SCIentIfIC REPORtS | (2018) 8:3422 | DOI:10.1038/s41598-018-21699-x
Synthetic dimensions in ultracold
, Bryce Gadway
& Kaden R. A. Hazzard
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space.
They allow, for example, a real three-dimensional system to act as eectively four-dimensional. Driven
by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold
matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions
extending to many – potentially hundreds of – synthetic lattice sites. Microwaves coupling rotational
states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band
structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice
with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow
strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a
membrane, with an emergent condensate that lives on this string or membrane. All these phases can be
detected using local measurements of rotational state populations.
Ultracold polar molecules oer unique possibilities for creating strongly correlated matter, owing to their strong
anisotropic long-ranged dipolar interactions and their complex rotational and vibrational structure
previous experimental and theoretical research has utilized the rotational degree of freedom
, it has used only
a few rotational or dressed rotational states.
In this article, we propose to use rotational states of polar molecules as a synthetic dimension, which can
have up to hundreds of synthetic lattice sites. e synthetic tunnelings are driven by microwaves resonant with
rotational state transitions. is gives rise to a system with a fully tunable synthetic single particle Hamiltonian,
which experiments can use to realize arbitrary synthetic band structures, including topological ones. We show
that dipole interactions in polar molecules lead to interesting phases, even without any special engineering or
ne tuning. For example, we show that molecules frozen in a periodic real space array undergo a spontaneous
dimensional reduction, forming a uctuating quantum string or membrane. At strong interactions, the string/
membrane hosts an emergent condensate of hardcore bosons. We show that ongoing experiments can realize and
probe these strings/membranes and condensate.
Researchers have created nearly quantum degenerate gases of several heteronuclear molecular species, such as
KRb, NaRb, NaK, and RbCs, in their ground state
. All of these have a strong electric dipole moment of about
a Debye. ese molecules also have a large number of rotational quantum states. We dene a synthetic lattice,
whose sites are a subset of a molecule’s rotational states. To create a large synthetic lattice, we propose to shine
several microwaves in parallel to drive transitions up to a highly excited rotational state, as illustrated in Fig.1.
ese transitions correspond to tunneling in the synthetic lattice. Experimentalists can simultaneously apply a
large number of microwaves with fully controllable amplitudes, phases, and frequencies ranging from a few to
several tens of GHz using commercially available technology (see Supplementary Materials).
Experimentalists have created synthetic dimensions in other ultracold gases from their motional
, or rotational
states that are coupled by Raman lasers, analogous to our proposal’s coupling of rota-
tional states with microwaves. Our proposal shares some features with these other methods. We can fully control
every tunneling amplitude and on-site potential by tuning the microwaves’ complex amplitudes and detunings.
By appropriate choice of the rotational states, we can impose periodic or open boundaries on the synthetic lattice,
or create other spatial topologies. We can image populations in the synthetic lattice with single-site resolution.
Additionally, realizing synthetic dimensions in polar molecules has signicant advantages over other systems.
First, the experimentally feasible size of the synthetic dimension is orders of magnitude larger. Second, since
the internal states are directly coupled via microwaves without an intermediate excited state, the system does
Department of Physics and Astronomy, Rice University, Houston, TX, 77251, USA.
Rice Center for Quantum
Materials, Rice University, Houston, TX, 77251, USA.
Department of Physics, University of Illinois at Urbana
Champaign, Urbana, IL, 61801, USA. Correspondence and requests for materials should be addressed to B.S. (email:
Received: 24 January 2018
Accepted: 8 February 2018
Published: xx xx xxxx