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arXiv:1007.1853 · Physical Review Letters

Comment on “Feshbach-Einstein Condensates”

María Eckholt, Tommaso Roscilde

Published Nov 5, 2010• 13 citations
arXivHTMLPDF

Abstract

In a recent paper (Phys. Rev. Lett. 102, 015301 (2009), arXiv:0810.3763) Rousseau and Denteneer claim that an unconventional "super-Mott" (SM) phase is realized by bosons trapped in an optical lattice close to a Feshbach resonance with a molecular state. The supposed SM phase, observed via quantum Monte Carlo (QMC) simulations of an atom-molecule Bose-Hubbard model, is an incompressible phase developing spontaneous atomic/molecular supercurrents which are perfectly anticorrelated. Here we show that the identification of this phase is based on a misinterpretation of the estimators of superfluidity in QMC, which break down in the presence of coherent atom/molecule conversion. Our conclusion is that the supposed SM phase is in fact a fully normal insulator.

DOI
10.1103/physrevlett.105.199603

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In a recent paper (Phys. Rev. Lett. 102, 015301 (2009), arXiv:0810.3763) Rousseau and Denteneer claim that an unconventional "super-Mott" (SM) phase is realized by bosons trapped in an optical lattice close to a Feshbach resonance with a molecular state. The supposed SM phase, observed via quantum Monte Carlo (QMC) simulations of an atom-molecule Bose-Hubbard model, is an incompressible phase developing spontaneous atomic/molecular supercurrents which are perfectly anticorrelated. Here we show that the identification of this phase is based on a misinterpretation of the estimators of superfluidity in QMC, which break down in the presence of coherent atom/molecule conversion. Our conclusion is that the supposed SM phase is in fact a fully normal insulator.
We investigate the phase diagram of a two-species Bose-Hubbard model describing atoms and molecules on a lattice, interacting via a Feshbach resonance. We identify a region where the system exhibits an exotic super-Mott phase and regions with phases characterized by atomic and/or molecular condensates. Our approach is based on a recently developed exact quantum Monte Carlo algorithm: the stochastic Green function algorithm with tunable directionality. We confirm some of the results predicted by mean-field studies, but we also find disagreement with these studies. In particular, we find a phase with an atomic but no molecular condensate, which is missing in all mean-field phase diagrams.
Feshbach resonances-namely, resonances between an unbound two-body (atomic) state and a bound (molecular) state, differing in magnetic moment-are a unique tool to tune the interaction properties of ultracold atoms. Here we show that the spin-changing interactions, coherently coupling the atomic and molecular states, can act as a novel mechanism to stabilize an insulating phase-the Feshbach insulator-for bosons in an optical lattice close to a narrow Feshbach resonance. Making use of quantum Monte Carlo simulations and mean-field theory, we show that the Feshbach insulator appears around the resonance, preventing the system from collapsing when the effective atomic scattering length becomes negative. On the atomic side of the resonance, the transition from condensate to Feshbach insulator has a characteristic first-order nature, due to the simultaneous loss of coherence in the atomic and molecular components. These features appear clearly in the ground-state phase diagram of, e.g., ^{87}Rb around its 414 G resonance, and they are therefore directly amenable to experimental observation.
We investigate the phase diagram of a two-species Bose-Hubbard model including a conversion term, by which two particles from the first species can be converted into one particle of the second species, and vice versa. The model can be related to ultracold atom experiments in which a Feshbach resonance produces long-lived bound states viewed as diatomic molecules. The model is solved exactly by means of quantum Monte Carlo simulations. We show that an ``inversion of population'' occurs, depending on the parameters, where the second species becomes more numerous than the first species. The model also exhibits an exotic incompressible ``super-Mott'' phase where the particles from both species can flow with signs of superfluidity, but without global supercurrent. We present two phase diagrams, one in the chemical potential, conversion plane, the other in the chemical potential, detuning plane.
We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with $\text{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, describing atoms and molecules on a two-dimensional optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean-field theory, we show that the conversion between the two species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term---the Feshbach insulator---instead of a standard Mott-insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with noncondensed atoms, and a mixed atomic-molecular condensate. Employing finite-size scaling analysis, we observe three-dimensional (3D) XYXYXY (3D Ising) transition when U(1)\text{U}(1)U(1) (Z2{\mathbb{Z}}_{2}Z2​) symmetry is broken, whereas the transition is first order when both U(1)\text{U}(1)U(1) and Z2{\mathbb{Z}}_{2}Z2​ symmetries are spontaneously broken. The finite-temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a signal compatible with a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.