Oct 2015

Oct 5-Oct 9 Max, Oct 12-Oct 16 Bo Liu, Oct 19-Oct 23 Haiyuan Zou, Oct 26-Oct 30 Ahmet Keles

Oct 26-30


Magnetic Impurity in a Tonks Gas of Fermions
Deping Zhang, Wei Chen, Hui Zhai
arXiv:1510.08303
In this letter we consider a magnetic impurity in a one-dimensional spin-1/2 Fermi gas with infinitely strong repulsive interaction between fermions. We rigorously prove that, independent of whether the magnetic coupling between impurity and fermions is ferromagnetic or anti-ferromagnetic, the ground state is always a fully polarized ferromagnetic state for the itinerant fermions. This ferromagnetism can be understood as a cooperative effect of avoiding frustration of magnetic coupling during fermion hopping and the large spin degeneracy of a fermion Tonks gas. By numerically diagonalizing a finite size system, we show that the spin gap first increases linearly with magnetic coupling strength in the weak coupling regime, while decreases in the strong coupling regime. Our results show that a magnetic impurity in a strongly correlated gas can exhibit effect different from the Kondo effect as in a weakly correlated Fermi liquid.

Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
David F. Mross, Jason Alicea, Olexei I. Motrunich
arXiv:1510.08455 
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED$_3$ scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and $N = 2$ QED$_3$.


Topological nature of nonlinear optical effects in solids
Takahiro Morimoto, Naoto Nagaosa
arXiv:1510.08112
There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by the nonlinear susceptibilities $\chi$'s, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under a electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. Here, we theoretically show by using the Floquet formalism that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. It is found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a new route to design the nonlinear optical materials.

Three Lectures On Topological Phases Of Matter
Edward Witten
arXiv:1510.07698 
These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological phases of matter that can be understood in terms of free fermions and band theory. They also contain an introduction to the fractional quantum Hall effect from the point of view of effective field theory.


Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
Julien Dujardin, Thomas Engl, Peter Schlagheck
arXiv:1510.06857 
We study the transport of an interacting Bose--Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to the diagonal approximation of a semiclassical van Vleck-Gutzwiller representation of this many-body transport process. We also argue that semiclassical corrections beyond this diagonal approximation are vanishing under disorder average, thus confirming the validity of the truncated Wigner method in this context. Numerical calculations show that, while for weak atom-atom interaction strength Anderson localization is preserved with a slight modification of the localization length, for larger interaction strenghts a crossover to a delocalized regime exists due to inelastic scattering. In this case, the transport is fully incoherent.
Oct 23

arXiv:1510.06403 [pdf, other]
Title: A Quantum Dipolar Spin Liquid
Authors: Norman Y. Yao, Michael P. Zaletel, Dan M. Stamper-Kurn, Ashvin Vishwanath
Comments: 11 pages, 8 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Gases (cond-mat.quant-gas)
Quantum spin liquids are a new class of magnetic ground state in which spins are quantum mechanically entangled over macroscopic scales. Motivated by recent advances in the control of polar molecules, we show that dipolar interactions between S=1/2 moments stabilize spin liquids on the triangular and kagome lattices. In the latter case, the moments spontaneously break time-reversal, forming a chiral spin liquid with robust edge modes and emergent semions. We propose a simple route toward synthesizing a dipolar Heisenberg antiferromagnet from lattice-trapped polar molecules using only a single pair of rotational states and a constant electric field.
Oct 22

arXiv:1510.06087 [pdf, other]
Title: Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
Authors: Lijun Yang, Xiaoling Cui
Comments: 11 pages, 7 figures
Subjects: Quantum Gases (cond-mat.quant-gas)
We present a general form of the effective spin-chain model for strongly interacting atomic gases with an arbitrary spin in the one-dimensional(1D) traps. In particular, for high-spin systems the atoms can collide in multiple scattering channels, and we find that the resulted form of spin-chain model generically follows the same structure as that of the interaction potentials. This is a unified form working for any spin, statistics (Bose or Fermi) and confinement potentials. We adopt the spin-chain model to reveal both the ferromagnetic(FM) and anti-ferromagnetic(AFM) magnetic orders for strongly interacting spin-1 bosons in 1D traps. We further show that by adding the spin-orbit coupling, the FM/AFM orders can be gradually destroyed and eventually the ground state exhibits universal spin structure and contacts that are independent of the strength of spin-orbit coupling.

Oct 21
arXiv:1510.05815 [pdf, other]
Title: Emergent Gauge Field for a Chiral Bound State on Curved Surface
Authors: Zhe-Yu Shi, Hui Zhai
Comments: 5 pages, 3 figures, 1 appendix
Subjects: Quantum Gases (cond-mat.quant-gas)
In this letter we show that there emerges a gauge field for two attractive particles moving on a curved surface when they form a chiral bound state. By solving a two-body problem on a sphere, we show explicitly that the center-of-mass wave functions of such deeply bound states are monopole harmonics instead of spherical harmonics. This indicates that the bound state experiences a gauge field identical to a magnetic monopole at the center of the sphere, with the monopole charge equal to the quantized relative angular momentum of this bound state. We show that this emergent gauge field is due to the coupling between the center-of-mass and the relative motion on curved surfaces. Our results can be generalized to an arbitrary curved surface where the emergent magnetic field is exactly the local Gaussian curvature. This result establishes an intriguing connection between space curvature and gauge field, paves an alternative way to engineer topological state with space curvature, and may be observed in cold atom system
Oct 20

arXiv:1510.05121 [pdf, ps, other]
Title: Anderson localization in optical lattices with correlated disorder
Authors: Elisa Fratini, Sebastiano Pilati
Comments: 9 pages, 7 figures
Subjects: Quantum Gases (cond-mat.quant-gas)
We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models which take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases measured in the moderate interaction regime.

Oct 19
arXiv:1510.04934 [pdf, ps, other]
New theoretical approaches to Bose polarons
Fabian Grusdt, Eugene Demler
Comments: 79 pages, 19 figures. Based on a course presented at the International School of Physics Enrico Fermi, Varenna, Italy 2014
Subjects: Quantum Gases (cond-mat.quant-gas); Other Condensed Matter (cond-mat.other)

The Fr\"ohlich polaron model describes a ubiquitous class of problems concerned with understanding properties of a single mobile particle interacting with a bosonic reservoir. Originally introduced in the context of electrons interacting with phonons in crystals, this model found applications in such diverse areas as strongly correlated electron systems, quantum information, and high energy physics. In the last few years this model has been applied to describe impurity atoms immersed in Bose-Einstein condensates of ultracold atoms. The tunability of microscopic parameters in ensembles of ultracold atoms and the rich experimental toolbox of atomic physics should allow to test many theoretical predictions and give us new insights into equilibrium and dynamical properties of polarons. In these lecture notes we provide an overview of common theoretical approaches that have been used to study BEC polarons, including Rayleigh-Schr\"odinger and Green's function perturbation theories, self-consistent Born approximation, mean-field approach, Feynman's variational path integral approach, Monte Carlo simulations, renormalization group calculations, and Gaussian variational ansatz. We focus on the renormalization group approach and provide details of analysis that have not been presented in earlier publications. We show that this method helps to resolve striking discrepancy in polaron energies obtained using mean-field approximation and Monte Carlo simulations. We also discuss applications of this method to the calculation of the effective mass of BEC polarons. As one experimentally relevant example of a non-equililbrium problem we consider Bloch oscillations of Bose polarons and demonstrate that one should find considerable deviations from the commonly accepted phenomenological Esaki-Tsu model. We review which parameter regimes of Bose polarons can be achieved in various atomic mixtures.


Oct 16

1. arXiv:1510.04401 [pdf, ps, other]
Strong-coupling corrections to spin susceptibility in the BCS-BEC crossover regime of a superfluid Fermi gas
H. Tajima, R. Hanai, Y. Ohashi

We theoretically investigate the uniform spin susceptibility χ in the superfluid phase of an ultracold Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In our previous paper [H. Tajima, {\it et. al.}, Phys. Rev. A {\bf 89}, 033617 (2014)], including pairing fluctuations within an extended T-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where χ is anomalously suppressed even in the normal state near the superfluid phase transition temperature Tc. In this paper, we extend this work to the superfluid phase below Tc, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA χ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below Tc in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a 6Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.


2. arXiv:1510.04311 (cross-list from math-ph) [pdf, other]
The one body density matrix of a quantum bright soliton from the coordinate Bethe ansatz
A. Ayet, J. Brand

In this article we compute the one body density matrix of a solitonic state for a one-dimensional system of bosons interacting via an attractive contact potential. The eigenstates of such a system can be computed exactly using the Bethe ansatz, and we construct a soliton (characterized by a peak of density in space) using a proper superposition of those. We expect this state to behave differently than the solution of the Gross-Pitaevskii equation, defining it as a quantum soliton. The full density matrix is computed using the coordinate version of the Bethe ansatz. We develop a numerical implementation of the relevant integrals based on a diagrammatic representation. We find that the diagonal elements of the matrix follow a Bell- shaped distribution, confirming that our state is a soliton, and that the whole matrix is localized around the diagonal. We then study, as an application of our formalism, the evolution of the highest eigenvalue of the matrix, the condensed fraction of the soliton, upon increasing of the width of the state in momentum space, and find that it saturates to a value very close to one.

Oct 15
1. arXiv:1510.04054 [pdf, other]
Bichromatic State-Insensitive Trapping of Cold 133Cs-87Rb Atomic Mixtures
M.M. Metbulut, F. Renzoni

We investigate simultaneous state-insensitive trapping of a mixture of two different atomic species, Caesium and Rubidium. The magic wavelengths of the Caesium and Rubidium atoms are different, 935.6 nm and 789.9 nm respectively, thus single-frequency simultaneous state-insensitive trapping is not possible. We thus identify bichromatic trapping as a viable approach to tune the two magic wavelengths to a common value. Correspondingly, we present several common magic wavelength combinations appropriate for simultaneous state-insensitive trapping of the two atomic species.




2. arXiv:1510.03851 [pdf, other]
Spin liquid phases of Mott insulating ultracold bosons
Todd C. Rutkowski, Michael J. Lawler

Mott insulating ultracold gases posses a unique whole-atom exchange interaction which enables large quantum fluctuations between the Zeeman sublevels of each atom. By strengthening this interaction---either through the use of large-spin atoms, or by tuning the particle-particle interactions via optical Feshbach resonance---one may enhance fluctuations and facilitate the appearance of the long sought-after quantum spin liquid phase---all in the highly tunable environment of cold atoms. To illustrate the relationship between the spin magnitude, interaction strength, and resulting magnetic phases, we present and solve a mean field theory for bosons optically confined to the one particle-per-site Mott state, using both analytic and numerical methods. We find on a square lattice with bosons of hyperfine spin f>2, that making the repulsive s-wave scattering length through the singlet channel small---relative to the higher-order scattering channels---accesses a short-range resonating valence bond (s-RVB) spin liquid phase.

Oct 14

1. arXiv:1510.03619 (cross-list from quant-ph) [pdf, ps, other]
Exploring the few- to many-body crossover using cold atoms in one dimension
Nikolaj Thomas Zinner

Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.

Oct 13
1. arXiv:1510.03369 [pdf, ps, other]
Strongly interacting Bose-Fermi mixtures in one dimension
Haiping Hu, Liming Guan, Shu Chen

We study one-dimensional strongly interacting Bose-Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the one-dimensional Bose-Fermi gas with equal boson-boson and boson-fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose-Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized noninteracting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose-Fermi configurations and are sensitive to the anisotropy of interactions.




Oct 6

arXiv:1510.01306 [pdf, other]

Second Sound in Ultracold Atomic Gases
Lev P. Pitaevskii, Sandro Stringari
Comments: 26 pages, 9 figures
Subjects: Quantum Gases (cond-mat.quant-gas)

We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.