Mean-field Shift Research Articles

Tunable Three-Body Interactions in Driven Two-Component Bose-Einstein Condensates.

We propose and demonstrate the appearance of an effective attractive three-body interaction in coherently driven two-component Bose-Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. Importantly, its strength can be controlled with the Rabi-coupling strength and it does not come with additional losses. In the experiment, the three-body interactions are adjusted to play a predominant role in the equation of state of a cigar-shaped trapped condensate. This is confirmed through two striking observations: a downshift of the radial breathing mode frequency and the radial collapses for positive values of the dressed-state scattering length.

Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas.

We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.

Theory and simulation of spectral line broadening by exoplanetary atmospheric haze

Atmospheric haze is the leading candidate for the flattening of expolanetary spectra, as it's also an important source of opacity in the atmospheres of solar system planets, satellites, and comets. Exoplanetary transmission spectra, which carry information about how the planetary atmospheres become opaque to stellar light in transit, show broad featureless absorption in the region of wavelengths corresponding to spectral lines of sodium, potassium and water. We develop a detailed atomistic model, describing interactions of atomic or molecular radiators with dust and atmospheric haze particulates. This model incorporates a realistic structure of haze particulates from small nano-size seed particles up to sub-micron irregularly shaped aggregates, accounting for both pairwise collisions between the radiator and haze perturbers, and quasi-static mean field shift of levels in haze environments. This formalism can explain large flattening of absorption and emission spectra in haze atmospheres and shows how the radiator - haze particle interaction affects the absorption spectral shape in the wings of spectral lines and near their centers. The theory can account for nearly all realistic structure, size and chemical composition of haze particulates and predict their influence on absorption and emission spectra in hazy environments. We illustrate the utility of the method by computing shift and broadening of the emission spectra of the sodium D line in an argon haze. The simplicity, elegance and generality of the proposed model should make it amenable to a broad community of users in astrophysics and chemistry.

Scale and Reynolds number dependence of stochastic subgrid energy transfer in turbulent channel flow

Abstract The forward and inverse cascades in turbulent channel flow are characterised by stochastic models developed from the statistics of reference direct numerical simulations (DNS) judiciously truncated into resolved and subgrid scales. The stochastic model consists of a meanfield shift, a deterministic drain dissipation acting on the resolved field and a stochastic backscatter force. The direction, magnitude and stochasticity of the energy transfer for the mean and fluctuating fields in scale space are determined from the spectral coefficients of the stochastic model. The meanfield is found to lose energy to the subgrid scales, whilst the fluctuating two-dimensional spanwise oriented wave receives a deterministic injection. For the three-dimensional fluctuations, there is a deterministic drain of energy out of the resolved scales, and a stochastic injection of energy into the system. Only the small vertical scales have a net injection of energy, where the stochastic backscatter overwhelms the drain dissipation. Results are presented for friction velocity based Reynolds numbers of 186, 546 and 945. The stochastic representation of the subgrid interactions are validated by producing large eddy simulations using these model coefficients that agree with the time averaged kinetic energy spectra of the DNS within the resolved scales.

Momentum-resolved spectroscopy of a Fermi liquid.

We consider a recent momentum-resolved radio-frequency spectroscopy experiment, in which Fermi liquid properties of a strongly interacting atomic Fermi gas were studied. Here we show that by extending the Brueckner-Goldstone model, we can formulate a theory that goes beyond basic mean-field theories and that can be used for studying spectroscopies of dilute atomic gases in the strongly interacting regime. The model hosts well-defined quasiparticles and works across a wide range of temperatures and interaction strengths. The theory provides excellent qualitative agreement with the experiment. Comparing the predictions of the present theory with the mean-field Bardeen-Cooper-Schrieffer theory yields insights into the role of pair correlations, Tan's contact, and the Hartree mean-field energy shift.

Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number of Reτ = 950 and centreline-based Reynolds number of Re0 = 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales.

Polarized Fermi gases at finite temperature in the BCS-BEC crossover

We consider a polarized Fermi gas in the BCS-BEC crossover region above the critical temperature within a T matrix formalism. By treating the mean-field like shift of the quasiparticle energies in a self-consistent manner, we avoid the known pathological behavior of the standard Nozieres-Schmitt-Rink approach in the polarized case, i.e., the polarization has the right sign and the spin polarizability is positive. The momentum distributions of the correlated system are computed and it is shown that, in the zero-temperature limit, they satisfy the Luttinger theorem. Results for the phase diagram, the spin susceptibility, and the compressibility are discussed.

Detecting quadrupole interactions in ultracold Fermi gases

We propose to detect quadrupole interactions of neutral ultra-cold atoms via their induced mean-field shift. We consider a Mott insulator state of spin-polarized atoms in a two-dimensional optical square lattice. The quadrupole moments of the atoms are aligned by an external magnetic field. As the alignment angle is varied, the mean-field shift shows a characteristic angular dependence, which constitutes the defining signature of the quadrupole interaction. For the $^{3}P_{2}$ states of Yb and Sr atoms, we find a frequency shift of the order of tens of Hertz, which can be realistically detected in experiment with current technology. We compare our results to the mean-field shift of a spin-polarized quasi-2D Fermi gas in continuum.

Stochastic self-energy subgrid model for the large eddy simulation of turbulent channel flows

This paper presents the large eddy simulation (LES) of turbulent channel flow using a self-energy (SE) subgrid model with coefficients determined from reference direct numerical simulations (DNSs). In contrast to standard approaches that develop subgrid models based upon physical hypotheses, in the present SE approach the model coefficients are determined from the subgrid statistics of a DNS, with physical interpretations made apostiori. This technique is applied here for the first time to wall-bounded flows, specifically channel flow. The stochastic SE subgrid model consists of a meanfield shift, deterministic drain dissipation acting on the resolved field and a stochastic backscatter force. The deterministic SE subgrid model comprises of a net dissipation representing the net effect of the drain and backscatter. We present LESs that reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales. The direction and magnitude of the energy transfers in scale space can then be determined from the coefficients of the SE subgrid model. Results are presented for friction velocity based Reynolds numbers up to Reτ = 950.

Nonequilibrium Phase Transition in a Dilute Rydberg Ensemble

We demonstrate a nonequilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain, we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain, we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α=-0.53±0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.

Spin Waves and Collisional Frequency Shifts of a Trapped-Atom Clock

We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.

Rabi spectroscopy and excitation inhomogeneity in a one-dimensional optical lattice clock

We investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep one-dimensional optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi line shapes of the carrier transition, we obtain a model to quantify trap-state-dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows $s$-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean-field shift of the clock transition.

Beyond Linear Response Spectroscopy of Ultracold Fermi Gases

We study rf spectroscopy of ultracold Fermi gas by going beyond the linear response in the field-matter interaction. Higher order perturbation theory allows virtual processes and energy conservation beyond the single-particle level. We formulate an effective higher order theory, which agrees quantitatively with experiments on the pairing gap and is consistent with the absence of the mean-field shift in the spin-flip experiment.

Decoherence and dephasing in strongly driven colliding Bose-Einstein condensates

We report on a series of measurements of decoherence and wave-packet dephasing between two colliding, strongly coupled, identical Bose-Einstein condensates. We measure, in the strong-excitation regime, a suppression of the mean-field shift, compared to the shift which is observed for a weak excitation. This suppression is explained by applying the Gross-Pitaevskii energy functional. By selectively counting only the nondecohered fraction in a time-of-flight image we observe oscillations for which both inhomogeneous and Doppler broadening are strongly suppressed. If no post-selection is used, the decoherence rate due to collisions can be extracted and is in agreement with the local density average calculated rate.

Very-high-precision bound-state spectroscopy near a85RbFeshbach resonance

We precisely measured the binding energy of a molecular state near the Feshbach resonance in a $^{85}$Rb Bose-Einstein condensate (BEC). Rapid magnetic field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B-field and fit the data to a coupled-channels model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length [-443(3) a$_0$] and yielded new values for $v_{DS}$, $v_{DT}$, and $C_6$. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to the binding energy.

Eliminating the mean-field shift in two-component bose-einstein condensates

We demonstrate that the nonlinear mean-field shift in a multicomponent Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification can be achieved by engineering the environment of the condensate. We consider the case of a two-component condensate in a quasi-one-dimensional atomic waveguide, achieving modification of the atom-atom interactions by varying the transverse wave functions of the components. Eliminating the density-dependent phase shift represents a promising potential application for multicomponent condensates in atom interferometry and precision measurements.

Magnetic resonance of type-I fcc antiferromagnets.

We calculate magnetic-resonance absorption curves for an assembly of classical spins located in an fcc lattice with spin-spin interactions which stabilize antiferromagnetic order of the first kind. The only source of anisotropy in the model is the dipole-dipole interaction which, at equilibrium, confines the ordered moments into planes perpendicular to the respective type-I ordering vectors. Our principal tool of analysis combines numerical integration of the equations of motion with Monte Carlo simulations. Complete absorption line shapes for classical spins can be calculated using this technique. Spin dynamics is investigated as well by extending our earlier mean-field analysis, the results of which are compared with the simulations. Special attention is paid to a sum rule that relates the intensities of the resonance peaks to the static susceptibility. To this end, we calculate the static susceptibility matrixes for certain single-k and triple-k type-I structures. We investigate, in particular, examples of cases where thermal fluctuations beyond the mean-field theory shift resonance lines from zero frequency to a finite value. It is demonstrated that this effect is related to the so-called ``ordering-by-disorder'' mechanism in which fluctuations stabilize a unique ground state in a continuously degenerate manifold. Our results explain several features observed in recent NMR studies of antiferromagnetic nuclear-spin ordering in copper and silver at nanokelvin temperatures. Analogies with spin dynamics in solid $^{3}\mathrm{He}$ and superfluid $^{3}\mathit{A}$ are briefly discussed. \textcopyright{} 1996 The American Physical Society.

Two-dimensional spin fluctuations of Ho3+ in HoBa2Cu3O7.

Neutron diffraction and inelastic neutron scattering results on ${\mathrm{HoBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ are presented. In the neutron diffraction experiments two-dimensional (2D) short-range order has been observed in the ${\mathrm{Ho}}^{3+}$ sublattice at 1.6 K, which is at a temperature far above the hyperfine-induced ordering temperature ${\mathit{T}}_{\mathit{N}}$=190 mK. A strong enhancement of the effective susceptibility (including the hyperfine interaction) compared with a Curie-Weiss susceptibility is found above 400 mK. This enhancement explains why short-range ordering of the ${\mathrm{Ho}}^{3+}$ spins with an in-plane correlation length of 13 \AA{} are detectable at these temperatures. In addition, a mean-field shift of the lowest lying crystal-field transition was observed between 9 and 300 mK, which is well described within our formalism. The anisotropic line shape of this transition could be understood by a Gaussian field distribution on the ${\mathrm{Ho}}^{3+}$ site, originated in the dynamic 2D short-range ordering. These results are in good agreement with muon spin rotation results. \textcopyright{} 1996 The American Physical Society.