Bosonic Dimers Research Articles

Fractionalized holes in one-dimensional Z2 gauge theory coupled to fermion matter: Deconfined dynamics and emergent integrability

We investigate the interplay of quantum one-dimensional discrete ${\mathbb{Z}}_{2}$ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entanglement and provide analytical understanding of its salient features. We also study the model enriched with a short-range interaction and clarify the nature of the resulting ground state at low filling of holes and identify deconfined hole excitations near the hole filling ${\ensuremath{\nu}}^{h}=1/3$.

Topologically-imposed vacancies and mobile solid 3He on carbon nanotube

Low dimensional fermionic quantum systems are exceptionally interesting because they reveal distinctive physical phenomena, including among others, topologically protected excitations, edge states, frustration, and fractionalization. Our aim was to confine 3He on a suspended carbon nanotube to form 2-dimensional Fermi-system. Here we report our measurements of the mechanical resonance of the nanotube with adsorbed sub-monolayer down to 10 mK. At intermediate coverages we have observed the famous 1/3 commensurate solid. However, at larger monolayer densities we have observed a quantum phase transition from 1/3 solid to an unknown, soft, and mobile solid phase. We interpret this mobile solid phase as a bosonic commensurate crystal consisting of helium dimers with topologically-induced zero-point vacancies which are delocalized at low temperatures. We thus demonstrate that 3He on a nanotube merges both fermionic and bosonic phenomena, with a quantum phase transition between fermionic solid 1/3 phase and the observed bosonic dimer solid.

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory.

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d-wave superconducting pairing amplitude when anti-ferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.

Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals.

We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

Chirality of Topological Gap Solitons in Bosonic Dimer Chains.

We study gap solitons which appear in the topological gap of 1D bosonic dimer chains within the mean-field approximation. We find that such solitons have a nontrivial texture of the sublattice pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in the presence of a localized energy potential.

Ising anyons in frustration-free Majorana-dimer models

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.

Electronic quasiparticles in the quantum dimer model: Density matrix renormalization group results

We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates. The model contains bosonic dimers, representing a spin-singlet valence bond between a pair of electrons, and fermionic dimers, representing a quasiparticle with spin-$1/2$ and charge $+e$. By density matrix renormalization group calculations on a long but finite cylinder, we obtain the ground-state density distribution of the fermionic dimers for a number of different total densities. From the Friedel oscillations at open boundaries, we deduce that the Fermi surface consists of small hole pockets near $(\pi/2, \pi/2)$, and this feature persists up to a doping density of $1/16$. We also compute the entanglement entropy and find that it closely matches the sum of the entanglement entropies of a critical boson and a low density of free fermions. Our results support the existence of a fractionalized Fermi liquid in this model.

Quantum simulators based on the global collective light-matter interaction

We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time posses properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e. infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support non-trivial superfluid states, bosonic dimer, trimers, etc. states and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.

Dynamical Spin Properties of Confined Fermi and Bose Systems in the Presence of Spin–Orbit Coupling

Due to the recent experimental progress, tunable spin-orbit (SO) interactions represent ideal candidates for the control of polarization and dynamical spin properties in both quantum wells and cold atomic systems. A detailed understanding of spin properties in SO coupled systems is thus a compelling prerequisite for possible novel applications or improvements in the context of spintronics and quantum computers. Here we analyze the case of equal Rashba and Dresselhaus couplings in both homogeneous and laterally confined two-dimensional systems. Starting from the single-particle picture and subsequently introducing two-body interactions we observe that periodic spin fluctuations can be induced and maintained in the system. Through an analytical derivation we show that the two-body interaction does not involve decoherence effects in the bosonic dimer, and, in the repulsive homogeneous Fermi gas it may be even exploited in combination with the SO coupling to induce and tune standing currents. By further studying the effects of a harmonic lateral confinement --a particularly interesting case for Bose condensates-- we evidence the possible appearance of non-trivial {\it spin textures}, whereas the further application of a small Zeeman-type interaction can be exploited to fine-tune the system polarizability.

Quantum dimer model for the pseudogap metal

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1/2, charge +e fermionic dimers. The model realizes a "fractionalized Fermi liquid" with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

High-temperature limit of the resonant Fermi gas

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a new formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range $R^*$ in the interaction. In the limit where the thermal wavelength $\lambda \ll R^*$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\lambda/|a| \gg 1$ and $R^*/\lambda \gg 1$, we estimate the value of the fourth virial coefficient at unitarity for $R^*=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density and entropy, as well as the spectral function at high temperatures.

Pair Correlations in the Two-Dimensional Fermi Gas

We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact for the normal state. Our calculated spectra are in qualitative agreement with recent photoemission measurements [M. Feld et al., Nature (London) 480, 75 (2011).], thus suggesting that the observed pairing gap is a feature of the high-temperature gas rather than being evidence of a pseudogap regime just above the superfluid transition temperature. We further argue that the strong pair correlations result from the fact that the crossover to bosonic dimers occurs at weaker interactions than previously assumed.

Vortex ring dynamics in trapped Bose-Einstein condensates

We use the time-dependent Gross-Pitaevskii equation to study the motion of a vortex ring produced by phase imprinting on an elongated cloud of cold atoms. Our approach models the experiments of Yefsah et al. [Nature (London) 499, 426 (2013)] on ${}^{6}$Li in the Bose-Einstein-condensate regime where the fermions are tightly bound into bosonic dimers. We find ring oscillation periods which are much larger than the period of the axial harmonic trap. Our results lend further strength to Bulgac et al.'s arguments (arXiv:1306.4266) that the ``heavy solitons'' seen in those experiments are actually vortex rings. We numerically calculate the periods of oscillation for the vortex rings as a function of interaction strength, trap aspect ratio, and minimum vortex ring radius. In the presence of axial anisotropies the rings undergo complicated internal dynamics where they break into sets of vortex lines, then later combine into rings. These structures oscillate with a similar frequency to simple axially symmetric rings.

Tonks-Girardeau and super-Tonks-Girardeau states of a trapped one-dimensional spinor Bose gas

A harmonically trapped ultracold 1D spin-1 Bose gas with strongly repulsive or attractive 1D even-wave interactions induced by a 3D Feshbach resonance is studied. The exact ground state, a hybrid of Tonks-Girardeau (TG) and ideal Fermi gases, is constructed in the TG limit of infinite even-wave repulsion by a spinor Fermi-Bose mapping to a spinless ideal Fermi gas. It is then shown that in the limit of infinite even-wave attraction this same state remains an exact many-body eigenstate, now highly excited relative to the collapsed generalized McGuire cluster ground state, showing that the hybrid TG state is completely stable against collapse to this cluster ground state under a sudden switch from infinite repulsion to infinite attraction. It is shown to be the TG limit of a hybrid super Tonks-Girardeau (STG) state which is metastable under a sudden switch from finite but very strong repulsion to finite but very strong attraction. It should be possible to create it experimentally by a sudden switch from strongly repulsive to strongly attractive interaction, as in the recent Innsbruck experiment on a spin-polarized bosonic STG gas. In the case of strong attraction there should also exist another STG state of much lower energy, consisting of strongly bound dimers, a bosonic analog of a recently predicted STG gas which is an ultracold gas of strongly bound bosonic dimers of fermionic atoms, but it is shown that this STG state cannot be created by such a switch from strong repulsion to strong attraction.

Universal ultracold collision rates for polar molecules of two alkali-metal atoms

Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).

Unitarity Schrödinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg–Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross–Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.

Bose-Fermi mixtures of self-assembled filaments of fermionic polar molecules

Fermionic polar molecules in deep one-dimensional (1D) optical lattices may form self-assembled filaments when the electric dipoles are oriented along the lattice axis. These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, which we discuss in detail for the simplest case of a three-well potential. We show that the interplay among filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers. We study the intriguing zero-temperature and finite-temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and we discuss possible methods to probe these chain mixtures.

Ground state of a tightly bound composite dimer immersed in a Fermi sea

In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order ${a}^{3}$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.

Collective mode damping and viscosity in a 1D unitary Fermi gas

We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant αζ = 0.38 in the viscosity ζ = αζℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.