We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven atomic transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the distinguishability of the discrete momentum states coupled in MSLs gives rise to an added exchange energy between condensate atoms in different momentum orders, relating to an effectively attractive, finite-ranged interaction in momentum space. We explore the types of phenomena that can result from this interaction, including the formation of chiral self-bound states in topological MSLs. We also discuss the prospects for creating squeezed states in momentum-space double wells.Quantum simulation with ultracold atoms [1,2] has been a powerful tool in the study of many-body physics and nonequilibrium dynamics. There has been recent interest in extending quantum simulation studies from real-space potentials to synthetic lattice systems composed of discrete internal [3,4] or external [5] states. These synthetic dimensions enable many unique capabilities for quantum simulation, including new approaches to engineering nontrivial topology [4,6], access to higher dimensions [3], and potential insensitivity to finite motional temperature.The recent development of momentum-space lattices (MSLs), based on the use of discrete momentum states as effective sites, has introduced a fully synthetic approach to simulating lattice dynamics [7][8][9][10][11]. As compared to partially synthetic systems [12,13], fully synthetic lattices offer complete microscopic control of system parameters. While this level of control is analogous to that found in photonic simulators [14,15], matter waves of atoms can interact strongly with one another.However, fully synthetic systems also present apparent challenges for studying nontrivial atomic interactions. Synthetic systems based purely on internal states suffer from limited state spaces, sensitivity to external noise for generic, field-sensitive states [16], and possible collisional relaxation [17] and three-body losses [18]. Furthermore, for isotropic scattering lengths as in 87 Rb [16] and alkaline earth atoms [19], interactions in the synthetic dimension are nearly all-to-all. Similarly, s-wave contact interactions relate to nearly infinite-ranged momentumspace interactions at low energy, and should naively be decoupled from particle dynamics in MSLs.Here, we investigate the role of atomic interactions in MSLs, showing that finite-ranged interactions in momentum space result from the exchange energy of bosonic condensate atoms in distinguishable momentum states. We explore potential interaction-driven phenomena that can be studied in topological MSLs, showing that chiral propagating bound states can emerge in the presence of an artificial magnetic flux. We additionally discuss the use of momentum-space double wells for the gener...

Dissipation can serve as a powerful resource for controlling the behavior of open quantum systems.Recently there has been a surge of interest in the influence of dissipative coupling on large quantum systems and, more specifically, how these processes can influence band topology and phenomena like many-body localization. Here, we explore the engineering of local, tunable dissipation in so-called synthetic lattices, arrays of quantum states that are parametrically coupled in a fashion analogous to quantum tunneling. Considering the specific case of momentum-state lattices, we investigate two distinct mechanisms for engineering controlled loss: one relying on an explicit form of dissipation by spontaneous emission, and another relying on reversible coupling to a large reservoir of unoccupied states. We experimentally implement the latter and demonstrate the ability to tune the local loss coefficient over a large range. The introduction of controlled loss to the synthetic lattice toolbox promises to pave the way for studying the interplay of dissipation with topology, disorder, and interactions.

Ergodicity and chaos play an integral role in the dynamical behavior of many-particle systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how randomness and chaos emerge in the dynamical evolution of closed quantum systems remains elusive. Here, we develop an experimental platform for the realization of canonical quantum chaotic Hamiltonians based on quantum simulation with synthetic lattices. We map the angular momentum projection states of an effective quantum spin onto the linear momentum states of a 87 Rb Bose-Einstein condensate, which can alternatively be viewed as lattice sites in a synthetic dimension. This synthetic lattice, with local and dynamical control of tight-binding lattice parameters, enables new capabilities related to the experimental study of quantum chaos. In particular, the capabilities of our system let us tune the effective size of our spin, allowing us to illustrate how classical chaos can emerge from a discrete quantum system. Moreover, spectroscopic control over our synthetic lattice allows us to explore unique aspects of our spin's dynamics by measuring the out-of-time-ordered correlation function, and enables future investigations into entirely new classes of chaotic systems. arXiv:1705.06714v1 [cond-mat.quant-gas]

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In this work we perform polarization spectroscopy of erbium atoms in a hollow cathode lamp (HCL) for the stabilization of a diode laser to the 401-nm transition. We review the theory behind Doppler-free polarization spectroscopy, theoretically model the expected erbium polarization spectra, and compare the numerically calculated spectra to our experimental data. We further analyze the dependence of the measured spectra on the HCL current and the peak intensities of our pump and probe lasers to determine conditions for optimal laser stabilization.