Coupling two order parameters in a quantum gas. (arXiv:1711.07988v1 [cond-mat.quant-gas])

Controlling matter to simultaneously support multiple coupled properties is
of fundamental and technological importance. For example, the simultaneous
presence of magnetic and ferroelectric orders in multiferroic materials leads
to enhanced functionalities. In high-temperature superconductors, intertwining
between charge- and spin-order can form superconducting states at high
transition temperatures. However, pinning down the microscopic mechanisms
responsible for the simultaneous presence of different orders is difficult,
making it hard to predict the phenomenology of a material or to experimentally
modify its properties. Here we use a quantum gas to engineer an adjustable
interaction at the microscopic level between two orders, and demonstrate
scenarios of competition, coexistence and coupling between them. In the latter
case, intriguingly, the presence of one order lowers the critical point of the
other. Our system is realized by a Bose-Einstein condensate which can undergo
self-organization phase transitions in two optical resonators, resulting in two
distinct crystalline density orders. We characterize the intertwining between
these orders by measuring the composite order parameter and the elementary
excitations. We explain our results with a mean-field free energy model, which
is derived from a microscopic Hamiltonian. Our system is ideally suited to
explore properties of quantum tricritical points as recently realized in and
can be extended to study the interplay of spin and density orders also as a
function of temperature.

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