We present a novel system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tunabilty of the hopping frequency by adjusting the axial trapping frequency, and the phonon-phonon repulsion via the laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.Comment: 4 pages, 3 figure
Recent experiments revealed the importance of higher-band effects for the Mott-insulator(MI)-superfluid transition(SF) of ultracold bosonic atoms or mixtures of bosons and fermions in deep optical lattices [Best et al., Phys. Rev. Lett. 102, 030408 (2009); Will et al., Nature (London) 465, 197 (2010)]. In the present work we derive an effective lowest-band Hamiltonian in three dimensions that generalizes the standard Bose-Fermi-Hubbard model taking these effects as well as nonlinear corrections of the tunneling amplitudes mediated by interspecies interactions into account. It is shown that a correct description of the lattice states in terms of the bare-lattice Wannier functions, rather than approximations such as harmonic-oscillator states, is essential. In contrast to self-consistent approaches based on effective Wannier functions, our approach captures the observed reduction of the superfluid phase for repulsive interspecies interactions.
We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible ͑Mott-insulating͒, and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group ͑DMRG͒ methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behavior. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.
We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-Q coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.
In our paper we discussed the ground-state phase diagram of a mixture of bosons and spin-polarized fermions in the limit of ultralight fermions. Unfortunately, we overlooked a factor of √ 2π in the solution of the free fermion problem in the presence of the boson-induced alternating potential. This factor leads to slight modifications of some of the equations resulting in a much better agreement of the numerical data to the analytic predictions.The main difference occurs in the definition of the amplitude factor a before Eq.(3). It should read0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.5 0.55 0.6 0.65 0.7 0.75 bosonic hopping J B chemical potential µ B CDW (ρ B =1/2) MI (ρ B =0) MI (ρ B =1) DMRG L=512 DMRG L=256 ED L=12 ED L=10 2nd order FIG. 1. (Color online) Boundaries of the incompressible Mott insulator (MI) phases and the CDW phase for half fermion filling ρ F = 1/2, J F = 10, and V = 1.25 obtained by the density-matrix renormalization group (DMRG) and for small values of J B by exact diagonalization (ED). One recognizes the partial overlap between the MI and CDW phases for small values of J B indicating regions of spatial phase separation (PS) between MI and CDW. The dashed lines are results from the second-order perturbation theory based on the effective bosonic model with the corrected amplitude, Eq. (1).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.