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last dipolar system being presented here are homonuclear Rb

molecules, with one of

the atoms excited to a high-lying Rydberg state [64]. Contrary to the general case of

homonuclear molecules, such system exhibits a large permanent electric dipole moment

through the asymmetric excitation between the atoms [65].

The active experimental branch in the ﬁeld of dipolar quantum gases evolves in a

symbiosis with the theoretical progress. Especially dipolar gases in reduced dimensions

have been subject to many theoretical studies in the recent years. One major property

of a dipolar BEC, strongly conﬁned along the polarization direction, is the roton-maxon

excitation spectrum [15, 16]: similar to the spectrum observed in liquid helium [17–19], the

energy of the excitations of a dipolar gas can show a local minimum at a ﬁnite momentum

value. Various structures in the atomic ground-state density of trapped dBECs [20, 21],

as well as supersolid phases in optical lattices [22, 23] are some of the most interesting

phenomena related to the rotonic excitation spectrum. These density modulations have

their beautiful analogon in the multi-peak structures of a classical ferroﬂuid that undergoes

a Rosensweig instability in an external magnetic ﬁeld [66]. For very large dipole strengths,

as can be provided by polar molecules, a quantum phase transition from a superﬂuid to

a strongly correlated crystalline phase is expected to occur in a two-dimensional (2D)

bosonic system [67, 68]. Two-dimensional dipolar condensates furthermore support the

formation of anisotropic bright solitons [69–71] and vortex lattices of diﬀerent symmetries

are predicted to form in rotating 2D dipolar BECs [72]. Dipolar many-body systems in

reduced dimensions thus hold many fascinating phenomena, with a detailed overview

given in two recent reviews [13, 14].

Regarding the experimental realization, low dimensional ultracold gases can be created

for example by using the optical lattice potentials discussed before [24, 25, 47]. An ultracold

cloud can thus be split into a linear array of spatially separated two-dimensional samples

when trapped in a one-dimensional (1D) lattice potential. In such lattice geometry, the

non-local character of the DDI has an interesting eﬀect: even if the tunneling of atoms

between the lattice sites is suppressed, the spatially separated samples interact with

each other through the long-range DDI. The physics of 2D dipolar condensates therefore

becomes even richer in such multi-layer geometry. In particular, the roton-maxon excitation

spectrum is expected to develop a band-like structure through the inter-site coupling of

the excitations [26, 27]. Furthermore, modulated ground-state structures of the 2D on-site

condensates are predicted to be enhanced [28, 29]. Experimentally, weak eﬀects of the

dipolar inter-site interactions were already observed in the damping of Bloch oscillations

of a

K BEC in a 1D lattice [51]. The properties of strongly dipolar BECs in optical

lattices, however, have not been studied so far, motivating the experimental investigations

presented in this thesis.

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Bose 2.2 User Manual Page 15