Session W15: Non-Equilibrium Phases Using Synthetic Dimensions

Bloch Oscillations Along a Synthetic Dimension of Atomic Trap States

Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and re-interpreted as lattice sites along an extra artificial dimension. We experimentally realise for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple atomic trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behaviour in the real space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. This experiment provides an intuitive approach for the manipulation and control of highly-excited trap states, and sets the stage for the future exploration of topological physics in higher dimensions.   

Energy pumping, quantum state boosting, and new topological phases of matter with multi-tone driving

Quantum simulators provide experimental access to the dynamics many body quantum systems coupled to a driving field. We show that this setting allows for new and robust topological phases of driven quantum matter: in systems of particles driven by multi-tone drives, we uncover the “anomalous localised topological phase” characterised by quantised edge modes which non-adiabatically pump energy. This phase has no analogue in static systems, and is robust to the presence of interactions.

 

The quantised pumping provides microscopic control over field modes: when one (or more) of the driving tones corresponds to a quantised field mode, as in cavity QED systems, energy pumping gives a coherent and controllable way of transferring photons into/from a field mode. This allows the coherent “boosting” of mode state to higher photon numbers, giving a new tool for the production of non-classical states of light, such as Fock and Cat states.   

Dynamical phases in quasi-periodically driven quantum many-body systems

Quantum many-body systems driven far-from-equilibrium display a rich set of universal phenomena, which can generalize the notion of equilibrium phases. In this talk, we will discuss how such dynamic phases arise when quasiperiodically driving an isolated interacting many-body system with two or more incommensurate frequencies. We can make precise a notion of multiple emergent time-translation symmetries, which allows the construction of phases that fundamentally cannot be realized in static or periodically driven systems. This includes time-quasicrystals and time-translation symmetry protected topological phases. For these new phases to meaningfully exist, they must resist unbounded heating for at least a parametrically long time. We establish regimes for which this is the case and, along the way, derive an analytical description of the preheating regime for high-frequency quasiperiodic driving. Finally, we discuss a recent experimental implementation of a time-translation symmetry protected topological phase on a trapped-ion quantum processor. Relying solely on the emergent time-translation symmetries provides a more stable protection of the topological edge states against coherent errors as compared to edge state protection in phases build on an approximate microscopic symmetry.   

Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit

Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our work opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semi-metals in synthetic dimensions.   

Solitons and quantization in nonlinear topological systems

The description of the topological properties of condensed matter, photonic, or other wave systems is most natural in the linear (i.e., non-interacting) domain, where invariants such as the Chern number can be described as integrals over momentum space.  Here we discuss several experiments on nonlinear topological systems, including the observation of optical spatial solitons therein, as well as the integer and fractional quantization of soliton motion in Thouless pumps.