Chiral Dynamics of Ultracold Atoms under a Tunable SU(2) Synthetic Gauge Field

Gauge theory is fundamental to our understanding of the quantum world, from particle interactions to emergent symmetries in strongly correlated matter. Synthetic gauge fields in quantum simulators offer opportunities to emulate natural gauge fields and explore exotic potentials. The synthesis of Abelian gauge fields has led to observations of chiral edge currents analogous to the Meissner effect in superconductors. However, the impact of non-Abelian gauge fields on dynamics remains largely unexplored. This research experimentally investigates the effects of a highly tunable SU(2) gauge field on the chiral dynamics of a spin-1/2 1D ladder, using a Raman momentum-lattice (RML) technique to encode spin and lattice-site degrees of freedom into hyperfine and momentum states of a ⁸⁷Rb Bose-Einstein condensate. The RML construction allows for convenient tuning of the gauge field's form and strength by manipulating laser parameters. The study aims to reveal the influence of non-Abelian gauge fields on the system's dynamic and transport properties, paving the way for future exploration of exotic gauge fields on momentum lattices.

Previous research has demonstrated the creation and manipulation of synthetic Abelian gauge fields in various quantum platforms, including ultracold atoms, superconducting qubits, and photonic systems. These experiments have led to observations of phenomena such as chiral edge currents, analogous to the Meissner effect in superconductors. The realization of synthetic non-Abelian gauge fields has also been achieved, sparking interest in simulating topological phenomena like the non-Abelian geometric phase and the quantum Hall effect. However, the influence of non-Abelian gauge fields on the dynamical properties of these systems has not been thoroughly explored. This study aims to address this gap by investigating the chiral dynamics in a system subjected to a tunable SU(2) gauge field.

The experiment utilizes a Raman momentum-lattice (RML) construction to create a spinful 1D ladder using a Bose-Einstein condensate of ⁸⁷Rb atoms. The spin and lattice-site degrees of freedom are encoded into the hyperfine and momentum states of the atoms. Raman and Bragg couplings, controlled by laser parameters, implement the ladder geometry and gauge couplings. The SU(2) gauge field is highly tunable through the manipulation of laser amplitudes and phases. The non-Abelian nature of the synthetic potential is demonstrated via the non-Abelian Aharonov-Bohm (AB) effect on a single plaquette. By sequentially switching on couplings, the path-dependent final states of atoms traversing the plaquette are observed, confirming the non-Abelian nature. Chiral dynamics are characterized by probing the chiral current, whose amplitude and direction are sensitive to gauge field parameters. The synthetic lattice is decomposed into two sets of overlaying flux ladders with distinct spin compositions. The observed chiral dynamics are analyzed in terms of the competition between these flux ladders, each exhibiting a unique spin-dependent chiral current. The Hamiltonian used is: H = Σ_n,m J(a†_n+1,mU(x)â_n,m + â†n,m+1U(x)â_n,m) + H.c, where J is the tunneling amplitude, â_n,m and â†_n,m are spinor annihilation and creation operators, and U(x) represents the spin-state rotation during hopping. The loop operators for clockwise (W_cw) and counter-clockwise (W_ccw) paths around a plaquette are defined and used to analyze the non-Abelian AB effect. The initial state of the atoms is prepared as |ψ_ini⟩ = (sinαe^iβ + cosα)|0,0⟩, with α determining spin composition and β the relative phase. The polarization ratio ρ is defined to characterize the internal-state response. Average displacement ⟨n_m(t)⟩ is defined to visualize directional flow, and chiral displacement (n_c) is used to characterize chirality. Numerical simulations complement the experimental results.

The experiment successfully demonstrates the non-Abelian Aharonov-Bohm effect, confirming the non-Abelian nature of the synthetic SU(2) gauge field. The chiral current along the two legs of the 1D ladder is observed to be spin-dependent and highly tunable through the parameters (θ, φ, ψ) of the gauge potential. The amplitude and direction of the chiral current are significantly modified as these parameters are tuned, revealing multiple dynamic regimes. By decomposing the synthetic lattice into two sets of overlaying flux ladders, the researchers show that the observed rich chiral dynamics stem from the competition between these ladders, each hosting a unique spin-dependent chiral current. In the Abelian limit (θ = 0), the two spin components decouple, resulting in two independent flux ladders. In the other limit (θ = π/2), the system reduces to decoupled zig-zag ladders with alternating spins. For intermediate values of θ, the chiral dynamics are a result of the competition between these two limiting cases. The experimental results for chiral displacement (n_c) are presented in parameter space (φ, ψ) for different θ values, showing the transitions between different dynamic regimes. The boundaries of these regimes are analyzed in terms of flux configurations and chirality.

The findings address the research question of how non-Abelian gauge fields affect chiral dynamics. The observed spin-dependent and tunable chiral current demonstrates the dramatic impact of these fields on system dynamics. The ability to tune the gauge field parameters and observe the resulting changes in chiral behavior allows for a detailed understanding of the competition between different flux ladders and their spin compositions. The results are significant as they provide experimental evidence for the rich dynamics induced by non-Abelian gauge fields in a controllable quantum system. This advances our understanding of the interplay between non-Abelian gauge fields and quantum dynamics, opening avenues for exploring more complex topological phenomena.

This work experimentally demonstrates spin-dependent chiral dynamics in a 1D ladder under a tunable SU(2) synthetic gauge field, showcasing the significant impact of non-Abelian gauge fields on quantum dynamics. The flexibility of the Raman momentum-lattice technique opens possibilities for exploring higher-dimensional systems and topological models involving various forms of non-Abelian gauge fields. Future research could focus on studying the interplay of many-body interactions and non-Abelian gauge fields to probe intrinsic topological order and fractional excitations on this versatile platform.

The current study focuses on a 1D ladder system. Extending the research to higher dimensions could reveal more complex chiral phenomena and further test the theoretical predictions. The system is also limited by the finite size of the momentum lattice, potentially affecting the observation of long-range correlations. The influence of experimental imperfections, such as laser noise and atomic interactions, could be further investigated to quantify their impact on the observed chiral dynamics. More detailed analysis of the impact of these limitations could strengthen the results.