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Ensembles with long-range interactions between particles are promising for revealing strong quantum collective effects and many-body phenomena. Here we study the ground-state phase diagram of a two-dimensional Bose system with quadrupolar interactions using a diffusion Monte Carlo technique. We predict a quantum phase transition from a gas to a solid phase. The Lindemann ratio and the condensate fraction at the transition point are $gamma=0.269(4)$ and $n_0/n=0.031(4)$, correspondingly. We observe the strong rotonization of the collective excitation branch in the vicinity of the phase transition point. Our results can be probed using state-of-the-art experimental systems of various nature, such as quasi-two-dimensional systems of quadrupolar excitons in transition metal dichalcogenide (TMD) trilayers, quadrupolar molecules, and excitons or Rydberg atoms with quadrupole moments induced by strong magnetic fields.
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Dynamical quantum phase transitions are closely related to equilibrium quantum phase transitions for ground states. Here, we report an experimental observation of a dynamical quantum phase transition in a spinor condensate with correspondence in an excited state phase diagram, instead of the ground state one. We observe that the quench dynamics exhibits a non-analytical change with respect to a parameter in the final Hamiltonian in the absence of a corresponding phase transition for the ground state there. We make a connection between this singular point and a phase transition point for the highest energy level in a subspace with zero spin magnetization of a Hamiltonian. We further show the existence of dynamical phase transitions for finite magnetization corresponding to the phase transition of the highest energy level in the subspace with the same magnetization. Our results open a door for using dynamical phase transitions as a tool to probe physics at higher energy eigenlevels of many-body Hamiltonians.
The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from gas to solid phase when the density increases. In the gas phase the condensate fraction is calculated as a function of the density. Using Feynman approximation, the collective excitation branch is studied and appearance of a roton minimum is observed. Results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindeman ratio at the transition point comes to be $gamma = 0.230(6)$. The condensate fraction in the gas phase is estimated as a function of the density.
Heat generated as a result of the breakdown of an adiabatic process is one of the central concepts of thermodynamics. In isolated systems, the heat can be defined as an energy increase due to transitions between distinct energy levels. Across a second-order quantum phase transition (QPT), the heat is predicted theoretically to exhibit a power-law scaling, but it is a significant challenge for an experimental observation. In addition, it remains elusive whether a power-law scaling of heat can exist for a first-order QPT. Here we experimentally observe a power-law scaling of heat in a spinor condensate when a system is linearly driven from a polar phase to an antiferromagnetic phase across a first-order QPT. We experimentally evaluate the heat generated during two non-equilibrium processes by probing the atom number on a hyperfine energy level. The experimentally measured scaling exponents agree well with our numerical simulation results. Our work therefore opens a new avenue to experimentally and theoretically exploring the properties of heat in non-equilibrium dynamics.
We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples, and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wavevector difference $Q$ of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing $Q$, or the system size. For moderate values of $Q$ above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave-functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultra-cold atom setup as a tunable platform studying quantum aspects of the Pokrovsky-Talapov theory in and out-of-equilibrium.
The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.
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