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arXiv:cond-mat/0602616 · Physical Review B

Commensurate mixtures of ultracold atoms in one dimension

Ludwig Mathey

Published Apr 24, 2007• 59 citations
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Abstract

We study binary mixtures of ultracold atoms, confined to one dimension in an optical lattice, with commensurate densities. Within a Luttinger liquid description, which treats various mixtures on equal footing, we derive a system of renormalization group equations at second order, from which we determine the rich phase diagrams of these mixtures. These phases include charge and spin density wave orders, singlet and triplet pairings, polaron pairing [L. Mathey et al., Phys. Rev. Lett. 93, 120404 (2004)], and a supersolid phase. Various methods to detect our results experimentally are discussed.

DOI
10.1103/physrevb.75.144510

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We use the bosonization approach to investigate quantum phases of boson-fermion mixtures (BFM) of atoms confined to one dimension by an anisotropic optical lattice. For a BFM with a single species of fermions we find a charge-density wave phase, a fermion pairing phase, and a phase separation regime. We also obtain the rich phase diagram of a BFM with two species of fermions. We demonstrate that these phase diagrams can be understood in terms of polarons, i.e., atoms "dressed" by screening clouds of the other atom species. Techniques to detect the resulting quantum phases are discussed.
We study the quantum phases of mixtures of ultracold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using the Tomonaga-Luttinger liquid theory as well as the numerical method of time-evolving block decimation (TEBD). We consider a binary mixture of equal density with repulsive intraspecies interactions and either repulsive or attractive interspecies interaction. For a homogeneous system, we find paired and counterflow superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge-density wave order. We show that the Tomonaga-Luttinger liquid theory and the TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state and a $\ensuremath{\pi}/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase.
We identify a one-dimensional supersolid phase in a binary mixture of near-hard-core bosons with weak, local interspecies repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasisuperfluidity and quasi-charge-density-wave order, can be produced and observed in finite ultracold atom systems in a harmonic trap. Our analysis is based on Luttinger liquid theory supported by numerical calculations using the time-evolving block decimation method. Clear experimental signatures of these two orders can be found, respectively, in time-of-flight interference patterns and the structure factor S(k)S(k)S(k) derived from density correlations.
Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.