Ehrenfest Dynamics and Frictionless Cooling Methods

Recently introduced methods which result in shortcuts to adiabaticity, particularly in the context of frictionless cooling, are rederived and discussed in the framework of an approach based on Ehrenfest dynamics. This construction provides physical insights into the emergence of the Ermakov equation, the choice of its boundary conditions, and the use of minimum uncertainty states as indicators of the efficiency of the procedure. Additionally, it facilitates the extension of frictionless cooling to more general situations of physical relevance, such as optical dipole trapping schemes. In this context, we discuss frictionless cooling in the short-time limit, a complementary case to the one considered in the literature, making explicit the limitations intrinsic to the technique when the full three-dimensional case is analyzed.Comment: 9 pages, 4 figures, v2: To appear in Physical Review A. (some minor typos corrected and some references added

Squeezing and robustness of frictionless cooling strategies

Quantum control strategies that provide shortcuts to adiabaticity are increasingly considered in various contexts including atomic cooling. Recent studies have emphasized practical issues in order to reduce the gap between the idealized models and actual ongoing implementations. We rephrase here the cooling features in terms of a peculiar squeezing effect, and use it to parametrize the robustness of frictionless cooling techniques with respect to noise-induced deviations from the ideal time-dependent trajectory for the trapping frequency. We finally discuss qualitative issues for the experimental implementation of this scheme using bichromatic optical traps and lattices, which seem especially suitable for cooling Fermi-Bose mixtures and for investigating equilibration of negative temperature states, respectively.Comment: 9 pages, 7 figures; To appear in Physical Review

Development of a high sensitivity torsional balance for the study of the Casimir force in the 1-10 micrometer range

We discuss a proposal to measure the Casimir force in the parallel plate configuration in the $1-10\mu$m range via a high-sensitivity torsional balance. This will allow to measure the thermal contribution to the Casimir force therefore discriminating between the various approaches discussed so far. The accurate control of the Casimir force in this range of distances is also required to improve the limits to the existence of non-Newtonian forces in the micrometer range predicted by unification models of fundamental interactions.Comment: 10 pages, 2 figure

On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at friction Reynolds number Re$_\tau$ = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associated to the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes

Detectability of dissipative motion in quantum vacuum via superradiance

We propose an experiment for generating and detecting vacuum-induced dissipative motion. A high frequency mechanical resonator driven in resonance is expected to dissipate energy in quantum vacuum via photon emission. The photons are stored in a high quality electromagnetic cavity and detected through their interaction with ultracold alkali-metal atoms prepared in an inverted population of hyperfine states. Superradiant amplification of the generated photons results in a detectable radio-frequency signal temporally distinguishable from the expected background.Comment: 4 pages, 2 figure

Equilibrium states of a test particle coupled to finite size heat baths

We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constraints the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle response with respect to the spectra of the two heat baths. Finally, we discuss implications of our results for the study of high-frequency nanomechanical resonators through cold damping cooling techniques, and for engineering reservoirs capable of mitigating the back-action on a mechanical system.Comment: Strongly related to arXiV:0810.3251 (appeared in European Physical Journal B 61, 271 (2008

Measurement-induced Squeezing of a Bose-Einstein Condensate

We discuss the dynamics of a Bose-Einstein condensate during its nondestructive imaging. A generalized Lindblad superoperator in the condensate master equation is used to include the effect of the measurement. A continuous imaging with a sufficiently high laser intensity progressively drives the quantum state of the condensate into number squeezed states. Observable consequences of such a measurement-induced squeezing are discussed.Comment: 4 pages, 2 figures, submitted to PR

Uncertainty-principle noise in vacuum-tunneling transducers

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied

Exotic Superconducting Phases of Ultracold Atom Mixtures on Triangular Lattices

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in Phys. Rev. Lett. {\bf 97}, 030601 (2006). Using functional renormalization group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of $s$-, $p$-, extended $d$-, and $f$-wave symmetry, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between $p$- and $f$-wave symmetry. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.Comment: 6 pages, 4 figures, extended version, slight modification

Cooling dynamics of ultracold two-species Fermi-Bose mixtures

We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.Comment: 4 pages, 3 figure