Correlated Dynamics in a Synthetic Lattice of Momentum States

Abstract

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...

Engineering a Flux-Dependent Mobility Edge in Disordered Zigzag Chains

“…The difference in localization properties for different energy eigenstates runs counter to our expectations of an energy-independent transition for the NN-coupled AA model, but can be explained by the presence of nonlinear atomic interactions in our momentum-space lattice [16,20]. In particular, the interactions between indistinguishable bosons in momentum space are effectively attractive and site local, in the sense that direct interactions are present for collisions between two atoms occupying any pair of momentum modes, while exchange interactions are present only when two identical bosons occupy distinguishable modes [41,42].…”

“…In addition to the SPME that results from multiranged hopping, we observe asymmetric (with applied flux) localization behavior of the system's lowest-energy and highest-energy eigenstates, caused by the presence of effectively attractive interparticle interactions in the lattice of momentum states [16]. The influence of interactions is even more strongly evident in the case of the 1D AA with only NN tunneling, where a drastic shift in the localization transition is observed between low-and high-energy eigenstates, corresponding to a mobility edge driven purely by interparticle interactions.…”

Engineering tunable local loss in a synthetic lattice of momentum states

“…In momentum space, this gives rise to an interaction parameter which is effectively infinite-ranged, nearly independent of the relative momentum of colliding atoms (for moderately low collision energies). However, the interaction energy of a pair of colliding identical bosons depends on their momentum: while the direct interaction of colliding identical bosons is essentially independent of momentum, a pair of bosons occupying distinct spatial modes will enjoy an added 'exchange interaction' [44,62]. The presence of this finite-ranged interaction and its resulting effects on various tight-binding models have been studied in our previous works [43,44].…”

“…However, as previous experiments on synthetic lattices of momentum states [43,44] have taken place in a regime in which a mean-field description of the interactions does a suitable job of describing the observed dynamics (as the population per momentum state is typically much greater than one), the effective non-Hermitian processes we have described could be incorporated into a nonlinear Schrödinger equation with interaction terms to describe the interplay of interactions and loss at the mean-field level.…”

Topological quantum matter in synthetic dimensions

“…For a synthetic direction made of harmonic oscillator eigenstates, the inter-particle interactions decay algebraically 44 , whereas that made of frequency modes in photonics 54,55 preserves the total synthetic positions of colliding particles, that is, ∝ m1+m2=m3+m4â † m1â † m2âm3âm4 . The momentum states of ultracold gases 38 give rise to effective locally attractive interaction in momentum states, and the localization transition under such an interaction has been experimentally investigated 42,116 .…”