum-space braiding processes characterized by new invariants such as paradigmatic Euler class, phenomena that intrinsically require at least two spatial dimensions. Extending such phases into the non-equilibrium regime is predicted to unlock even richer multi-gap topologies beyond static settings, yet their experimental realization has remained elusive due to the stringent requirements on dimensionality, symmetry, and dynamical control. Here, we theoretically demonstrate and, for the first time, experimentally realize two-dimensional (2D) Floquet non-Abelian band topology in photonic scattering networks. Within this platform, we uncover a sequence of topological phenomena unique to 2D multi-gap systems far from equilibrium, including anomalous multi-gap phases interconnected by band nodes, Floquet Euler transfer, gapped phases with anomalous Dirac string configurations, and Floquet-induced non-Abelian braiding of band nodes. In addition, we observe Floquet-periodic anomalous edge states across multiple gaps, providing experimental signatures of these sought-after 2D multi-gap Floquet topological phases. Our results establish photonic scattering networks as a practical and versatile route to non-Abelian Floquet systems, opening avenues for dynamical topological physics with braiding capability and robust photonic functionalities.
Constructing new topological materials is of vital interest for the development of robust quantum applications. However, engineering such materials often causes technological overhead, such as large magnetic fields, spin-orbit coupling, or dynamical superlattice potentials. Simplifying the experimental requirements has been addressed on a conceptual level-by proposing to combine simple lattice structures with Floquet engineering-but there has been no experimental implementation. Here, we demonstrate topological pumping in a Floquet-Bloch band using a plain sinusoidal lattice potential and two-tone driving with frequencies ω and 2ω. We adiabatically prepare a near-insulating Floquet band of ultracold fermions via a frequency chirp, which avoids gap closings en route from trivial to topological bands. Subsequently, we induce topological pumping by slowly cycling the amplitude and the phase of the 2ω drive. Our system is well described by an effective Shockley model, establishing a novel paradigm to engineer topological matter from simple underlying lattice geometries. This approach could enable the application of quantized pumping in metrology, following recent experimental advances on two-frequency driving in real materials.