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Register a new userThe low-energy excitation spectrum of one-dimensional dipolar quantum gases
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We determine the excitation spectrum of a bosonic dipolar quantum gas in a one-dimensional geometry, from the dynamical density-density correlation functions simulated by means of Reptation Quantum Monte Carlo techniques. The excitation energy is always vanishing at the first vector of the reciprocal lattice in the whole crossover from the liquid-like at low density to the quasi-ordered state at high density, demonstrating the absence of a roton minimum. Gaps at higher reciprocal lattice vectors are seen to progressively close with increasing density, while the quantum state evolves into a quasi-periodic structure. The simulational data together with the uncertainty-principle inequality also provide a rigorous proof of the absence of long-range order in such a super-strongly correlated system. Our conclusions confirm that the dipolar gas is in a Luttinger-liquid state, significantly affected by the dynamical correlations. The connection with ongoing experiments is also discussed.
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In this letter we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound state and cause scattering resonances. This represents the dipole induced resonance in low-dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using asymptotic Bethe ansatz. Despite of long-range nature of dipolar interaction, we find that a behavior similar as short-range Lieb-Linger gas emerges at the resonance regime.
We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $omega_2=2omega_0$ to the quasi-ordered, super-strongly interacting value $omega_2=sqrt{5}omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.
The ground state and structure of a one-dimensional Bose gas with dipolar repulsions is investigated at zero temperature by a combined Reptation Quantum Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid behavior emerges in a wide range of intermediate densities, evolving into a Tonks-Girardeau gas at low density and into a classical quasi-ordered state at high density. The density dependence of the Luttinger exponent is extracted from the numerical data, providing analytical predictions for observable quantities, such as the structure factor and the momentum distribution. We discuss the accessibility of such predictions in current experiments with ultracold atomic and molecular gases.
We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, omega).$ The description of the singularities of dynamic response functions near an edge $epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.
We consider dipolar bosons in two tubes of one-dimensional lattices, where the dipoles are aligned to be maximally repulsive and the particle filling fraction is the same in each tube. In the classical limit of zero inter-site hopping, the particles arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devils staircase like in the single tube case. Turning on hopping within each tube then gives rise to a competition between the crystalline Mott phases and a liquid of defects or solitons. However, for the two-tube case, we find that solitons from different tubes can bind into pairs for certain topologies of the filling fraction. This provides an intriguing example of pairing that is purely driven by correlations close to a Mott insulator.
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