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arXiv:1002.4918 · Physical Review A

Noise correlations of one-dimensional Bose mixtures in optical lattices

Anzi Hu, Ludwig Mathey, Carl J. Williams, Charles W. Clark

Published Jun 2, 2010• 8 citations
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Abstract

We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work [Phys. Rev. A 80, 023619 (2009)], we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy.

DOI
10.1103/physreva.81.063602

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We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work [Phys. Rev. A 80, 023619 (2009)], we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy.
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 study the quantum phases of one-dimensional Bose-Fermi mixtures in optical lattices. Assuming repulsive interparticle interactions, equal mass, and unit total filling, we calculate the ground-state phase diagram by means of both the Tomonaga-Luttinger liquid theory and time-evolving block decimation method. We demonstrate the existence of a counterflow superfluid phase of polaron pairs, which are composite particles consisting of two fermions and two bosonic holes, in a broad range of the parameter space. We find that this phase naturally emerges in 174{}^{174}174Yb-173{}^{173}173Yb mixtures, realized in recent experiments, at low temperatures.
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.
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.
We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.
We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the noise correlations contain full information on the most important fluctuations present in the system. We point out the importance of the sum rules fulfilled by the noise correlations and show that they yield nonsingular structures beyond the predictions of bosonization approaches. Noise correlations can thus serve as a universal probe of order and can be used to characterize the many-body states of cold atoms in optical lattices.