Bose Fermi Research Articles

Deformation dependence of breathing oscillations in Bose–Fermi mixtures at zero temperature

We study the breathing oscillations in Bose–Fermi mixtures in axially symmetric deformed traps of prolate, spherical and oblate shapes, and clarify the deformation dependence of the frequencies and the characteristics of the collective oscillations. The collective oscillations of the mixtures in the deformed traps are calculated using a scaling method. We obtain for the greatly deformed prolate and oblate limits and the spherical limit analytical expressions for the collective frequencies. The full calculation shows that the collective oscillations become consistent with the frequencies obtained analytically when the system is deformed into prolate or oblate regions. Complicated changes of the oscillation characteristics are shown to occur in the transcendental regions around the spherically deformed region. We find that these critical changes in oscillation characteristics are explained by the level crossing behaviors of the intrinsic oscillation modes. Approximate expressions are obtained for the level crossing points that determine the transcendental regions. We also compare the results from the scaling method with those from the dynamical approach.

Collapse and revivals for systems of short-range phase coherence

We predict the existence of novel collapse and revival oscillations that are a distinctive signature of the short-range off-diagonal coherence. Starting with an atomic Mott state in a one-dimensional optical lattice, suddenly raising the lattice depth freezes particle–hole pairs in place and induces phase oscillations. The peak of the quasi-momentum distribution, revealed through time-of-flight interference, oscillates between a maximum occupation at zero quasi-momentum (the Γ point) and the edge of the Brillouin zone. We show that the population enhancements at the edge of the Brillouin zone are due to short-range coherence due to particle–hole pairs, and we find similar effects for fermions and Bose–Fermi mixtures in a lattice. Our results open a new dynamic probe for strongly correlated many-body states with short-range phase coherence that is distinct from the matter–wave collapse and revivals previously observed in the long-range coherent superfluid regime.

Thermodynamic Equivalent between Noninteracting Bose and Fermi Gas in Metallic Carbon Nanotubes

The equivalent between Bose and Fermi ideal gases is usually taken in high temperature limit only. Recently, there has been considerable interest in surprising thermodynamic ``equivalences'' between certain ideal Bose and spineless Fermi gas systems in lower temperature. In this work, we follow that idea to investigate the quasi one-dimensional system of metallic carbon nanotubes. Due to the linear dispersion law, the non-interacting Bose and Fermi gases in metallic carbon nanotubes are equivalent. This equivalence could be applied to the gas systems of exciton photon (Bose particles) and electron hole (Fermi particles) in metallic carbon nanotubes.

A bosonized formulation of the supersymmetric quantum mechanics for shape-invariant potential systems

We consider the minimal bosonization realization of supersymmetric shape-invariant systems where generalized supercharge operators are constructed using the partner supersymmetric operators, the parameter potential translation formalism and the reflection operator. We obtain the solution of the eigenvalue equation and study the quantum dynamics of the supersymmetric system including terms in the Hamiltonian which are constructed using the combination of the bosonized supercharge operators. The connections between the bosonized supersymmetric formalism, the Bose–Fermi transformation and the generalization of the -deformed Heisenberg algebra are discussed. As an illustration, we apply the generalized formalism for the case of the trigonometric Rosen–Morse potential.

Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy

In this paper we develop high order asymptotic preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi (J Comput Phys 259:402–420, 2014) where asymptotic preserving exponential Runge–Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes achieve high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen number ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas.

Optimized Degenerate Bose—Fermi Mixture in Microgravity: DSMC Simulation of Sympathetic Cooling

Applying the direct simulation Monte Carlo (DSMC) method developed for the cold atom system, we explore the possibility of a high-efficiency sympathetic cooling process between 87Rb and 40K without gravitational force in an optical trap. The relation between the pre-cooling of Bosons and the sympathetic cooling efficiency is also studied. We find that the absence of gravitational force is beneficial to the process of sympathetic cooling. Furthermore, an inefficient pre-cooling process will in fact hamper the creation of Fermi degenerate gases. This suggests the advantages of sympathetic cooling in microgravity.

The coherence of boson–fermion mixed system

In this paper, we investigate the quantum coherence of Bose–Fermi mixtures of ultracold dipolar particles trapped in a three-site Bose–Fermi–Hubbard model. We show that the interplay between the boson–boson on-site interaction, boson–fermion on-site interaction, and boson–fermion inter-site dipole–dipole interaction (DDI) results in interesting coherence characters. When boson–boson on-site interaction is present, the resonance character of coherence against both boson–fermion DDI and boson–fermion on-site interaction emerges, the coherence of the system can be enhanced at certain values of boson–fermion on-site interaction and boson–fermion DDI. DDI of fermion–fermion affects the coherence weak and the phase coherence decreases monotonically for all the values of fermion–fermion DDI. The obtained coherent characters are further confirmed within the variational analyzing of the ground state energy.

Persistent Current in Bose–Fermi Mixture on a Ring

Persistent current of a Bose–Fermi mixture confined in a ring geometry threaded by a synthesized magnetic field is theoretically investigated. Numerical simulations are performed to study the role of boson–boson interactions and that of boson–fermion interactions on the transport property. The result shows that the boson–fermion interactions enhance the phase stiffness, which is a measure of the magnitude of the persistent current, more for the bosons than for the fermions. The same behavior is verified by a renormalization group calculation. The difference in the stiffness enhancement can be attributed to the difference in the localization property of the bosons and the fermions in one dimension.

Bose–Fermi symmetry in the odd–even gold isotopes

Abstract In this work the results of an in-beam experiment on 195 Au are presented, yielding new spins, multipole mixing ratios, and new low-lying states essential for the understanding of this nucleus. The positive-parity states from this work together with compiled data from the available literature for 185–199 Au are compared to Interacting Boson Fermion Model calculations employing the Spin(6) Bose–Fermi symmetry. The evolution of the parameters for the τ splitting and the J splitting reveals a smooth behavior. Thereby, a common description based on the Bose–Fermi symmetry is found for 189–199 Au. Furthermore, the calculated E 2 transition strengths are compared to experimental values with fixed effective boson and fermion charges for all odd–even gold isotopes, emphasizing that the Spin(6) Bose–Fermi symmetry is valid for the gold isotopes.

Exact Analysis of a One-Dimensional Weakly Repulsive Bose-Fermi Mixture

We study a one-dimensional system of Bose–Fermi mixture with repulsive \(\delta \)-function interactions using the nested Bethe ansatz method. This system is integrable when the masses of bonsons and fermions are equal and the interactions between Bose–Bose and Bose–Fermi particles are equal. By use of the power series expansion method, the Surtherland integral equation, which describes the ground state properties, is solved analytically in the weak coupling regime. Physical quantities such as the ground state energy, the sound velocity, and the chemical potential are explicitly expressed in terms of a dimensionless interaction parameter \(\gamma =c/D\) and boson fraction \(\alpha =N_{b}/N\), where \(c\) is the interaction strength, \(D\) is the number density, \(N_{b}\) is the number of bosons, and N is the total number of particles.

The structure of 193Au within the Interacting Boson Fermion Model

Abstract A γγ angular correlation experiment investigating the nucleus 193Au is presented. In this work the level scheme of 193Au is extended by new level information on spins, multipolarities and newly observed states. The new results are compared with theoretical predictions from a general Interacting Boson Fermion Model (IBFM) calculation for the positive-parity states. The experimental data is in good agreement with an IBFM calculation using all proton orbitals between the shell closures at Z = 50 and Z = 126 . As a dominant contribution of the d 3 / 2 orbital to the wave function of the lowest excited states is observed, a truncated model of the IBFM using a Bose–Fermi symmetry is applied to the describe 193Au. Using the parameters of a fit performed for 193Au, the level scheme of 192Pt, the supersymmetric partner of 193Au, is predicted but shows a too small boson seniority splitting. We obtained a common fit by including states observed in 192Pt. With the new parameters a supersymmetric description of both nuclei is established.

Weyl spin-orbit-coupling-induced interactions in uniform and trapped atomic quantum fluids

We establish through analytical and numerical studies of thermodynamic quantities for noninteracting atomic gases that the isotropic three-dimensional spin-orbit coupling, the Weyl coupling, induces interaction which counters "effective" attraction (repulsion) of the exchange symmetry present in zero-coupling Bose (Fermi) gas. The exact analytical expressions for the grand potential and hence for several thermodynamic quantities have been obtained for this purpose in both uniform and trapped cases. It is enunciated that many interesting features of spin-orbit coupled systems revealed theoretically can be understood in terms of coupling-induced modifications in statistical interparticle potential. The temperature-dependence of the chemical potential, specific heat and isothermal compressibility for a uniform Bose gas is found to have signature of the incipient Bose-Einstein condensation in very weak coupling regime although the system does not really go in the Bose-condensed phase. The transition temperature in harmonically trapped case decreases with increase of coupling strength consistent with the weakening of the statistical attractive interaction. Anomalous behavior of some thermodynamic quantities, partly akin to that in dimensions less than two, appears for uniform fermions as soon as the Fermi level goes down the Dirac point on increasing the coupling strength. It is suggested that the fluctuation-dissipation theorem can be utilized to verify anomalous behaviors from studies of long-wavelength fluctuations in bunching and antibunching effects.

Topological properties of one-dimensional hardcore Bose—Fermi mixture

We study the topological properties of a one-dimensional (1D) hardcore Bose—Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose—Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.

Mott Transition of Bose–Fermi Mixtures in Optical Lattices Induced by Attractive Interactions

We numerically studied Bose–Fermi mixtures in one-dimensional optical lattices using a modified Bose–Fermi–Hubbard model. We derived the modified Bose–Fermi–Hubbard model in a tight-binding approximation, retaining the terms which were usually ignored. Quantum Monte Carlo simulations were then performed on the model to demonstrate a bosonic Mott transition of the Bose–Fermi mixtures. This gives another scenario of the fermion-induced decoherence of bosons observed in some experiments.

Visibility pattern of Bose–Fermi mixtures in one-dimensional incommensurate lattices

We performed numerical simulations to demonstrate localization phenomena of Bose–Fermi mixture systems on incommensurate optical lattices by changing Bose–Bose and Bose–Fermi interactions. Visibility patterns of the bosons were measured to observe bosonic coherence in various selections of the interaction parameters. We found that the coherence was enhanced with repulsive Bose–Fermi interactions. It was also enhanced with attractive Bose–Fermi interactions but only in certain conditions. The enhancement by repulsive interactions and that by attractive interactions occurred with different mechanisms.

Supersolid in Bose–Bose–Fermi mixtures subjected to a square lattice

Two-component Bose condensates with repulsive interaction are stable when g1g2 > g212 is satisfied. By tuning the interactions, we show that the instability corresponding to Bose–Bose phase separation always happens at a higher temperature than that corresponding to Bose–Fermi phase separation. Moreover, we find the transition temperatures TDW of both the supersolid and coherence peak at kDW are enhanced in the mixtures studied. These will make the observation of a supersolid in experiments more reachable.

Longitudinal and transverse breathing oscillations in Bose–Fermi mixtures of Yb atoms at zero temperature in the largely prolate deformed traps

We study the breathing oscillations in Bose–Fermi mixtures of Yb isotopes in the largely prolate deformed trap, which are realized by the Kyoto group. We take three combinations of the Yb isotopes, 170Yb–171Yb , 170Yb–173Yb and 174Yb–173Yb , whose boson–fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. The collective oscillations in the deformed trap are calculated in the dynamical time-development approach, which is formulated with the time-dependent Gross–Pitaevskii and Vlasov equations. We analyse the results with the intrinsic oscillation modes of the deformed system, obtained in the scaling method, and show that the damping and forced-oscillation effects of the intrinsic modes explain time-variation behaviour of oscillations, especially, in the fermion transverse mode.

Bose–Fermi duality and entanglement entropies

Entanglement (Rényi) entropies of spatial regions are a useful tool for characterizing the ground states of quantum field theories. In this paper we investigate the extent to which these are universal quantities for a given theory, and to which they distinguish different theories, by comparing the entanglement spectra of the massless Dirac fermion and the compact free boson in two dimensions. We show that the calculation of Rényi entropies via the replica trick for any orbifold theory includes a sum over orbifold twists on all cycles. In a modular-invariant theory of fermions, this amounts to a sum over spin structures. The result is that the Rényi entropies respect the standard Bose–Fermi duality. Next, we investigate the entanglement spectrum for the Dirac fermion without a sum over spin structures, and for the compact boson at the self-dual radius. These are not equivalent theories; nonetheless, we find that (1) their second Rényi entropies agree for any number of intervals, (2) their full entanglement spectra agree for two intervals, and (3) the spectrum generically disagrees otherwise. These results follow from the equality of the partition functions of the two theories on any Riemann surface with imaginary period matrix. We also exhibit a map between the operators of the theories that preserves scaling dimensions (but not spins), as well as OPEs and correlators of operators placed on the real line. All of these coincidences can be traced to the fact that the momentum lattice for the bosonized fermion is related to that of the self-dual boson by a 45° rotation that mixes left- and right-movers.

Elastic collision properties of ultracold calcium atoms

The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms and those values are very sensitive to small changes of the reduced mass. These results rely on a recent measurement of the 40Ca–40Ca scattering length in a Bose condensate of 40Ca and making small corrections to a Born–Oppenheimer potential that reproduces all known spectroscopic data. We find that the 42Ca isotope has a scattering length of 417.5a0 and, thus, can be Bose condensed. The large interisotope scattering length between 43Ca and 42Ca indicates that sympathetic cooling of 43Ca by 42Ca atoms will be effective, and 43Ca–42Ca can also be used to study isotopic Bose–Fermi mixtures. We also predict a d-wave shape resonance for collisions of fermionic 43Ca atoms in different spin components.

Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states that support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.