Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Quantum critical behavior near a density-wave instability in an isotropic fermi liquid

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) approximately Sigma(k) to Sigma(k,omega) approximately Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.     

Stripes, topological order, and deconfinement in a planar t-Jz model

We determine the quantum phase diagram of a two-dimensional bosonic t-Jz model as a function of the lattice anisotropy gamma, using a quantum Monte Carlo loop algorithm. We show analytically that the low-energy sectors of the bosonic and the fermionic t-Jz models become equivalent in the limit of small gamma. In this limit, the ground state represents a static stripe phase characterized by a nonzero value of a topological order parameter. This phase remains up to intermediate values of gamma, where there is a quantum phase transition to a phase-segregated state or a homogeneous superfluid with dynamic stripe fluctuations depending on the ratio Jz/t.     

Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

Can supersymmetric theories be bosonized?

We investigate the possibility of transforming supersymmetric theories into pure;y fermionic or bosonic forms. The supersymmetric sine-Gordon lagrangian is rewritten in a purely fermionic form, and the Fermi equivalent of the original supersymmetry transformation is derived. This transformation represents an invariance only at the quantum level, when the effects of the chiral anomaly have been taken into account. When supersymmetric theories are written in purely bosonic forms, a non-local bosonic transformation takes place of the supersymmetry transformation. In both cases the supersymmetry algebra, as realized on the fields, is lost.     

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.     

Atomic four-wave mixing: fermions versus bosons

We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as "Bose enhancement."     

Collisional stability of fermionic Feshbach molecules

Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resonance.     

Fermi-Bose quantum degenerate 40K-87Rb mixture with attractive interaction

We report on the achievement of simultaneous quantum degeneracy in a mixed gas of fermionic 40K and bosonic 87Rb. Potassium is cooled to 0.3 times the Fermi temperature by means of an efficient thermalization with evaporatively cooled rubidium. Direct measurement of the collisional cross-section confirms a large interspecies attraction. This interaction is shown to affect the expansion of the Bose-Einstein condensate released from the magnetic trap, where it is immersed in the Fermi sea.     

Quantum simulation of quantum field theories in trapped ions

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Degenerate Bose-Fermi mixture of metastable atoms

We report the observation of simultaneous quantum degeneracy in a dilute gaseous Bose-Fermi mixture of metastable atoms. Sympathetic cooling of helium-3 (fermion) by helium-4 (boson), both in the lowest triplet state, allows us to produce ensembles containing more than 10(6) atoms of each isotope at temperatures below 1 microK, and achieve a fermionic degeneracy parameter of T/TF = 0.45. Because of their high internal energy, the detection of individual metastable atoms with subnanosecond time resolution is possible, permitting the study of bosonic and fermionic quantum gases with unprecedented precision. This may lead to metastable helium becoming the mainstay of quantum atom optics.     

Quantum degenerate two-species fermi-fermi mixture coexisting with a bose-einstein condensate

We report on the generation of a quantum degenerate Fermi-Fermi mixture of two different atomic species. The quantum degenerate mixture is realized employing sympathetic cooling of fermionic 6Li and 40K gases by an evaporatively cooled bosonic 87Rb gas. We describe the combination of trapping and cooling methods that proved crucial to successfully cool the mixture. In particular, we study the last part of the cooling process and show that the efficiency of sympathetic cooling of the 6Li gas by 87Rb is increased by the presence of 40K through catalytic cooling. Because of the differing physical properties of the two components, the quantum degenerate 6Li-40K Fermi-Fermi mixture is an excellent candidate for a stable, heteronuclear system allowing the study of several so far unexplored types of quantum matter.     

轴对称黑洞的量子统计熵

避开了求解黑洞背景下波动方程的因难,应用量子统计方法,通过应用在量子引力中、由广义测不准关系得出的新态密度方程,直接求解轴对称Kerr黑洞背景下玻色场和费米场的配分函数.然后,在视界附近计算黑洞背景下玻色场和费米场的熵.得到用收敛级数表达的黑洞熵.在计算中不存在用brick wall模型计算黑洞熵时出现的发散项和小质量近似,使人们对非球对称时空中黑洞的统计熵有更深入的认识. 关键词： 量子统计 非球对称时空 广义测不准关系 黑洞熵     

Metal to Orthogonal Metal Transition

Orthogonal metal is a new quantum metallic state that conducts electricity but acquires no Fermi surface(FS)or quasiparticles, and hence orthogonal to the established paradigm of Landau's Fermi-liquid(FL). Such a state may hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL, i.e., dubbed non-Fermi-liquid(nFL), ranging from the Cu-and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to fully understand such an exotic state of matter, at least theoretically, one would like to construct a lattice model and to solve it with unbiased quantum many-body machinery. Here we achieve this goal by designing a 2D lattice model comprised of fermionic and bosonic matter fields coupled with dynamic Z_2 gauge fields, and obtain its exact properties with sign-free quantum Monte Carlo simulations. We find that as the bosonic matter fields become disordered, with the help of deconfinement of the Z_2 gauge fields, the system reacts with changing its nature from the conventional normal metal with an FS to an orthogonal metal of n FL without FS and quasiparticles and yet still responds to magnetic probe like an FL. Such a quantum phase transition from a normal metal to an orthogonal metal, with its electronic and magnetic spectral properties revealed, is calling for the establishment of new paradigm of quantum metals and their transition with conventional ones.     

Ultracold Li + Li2 collisions: bosonic and fermionic cases

We have carried out quantum dynamical calculations of vibrational quenching in Li + Li(2) collisions for both bosonic (7)Li and fermionic (6)Li. These are the first ever such calculations involving fermionic atoms. We find that for the low initial vibrational states considered here (v < or = 3), the quenching rates are not suppressed for fermionic atoms. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.     

Superfluidity near phase separation in Bose-Fermi mixtures

We study the transition to fermion pair superfluidity in a mixture of interacting bosonic and fermionic atoms. The fermion interaction induced by the bosons and the dynamical screening of the condensate phonons due to fermions are included using the nonperturbative Hamiltonian flow equations. We determine the bosonic spectrum near the transition towards phase separation and find that the superfluid transition temperature may be increased substantially due to phonon damping.     

Observation of resonance condensation of fermionic atom pairs

We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic 40K atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field Feshbach resonance is used to control the atom-atom interactions. The location of this resonance is precisely determined from low-density measurements of molecule dissociation. In order to search for condensation on either side of the resonance, we introduce a technique that pairwise projects fermionic atoms onto molecules; this enables us to measure the momentum distribution of fermionic atom pairs. The transition to condensation of fermionic atom pairs is mapped out as a function of the initial atom gas temperature T compared to the Fermi temperature T(F) for magnetic-field detunings on both the BCS and BEC sides of the resonance.