Zero Temperature Thermodynamics of Asymmetric Fermi Gases at Unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one non-trivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the T=0 equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.Comment: 10 pages and 7 figures. (Minor changes to correspond with published version.

Potential-energy (BCS) to kinetic-energy (BEC)-driven pairing in the attractive Hubbard model

The BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experiment in cuprates. Phase coherence leads to the appearance of a collective Bogoliubov mode in the density-density correlation function and to the sharpening of the spectral function.Comment: 5 pages, 4 figure

Detection of Macroscopic Entanglement by Correlation of Local Observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.Comment: Although the index q was proposed for mixed states, it is also applicable to pure states, on which we fix minor bugs (that will be reported in PRL as erratum). The conclusions of the paper remain unchanged. (4 pages, no figures.

Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario

We act on the suggestion that an excitonic insulator state might separate---at very low temperatures---a semimetal from a semiconductor and ask for the nature of these transitions. Based on the analysis of electron-hole pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb attraction between both species, a continuous crossover between a BCS-like transition of Cooper-type pairs and a Bose-Einstein condensation of preformed tightly-bound excitons might be achieved in a solid-state system. The precursor of this crossover in the normal state might cause the transport anomalies observed in several strongly correlated mixed-valence compounds.Comment: 5 pages, 5 figures, substantially revised versio

Superconductor-insulator transition in Coulomb disorder

Superconductor-insulator transition driven by the decreasing concentration of electrons $n$ is studied in the case of the disorder potential created by randomly positioned charged impurities. Electrons and Cooper pairs (formed by an non-Coulomb attraction) nonlinearly screen the random potential of impurities. Both electrons and Cooper pairs can be delocalized or localized in the resulting self-consistent potential. The border separating the superconductor and insulator phases in the plane of the concentration of electrons and the length of the Cooper pair is found. For a strong disorder the central segment of this border follows the BEC-BCS crossover line defined for a clean sample.Comment: 4.5 pages, introduction rewritten, a dozen of references added, 2D case adde

One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons

We study a ultra-cold and dilute superfluid Bose-Fermi mixture confined in a strictly one-dimensional atomic waveguide by using a set of coupled nonlinear mean-field equations obtained from the Lieb-Liniger energy density for bosons and the Gaudin-Yang energy density for fermions. We consider a finite Bose-Fermi inter-atomic strength g_{bf} and both periodic and open boundary conditions. We find that with periodic boundary conditions, i.e. in a quasi-1D ring, a uniform Bose-Fermi mixture is stable only with a large fermionic density. We predict that at small fermionic densities the ground state of the system displays demixing if g_{bf}>0 and may become a localized Bose-Fermi bright soliton for g_{bf}<0. Finally, we show, using variational and numerical solution of the mean-field equations, that with open boundary conditions, i.e. in a quasi-1D cylinder, the Bose-Fermi bright soliton is the unique ground state of the system with a finite number of particles, which could exhibit a partial mixing-demixing transition. In this case the bright solitons are demonstrated to be dynamically stable. The experimental realization of these Bose-Fermi bright solitons seems possible with present setups.Comment: 11 pages, 11 figure

Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators

We report the observation of discrete displacement of nanomechanical oscillators with gigahertz-range resonance frequencies at millikelvin temperatures. The oscillators are nanomachined single-crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. With this novel design, femtometer-level displacement of the frequency-determining element is amplified into collective motion of the entire micron-sized structure. The observed discrete response possibly results from energy quantization at the onset of the quantum regime in these macroscopic nanomechanical oscillators.Comment: 4 pages, two-column format. Related papers available at http://nano.bu.edu

Application of the Feshbach-resonance management to a tightly confined Bose-Einstein condensate

We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schroedinger equation (NPSE) for BEC trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.Comment: Physical Review A, in pres

Dynamics of Two-Level System Interacting with Random Classical Field

The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time.Comment: 5 page

Macroscopic entanglement of many-magnon states

We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge whether such superposition is hidden in a general state, we use an essentially unique index p: A pure state is macroscopically entangled if p=2, whereas it may be entangled but not macroscopically if p<2. This index is directly related to the stability of the state. We calculate the index p for various states in which magnons are excited with various densities and wavenumbers. We find macroscopically entangled states (p=2) as well as states with p=1. The former states are unstable in the sense that they are unstable against some local measurements. On the other hand, the latter states are stable in the senses that they are stable against local measurements and that their decoherence rates never exceed O(N) in any weak classical noises. For comparison, we also calculate the von Neumann entropy S(N) of a subsystem composed of N/2 spins as a measure of bipartite entanglement. We find that S(N) of some states with p=1 is of the same order of magnitude as the maximum value N/2. On the other hand, S(N) of the macroscopically entangled states with p=2 is as small as O(log N)<< N/2. Therefore, larger S(N) does not mean more instability. We also point out that these results are analogous to those for interacting many bosons. Furthermore, the origin of the huge entanglement, as measured either by p or S(N), is discussed to be due to the spatial propagation of magnons.Comment: 30 pages, 5 figures. The manuscript has been shortened and typos have been fixed. Data points of figures have been made larger in order to make them clearly visibl