Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter (1812.05895v2)

Abstract: Gauge fields that appear in models of high-energy and condensed matter physics are dynamical quantum degrees of freedom due to their coupling to matter fields. Since the dynamics of these strongly correlated systems is hard to compute, it was proposed to implement this basic coupling mechanism in quantum simulation platforms with the ultimate goal to emulate lattice gauge theories. Here, we realize the fundamental ingredient for a density-dependent gauge field acting on ultracold fermions in an optical lattice by engineering non-trivial Peierls phases that depend on the site occupations. We propose and implement a Floquet scheme that relies on breaking time-reversal symmetry (TRS) by driving the lattice simultaneously at two frequencies which are resonant with the onsite interactions. This induces density-assisted tunnelling processes that are controllable in amplitude and phase. We demonstrate techniques in a Hubbard dimer to quantify the amplitude and to directly measure the Peierls phase with respect to the single-particle hopping. The tunnel coupling features two distinct regimes as a function of the modulation amplitudes, which can be characterised by a $\mathbb{Z}_2$-invariant. Moreover, we provide a full tomography of the winding structure of the Peierls phase around a Dirac point that appears in the driving parameter space.

Overview of Density-Dependent Peierls Phases in Ultracold Matter

The paper "Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter" presents a significant advancement in quantum simulation, specifically focusing on the emulation of lattice gauge theories. This research elegantly demonstrates how density-dependent Peierls phases can be realized to simulate gauge fields that dynamically interact with ultracold matter in an optical lattice, providing a meticulous exploration of density-dependent tunneling phenomena and gauge field dynamics.

Key Contributions

1. Density-Dependent Gauge Fields: The authors introduce a novel Floquet scheme for inducing density-dependent Peierls phases in ultracold fermionic systems. This is achieved by breaking TRS through modulation of the optical lattice at two resonant frequencies. Such a configuration allows the encoding of synthetic gauge fields that respond dynamically to the spatial configurations and motion of fermions, analogous to natural gauge fields.
2. Experimental Realization: The paper experimentally realizes a density-dependent gauge field by implementing time-dependent modulation in optical lattices occupied by ultracold atoms. Through careful control over the modulation parameters, including amplitude and phase, the paper demonstrates the ability to tune both the Peierls phase and the tunneling amplitude independently.
3. Floquet Engineering: Employing Floquet theory, the researchers derive an effective Hamiltonian that succinctly describes the long-term dynamics of these driven systems. This Hamiltonian illustrates how density-assisted tunneling processes are modified by photon exchanges with the drive, showcasing complex behavior that could be manipulated to emulate lattice gauge theories.
4. Topological Characterization: The paper characterizes the phase transitions within this system using a $\mathbb{Z}_2$ invariant, highlighting two distinct regimes of tunneling. Moreover, it provides a comprehensive tomography of the phase vortex around a Dirac point in the driving parameter space—a critical point where the tunneling amplitude vanishes and the phase of the system undergoes a nontrivial change.

Numerical and Theoretical Insights

The derivations utilize high-frequency expansions and numerical simulations to elucidate the quasienergy spectra and eigenstate compositions within the driven double-well setup. These simulations help capture resonance phenomena and critical points where the influence of gauge fields can drastically modify many-body dynamics, thus enriching our understanding of nonequilibrium thermodynamics in lattice systems.

Implications and Future Directions

The implications of this work extend beyond fundamental research into lattice gauge theories. It sets the stage for future explorations into synthetic quantum systems simulating charged particle dynamics under electromagnetic forces. The ability to engineer interactions such as density-dependent gauge fields opens avenues for studying phenomena like the quantum Hall effect, anyonic statistics, and flux attachment in optical lattices.

Potential developments could further tailor temporal or spatial driving dependencies, transforming the presented Dirac points into varied parameter spaces. Expansion of this framework to incorporate more complex lattice configurations or higher-dimensional systems may facilitate deeper insights into high-energy physics concepts using cold atom experiments.

Additionally, the prospect of disentangling gauge and matter particles offers the tantalizing capability to mimic complex interactions from quantum field theories more comprehensively, particularly when combined with spin-selective modulation techniques.

In conclusion, this paper provides a well-established foundation for simulating lattice gauge theories and demonstrates robust control over quantum interactions. This research significantly enhances the versatility of optical lattice systems as platforms for quantum simulations, paving the way toward new discoveries in synthetic quantum matter.