Abstract
Activating transitions between a set of atomic internal states has emerged as an elegant scheme by which lattice models can be designed in ultracold atomic gases. In this approach, the internal states can be viewed as fictitious lattice sites defined along a synthetic dimension, hence offering a powerful method by which the spatial dimensionality of the system can be extended. Inter-particle collisions generically lead to infinite-range interactions along the synthetic dimensions, which a priori precludes the design of Bose-Hubbard-type models featuring on-site interactions. In this article, we solve this obstacle by introducing a protocol that realizes strong and tunable "on-site" interactions along an atomic synthetic dimension. Our scheme is based on pulsing strong intra-spin interactions in a fast and periodic manner, hence realizing the desired "on-site" interactions in a digital (Trotterized) manner. We explore the viability of this protocol by means of numerical calculations, which we perform on various examples that are relevant to ultracold-atom experiments. This general method, which could be applied to various atomic species by means of fast-response protocols based on Fano-Feshbach resonances, opens the route for the exploration of strongly-correlated matter in synthetic dimensions.
Highlights
Quantum simulation offers a method by which complex phenomena can be analyzed using well-designed quantum systems [1]
One considers an experimental situation where one activates a strong interaction U11 for a short duration τ, U22 for the same duration τ, etc., while keeping the background interactions [see Eq (4) below] approximately constant and small. This requires enhancing the intraspin scattering lengths, one at a time, in a periodic manner. This protocol allows one to investigate the Bose-Hubbard model in synthetic dimensions, under the condition that the individual scattering lengths are modified on sufficiently small time scales
In order to explore the physics of the Bose-Hubbard model at unit filling (n = 1), we will set N = M, where M corresponds to the number of available internal states, i.e., the number of sites along the synthetic dimension
Summary
Quantum simulation offers a method by which complex phenomena can be analyzed using well-designed quantum systems [1]. The effects generated by SU(M ) interactions are generically captured by mean-field approaches These observations indicate that genuine 2D interacting quantum states, such as fractional quantum Hall (FQH) states [43,44,45], cannot be created by combining a real lattice system (with on-site interactions) and a synthetic dimension with infinite-range interactions; the absence of FQH states in such a setting was analyzed numerically in Ref. We consider the bosonic Mott-superfluid transition and the formation of an effective antiferromagnetic order in a single synthetic dimension, as well as the creation of a chiral Mott-Meissner phase in a synthetic ladder geometry with an effective magnetic flux The latter setting, which features a combination of effective on-site interactions and artificial magnetic flux, constitutes a promising starting point for the study of FQH physics in synthetic dimensions
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