Quantum Phases of a Two-Dimensional Dipolar Fermi Gas

Journal of Superconductivity and Novel Magnetism

We investigate the effects of exchange and correlation on the quasiparticle properties such as the self-energy, the manybody effective mass and the renormalization constant in a two-dimensional system of ultracold dipolar fermions with dipole moments aligned in the perpendicular direction to the plane. We use the G 0 W approximation along with the generalized random phase approximation, where the many-body effects have been incorporated in the effective interaction W through the Hubbard local-field factor. The many-body effective mass and the renormalization constant are reduced with the increase of coupling strength. We also study the effect of dipole-dipole interaction on the single-particle spectral function of the two dimensional dipolar Fermi liquid. We observe composite hole-zero sound excitation which is a bound state of quasiparticles with the collective mode (i.e. zero-sound) at intermediate and high coupling constants. These composite excitations are undamped at small wave vectors. Due to repulsion between quasiparticle and composite excitation resonances, we find a gap-like feature between quasiparticle and composite excitation dispersions at long wavelengths. Keywords Dipolar Fermi liquid • G 0 W • Effective mass • Renormalization constant • Spectral function • Composite quasiparticles 1 Introduction Ultracold atomic gases are classified as a member of relatively strongly correlated systems due to their longrange and anisotropic interactions [1, 2]. They have many interesting applications in chemical reactions, quantum information and novel quantum phase transitions [3-6]. Instabilities occur in dipolar quantum gases when interactions are sufficiently strong and attractive [7-9]. The long-range interaction leads to the emergence of a variety of quantum phases [2, 10, 11]. The many-body B.

The European Physical Journal D, 2012

We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the Hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule harmonic potential and discuss how its strength can be related to the real dipolar potential. However, to explore different structures with more than one molecule in each layer, we treat the repulsive harmonic strength as an independent variable in the problem. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. For the acoustic modes, our model predicts a smaller sound speed than one would naively get from expansion of the dipolar potential to second order around the origin. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers, and our model predicts how the breakup takes places. Lastly, we consider experimentally relevant regimes to observe the structures. The harmonic model considerd here predicts that for the multi-layer systems under current study chains with one molecule in each layer are always bound whereas two chains comprised of two molecules in each layer will not be bound. However, since realistic systems have external confinement prevention the molecules from escaping to infinity, we still expect the unstable modes to show up as resonances in the dynamics.

Physical Review A, 2011

We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical nondestructive detection scheme that enables in-situ observation of the creation and dissociation of the few-body complexes. A detailed description of the expected signal of such measurements is given using the numerically calculated wave functions of the bound states. We also discuss implications on the many-body physics of dipolar systems in tubular geometries, as well as experimental issues related to the external harmonic confinement along the tube and the prospect of applying an in-tube optical lattice to increase the effective dipole strength.

Physical Review B, 2021

We exploit the Quantum Cluster Variational Method (QCVM) to study the $J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other Mean Field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between $g = J_2/J_1$ , the temperature and the longitudinal and transverse external fields. Our results show that quantum fluctuations may change the order of the transition and induce a gap between the ferromagnetic and the stripe phases. Moreover, when both longitudinal and transverse fields are present, thermal fluctuations and quantum effects contribute to the appearance of a nematic phase.

Physical Review B, 2020

Motivated by recent experiments in fermionic polar gases, we study the non-equilibrium dynamics of two component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a spin-SU(2) symmetric fermionic Hamiltonian, by calculating experimentally accessible dynamical observables. To study the nonequilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons | ↑↓ 0 ↑↓ 0 ↑↓ 0 ↑↓ 0 ↑↓〉 and (ii) product state with singlons | ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ 〉. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization and the matrix-product state formalism, within experimentally relevant time scales. For the product state with doublons, we observe a delocalized to localized phase transition, by monitoring the decay of charge imbalance with time. For the product state with singlons, and considering strong enough disorde...

Physical Review A, 2013

We point out the possibility of occurring instabilities in Laughlin liquids of rotating dipolar fermions with zero thickness. Previously such a system was predicted to be the Laughlin liquid for filling factors ν ≥ 1/7. However, from intra-Landau-level excitations of the liquid in the single-mode approximation, the roton minima become negative and Laughlin liquids are unstable for ν ≤ 1/7. We then conclude that there are correlated Wigner crystals for ν ≤ 1/7.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2011

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Physical Review A, 2016

Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly, and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low temperature phase diagram by numerically solving the functional renormalization group flow equations and find a new density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.

Physical Review A, 2011

Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the different rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the p-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state are necessary to reach future precision goals. Finally, we consider the spectra in a deep 3D lattice and show how they give a great deal of information about static correlation functions, including all the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment.

Scientific reports, 2012

Recently, cold atomic Fermi gases with the large magnetic dipolar interaction have been laser cooled down to quantum degeneracy. Different from electric-dipoles which are classic vectors, atomic magnetic dipoles are quantum-mechanical matrix operators proportional to the hyperfine-spin of atoms, thus provide rich opportunities to investigate exotic many-body physics. Furthermore, unlike anisotropic electric dipolar gases, unpolarized magnetic dipolar systems are isotropic under simultaneous spin-orbit rotation. These features give rise to a robust mechanism for a novel pairing symmetry: orbital p-wave (L = 1) spin triplet (S = 1) pairing with total angular momentum of the Cooper pair J = 1. This pairing is markedly different from both the (3)He-B phase in which J = 0 and the (3)He-A phase in which J is not conserved. It is also different from the p-wave pairing in the single-component electric dipolar systems in which the spin degree of freedom is frozen.

Physical Review A, 2016

We study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum across this transition by using microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value.

Physical Review A, 2012

We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS theory approach that is most realiable at weak-coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecules in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low density limit and a paired superfluid (BCS) state in the high density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover, and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly-coupled dimer picture yield similar predictions for the parameters of the crossover regime. The BKT transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.

Physical Review A, 2016