We analytically study the expansion of a Bose-Einstein condensate in a ring-shaped trap with an increasing central radius. The evolution of the ground state is described using a scaling transform. Additionally, the dynamics of excited azimuthal modes
over the varying ground state is analyzed through a generalization of the Bogoliubov-de Gennes approach. Our results explain some of the features observed in recent experiments focused on testing the applicability of the system as a parallel of cosmological inflationary models. The radial dynamics, which corresponds to the inflaton field of the cosmological counterpart, is analytically characterized: The expansion is found to induce the oscillatory displacement of the condensate as well as the coupled variation of the radial and vertical widths. Our findings account also for the observed redshift and emergence of the Hubble friction in the evolution of initially-prepared azimuthal modes. Our description, which traces the role of the different components of the setup in the expansion, enhances the controllability, and, therefore, the potential of the system as a ground for emulating the inflationary dynamics of cosmological models.
We present a theoretical study on the origin of some findings of recent experiments on sonic analogs of gravitational black holes. We focus on the realization of a black-hole lasing configuration, where the conclusive identification of stimulated Haw
king radiation requires dealing with the implications of the nonstationary character of the setup. To isolate the basic mechanisms responsible for the observed behavior, we use a toy model where nonstationarity can be described in terms of departures from adiabaticity. Our approach allows studying which aspects of the characterization of black-hole lasing in static models are still present in a dynamical scenario. In particular, variations in the role of the dynamical instabilities can be traced. Arguments to conjecture the twofold origin of the detected amplification of sound are given: the differential effect of the instabilities on the mean field and on the quantum fluctuations gives some clues to separate a deterministic component from self-amplified Hawking radiation. The role of classical noise, present in the experimental setup, is also tackled: we discuss the emergence of differences with the effect of quantum fluctuations when various unstable modes are relevant to the dynamics.
Thorough characterization of the thermo-mechanical properties of materials requires difficult and time-consuming experiments. This severely limits the availability of data and it is one of the main obstacles for the development of effective accelerat
ed materials design strategies. The rapid screening of new potential systems requires highly integrated, sophisticated and robust computational approaches. We tackled the challenge by surveying more than 3,000 crystalline solids within the AFLOW framework with the newly developed Automatic Elasticity Library combined with the previously implemented GIBBS method. The first extracts the mechanical properties from automatic self-consistent stress-strain calculations, while the latter employs those mechanical properties to evaluate the thermodynamics within the Debye model. The new thermo-elastic library is benchmarked against a set of 74 experimentally characterized systems to pinpoint a robust computational methodology for the evaluation of bulk and shear moduli, Poisson ratios, Debye temperatures, Gruneisen parameters, and thermal conductivities of a wide variety of materials. The effect of different choices of equations of state is examined and the optimum combination of properties for the Leibfried-Schlomann prediction of thermal conductivity is identified, leading to improved agreement with experimental results than the GIBBS-only approach.
We analytically study the effect of gravitational and harmonic forces on ultra-cold atoms with synthetic spin-orbit coupling (SOC). In particular, we focus on the recently observed transitions between internal states induced by acceleration of the ex
ternal modes. Our description corresponds to a generalized version of the Landau-Zener (LZ) model: the dimensionality is enlarged to combine the quantum treatment of the external variables with the internal-state characterization; additionally, atomic-interaction effects are considered. The emergence of the basic model is analytically traced. Namely, by using a sequence of unitary transformations and a subsequent reduction to the spin space, the SOC Hamiltonian, with the gravitational potential incorporated, is exactly converted into the primary LZ scenario. Moreover, the transitions induced by harmonic acceleration are approximately cast into the framework of the basic LZ model through a complete analytical procedure. We evaluate how the validity of our picture depends on the system preparation and on the magnitude of atomic-interaction effects. The identification of the regime of applicability and the rigorous characterization of the parameters of the effective model provide elements to control the transitions.
The lack of computationally inexpensive and accurate ab-initio based methodologies to predict lattice thermal conductivity, without computing the anharmonic force constants or time-consuming ab-initio molecular dynamics, is one of the obstacles preve
nting the accelerated discovery of new high or low thermal conductivity materials. The Slack equation is the best alternative to other more expensive methodologies but is highly dependent on two variables: the acoustic Debye temperature, $theta_a$, and the Gr{u}neisen parameter, $gamma$. Furthermore, different definitions can be used for these two quantities depending on the model or approximation. In this article, we present a combinatorial approach to elucidate which definitions of both variables produce the best predictions of the lattice thermal conductivity, $kappa_l$. A set of 42 compounds was used to test accuracy and robustness of all possible combinations. This approach is ideal for obtaining more accurate values than fast screening models based on the Debye model, while being significantly less expensive than methodologies that solve the Boltzmann transport equation.
We focus on a technique recently implemented for controlling the magnitude of synthetic spin-orbit coupling (SOC) in ultra-cold atoms in the Raman-coupling scenario. This technique uses a periodic modulation of the Raman-coupling amplitude to tune th
e SOC. Specifically, it has been shown that the effect of a high-frequency sinusoidal modulation of the Raman-laser intensity can be incorporated into the undriven Hamiltonian via effective parameters, whose adiabatic variation can then be used to steer the SOC. Here, we characterize the heating mechanisms that can be relevant to this method. We identify the main mechanism responsible for the heating observed in the experiments as basically rooted in driving-induced transfer of population to excited states. Characteristics of that process determined by the harmonic trapping, the decay of the excited states, and the technique used for preparing the system are discussed. Additional heating, rooted in departures from adiabaticity in the variation of the effective parameters, is also described. Our analytical study provides some clues that may be useful in the design of strategies for curbing the effects of heating on the efficiency of the control methods.
We study the dynamics of a classical nonlinear oscillator subject to noise and driven by a sinusoidal force. In particular, we give an analytical identification of the mechanisms responsible for the supernarrow peaks observed recently in the spectrum
of a mechanical realization of the system. Our approach, based on the application of averaging techniques, simulates standard detection schemes used in practice. The spectral peaks, detected in a range of parameters corresponding to the existence of two attractors in the deterministic system, are traced to characteristics already present in the linearized stochastic equations. It is found that, for specific variations of the parameters, the characteristic frequencies near the attractors converge on the driving frequency, and, as a consequence, the widths of the peaks in the spectrum are significantly reduced. The implications of the study to the control of the observed coherent response of the system are discussed.
We present a proposal for controlling the conversion of ultracold atoms into molecules by fixing the phase difference between two oscillating magnetic fields. The scheme is based on the use of a magnetic Feshbach resonance with a field modulation tha
t incorporates terms oscillating with frequencies corresponding to the main resonance and one of the subharmonics. The interference between the two association processes activated by the oscillating terms is controlled via the phase difference. As a result, significant increase or decrease of the effective interaction strength can be achieved. The realization of the proposal is feasible under standard technical conditions. In particular, the method is found to be robust against the effect of the sources of decoherence present in the practical setup. The applicability of the approach to deal with quadratic terms in the field modulation is discussed.
Heating induced by an oscillating modulation of the interaction strength in an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model, generalized by incorporating a time-dependent intermode coupling through a magnetic Feshbach r
esonance, is applied. The dynamics is analytically characterized in a perturbative scheme. The results account for experimental findings which have uncovered a damped and delayed response of the condensate to the modulation. The delay is due to the variation of the quasiparticle energies and the subsequent relaxation of the condensate. The detected damping results from the excitations induced by a nonadiabatic modulation: for driving frequencies larger than twice the pairing gap, quasiparticles are generated, and, consequently, heating sets in.
The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body
effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom-molecule conversion process.
