Trap Frequency Research Articles

Third- and fourth-order virial coefficients of harmonically trapped fermions in a semiclassical approximation

Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency and coupling strength. Our simple, analytic results for the interaction-induced changes $\Delta b_3$ and $\Delta b_4$ agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of three-dimensional Fermi gases.

Measurement and feedback for cooling heavy levitated particles in low-frequency traps

We consider a possible route to ground state cooling of a levitated nanoparticle, magnetically trapped by a strong permanent magnet, using a combination of measurement and feedback. The trap frequency of this system is much lower than those involving trapped ions or nano-mechanical resonators. Minimisation of environmental heating is therefore challenging as it requires control of the system on a timescale comparable to the inverse of the trap frequency. We show that these traps are an excellent platform for performing optimal feedback control via real-time state estimation, for the preparation of motional states with measurable quantum properties.

Repeated measurements with minimally destructive partial-transfer absorption imaging.

We demonstrate partial-transfer absorption imaging as a technique for repeatedly imaging an ultracold atomic ensemble with minimal perturbation. We prepare an atomic cloud in a state that is dark to the imaging light. We then use a microwave pulse to coherently transfer a small fraction of the ensemble to a bright state, which we image using in situ absorption imaging. The amplitude or duration of the microwave pulse controls the fractional transfer from the dark to the bright state. For small transfer fractions, we can image the atomic cloud up to 50 times before it is depleted. As a sample application, we repeatedly image an atomic cloud oscillating in a dipole trap to measure the trap frequency.

Ideal gas model of Bose-Einstein condensates confined in the parabolic trap

By using the one-dimensional canonical partition function, we modelled an ideal gas-like form of a set of Bose-Einstein condensates confined by a three-dimensional anisotropic parabolic trap. The model itself was constructed by taking the eigenenergies of the one-dimensional Gross-Pitaevskii equation in the longitudinal direction and enabling the harmonic volume as the inverse cube of average geometric trapping frequency to substitute the real volume. In this paper, we showed that the condensates form an ideal gas represented by its equation of state and have similar mature to Einstein’s solid-like model with the corrections in both the low and high temperatures in the internal energy formulations.

Selective UV‐Gating Organic Memtransistors with Modulable Levels of Synaptic Plasticity

AbstractTargeting the emulation of diverse synapses in the brain, organic thin‐film memtransistors gated remotely by UV light are achieved and analytically modeled. They show continuously and reversibly variable device states, and the degree of the variability can also be controlled by selective UV gating. The modulable memristive characteristics cover a wide range of four orders in reading current, all with excellent state retention upon reading or power‐off. The UV‐gating effect stems from the UV‐enhanced cumulative charge trapping/detrapping in the polymer electret layer, expressed as a linear relationship between the characteristic trapping frequency and UV power density. The organic memtransistors are utilized to successfully mimic various synapses at newborn, young, and mature stages that have different levels of synaptic plasticity, as well as the synaptic functions of paired‐pulse facilitation and paired‐pulse depression. The realization of versatile synaptic emulation in a single device may pave the way toward organic‐based neuromorphic circuits, where UV gating could be used for remote regulation of circuit learning rate.

Finite-temperature dynamics of a Tonks-Girardeau gas in a frequency-modulated harmonic trap

We study the out-of-equilibrium dynamics of a finite-temperature harmonically trapped Tonks-Girardeau gas induced by periodic modulation of the trap frequency. We give explicit exact solutions for the real-space density and momentum distributions of this interacting many-body system and characterize the stability diagram of the dynamics by mapping the many-body solution to the solution and stability diagram of Mathieu's differential equation. The mapping allows one to deduce the exact structure of parametric resonances in the parameter space characterized by the driving amplitude and frequency of the modulation. Furthermore, we analyze the same problem within the finite-temperature hydrodynamic approach and show that the respective solutions to the hydrodynamic equations can be mapped to the same Mathieu equation. Accordingly, the stability diagram and the structure of resonances following from the hydrodynamic approach is exactly the same as those obtained from the exact many-body solution.

Energy trapping of circumferential resonant modes at a thin-walled groove in a hollow cylinder

Energy trapping of circumferential resonant modes at a thin-walled groove in a hollow cylinder is discussed using theoretical dispersion curves of guided waves, semi-analytical finite element (SAFE) calculations, and experiments. The analysis of the dispersion curves predicts the energy trapping at a thin-walled groove using the analogy of energy trapping of Lamb waves in a stepped plate. The energy trapping frequencies and displacement distributions at these frequencies were independently obtained with SAFE calculations and experiments. They agreed well with each other and proved that the energy trapping modes exist at the thin-walled groove in the hollow cylinder.

Asymmetric heat transport in ion crystals.

We numerically demonstrate heat rectification for linear chains of ions in trap lattices with graded trapping frequencies, in contact with thermal baths implemented by optical molasses. To calculate the local temperatures and heat currents we find the stationary state by solving a system of algebraic equations. This approach is much faster than the usual method that integrates the dynamical equations of the system and averages over noise realizations.

Vortex lattice formation in dipolar Bose-Einstein condensates via rotation of the polarization

The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.

Resonantly interacting p -wave Fermi superfluid in two dimensions: Tan's contact and the breathing mode

Inspired by the renewed experimental activities on $p$-wave resonantly interacting atomic Fermi gases, we theoretically investigate some experimental observables of such systems at zero temperature in two dimensions, using both mean-field theory and Gaussian pair fluctuation theory. These observables include the two $p$-wave contact parameters and the breathing mode frequency, which can be readily measured in current cold-atom setups with $^{40}$K and $^{6}$Li atoms. We find that the many-body component of the two contact parameters exhibits a pronounced peak slightly above the resonance and consequently leads to a dip in the breathing mode frequency. In the resonance limit, we discuss the dependence of the equation of state and the breathing mode frequency on the dimensionless effective range of the interaction, $k_{F}R_{p}\ll1$, where $k_{F}$ is the Fermi wavevector and $R_{p}$ is the effective range. The breathing mode frequency $\omega_{B}$ deviates from the scale-invariant prediction of $\omega_{c}=2\omega_{0}$, where $\omega_{0}$ is the trapping frequency of the harmonic potential. This frequency shift is caused by the necessary existence of the effective range. In the small range limit, we predict that the mode frequency deviation at the leading order is given by, $\delta\omega_{B}\simeq-(\omega_{0}/4)\ln^{-1}(k_{F}R_{p})$.

Validity of Gross–Pitaevskii solutions of harmonically confined BEC gases in reduced dimensions

By exact numerical solutions of the Gross–Pitaevskii (GP) equation in 3D, we assess the validity of 1D and 2D approximations in the study of Bose–Einstein condensates confined in harmonic trap potentials. Typically, these approximations are performed when one or more of the harmonic frequencies are much greater than the remaining ones, using arguments based on the adiabatic evolution of the initial approximated state. Deviations from the 3D solution are evaluated as a function of both the effective interaction strength and the ratio between the trap frequencies that define the reduced dimension where the condensate is confined. The observables analyzed are both of stationary and dynamical character, namely, the chemical potential, the wave function profiles, and the time evolution of the approximated 1D and 2D stationary states, considered as initial states in the 3D GP equation. Our study, besides setting quantitative limits on approximations previously developed, should be useful in actual experimental studies where quasi-1D and quasi-2D conditions are assumed. From a qualitative perspective, 1D and 2D approximations certainly become valid when the anisotropy is large, but in addition the interaction strength needs to be above a certain threshold.

Heat current control in trapped Bose–Einstein Condensates

We investigate the heat transport and the control of heat current among two spatially separated trapped Bose–Einstein Condensates (BECs), each of them at a different temperature. To allow for heat transport among the two independent BECs we consider a link made of two harmonically trapped impurities, each of them interacting with one of the BECs. Since the impurities are spatially separated, we consider long-range interactions between them, namely a dipole–dipole coupling. We study this system under theoretically suitable and experimentally feasible assumptions/parameters. The dynamics of these impurities is treated within the framework of the quantum Brownian motion model, where the excitation modes of the BECs play the role of the heat bath. We address the dependence of heat current and current–current correlations on the physical parameters of the system. Interestingly, we show that heat rectification, i.e. the unidirectional flow of heat, can occur in our system, when a periodic driving on the trapping frequencies of the impurities is considered. Therefore, our system is a possible setup for the implementation of a phononic circuit. Motivated by recent developments on the usage of BECs as platforms for quantum information processing, our work offers an alternative possibility to use this versatile setting for information transfer and processing, within the context of phononics, and more generally in quantum thermodynamics.

Real Time Electronic Feedback for Improved Acoustic Trapping of Micron-Scale Particles.

Acoustic differential extraction has been previously reported as a viable alternative to the repetitive manual pipetting and centrifugation steps for isolating sperm cells from female epithelial cells in sexual assault sample evidence. However, the efficiency of sperm cell isolation can be compromised in samples containing an extremely large number of epithelial cells. When highly concentrated samples are lysed, changes to the physicochemical nature of the medium surrounding the cells impacts the acoustic frequency needed for optimal trapping. Previous work has demonstrated successful, automated adjustment of acoustic frequency to account for changes in temperature and buffer properties in various samples. Here we show that, during acoustic trapping, real-time monitoring of voltage measurements across the piezoelectric transducer correlates with sample-dependent changes in the medium. This is achieved with a wideband peak detector circuit, which identifies the resonant frequency with minimal disruption to the applied voltage. We further demonstrate that immediate, corresponding adjustments to acoustic trapping frequency provides retention of sperm cells from high epithelial cell-containing mock sexual assault samples.

Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps

We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form , where N is the number of particles, —the harmonic trap frequency, d—system’s dimensionality, and a is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within the model, the imperfect gas of trapped repulsive bosons undergoes the Bose–Einstein condensation provided d > 1. The main result of our analysis is that in d = 1 the gas of attractive imperfect fermions with is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.

Fragility of the bosonic Laughlin state

When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency which is close to the trap frequency, its many-body state becomes highly correlated, with the most well-known being the bosonic Laughlin state. To take into account that in a real experiment no trapping potential is ever exactly harmonic, we introduce an additional weak, quartic potential and demonstrate that the Laughlin state is highly sensitive to this extra potential. Our results imply that achieving these states experimentally is essentially impossible, at least for a macroscopic atom number.

Dynamical Symmetry and Breathers in a Two-Dimensional Bose Gas

A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross--Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies and interaction parameters by a scaling transform. Finally we show that some specific initial shapes - uniformly-filled triangles or disks - may lead to a periodic evolution, corresponding to a novel type of breather for the two-dimensional Gross--Pitaevskii equation.

Normalized standing waves for the Hartree equations

In this paper, we study the existence and stability/instability of standing waves with a prescribed L2-norm for the following Hartree equation(0.1)iut+Δu−a|x|2u+(|x|−λ⁎|u|2)u=0,(t,x)∈R+×RN, where t is time, N≥3, λ∈(0,N) and a≥0 is a constant. To get such solutions, we look for normalized solutions of the associated stationary equation(0.2)−Δu+a|x|2u+ωu−(|x|−λ⁎|u|2)u=0,x∈RN. Two cases are considered: (i) the system is free (a=0) and (ii) a harmonic trapping potential is added in the system (a>0). In case (i), by constructing a suitable submanifold of a L2-sphere, we prove the existence of a normalized solution for problem (0.2) with least energy in the L2-sphere, which corresponds to a normalized ground state standing wave of problem (0.1). Then, we show that each normalized ground state of problem (0.2) coincides a ground state of problem (0.2) in the usual sense. Furthermore, we give a global existence result for problem (0.1) and also show that any normalized ground state standing wave is strongly unstable. In case (ii), for small a>0, we prove the existence of two different standing waves, one corresponds to a topological local minimizer of the constrained energy functional, the other corresponds to a mountain pass type solution of problem (0.2) with its energy strictly larger than that of the normalized ground state. Moreover, we show that the set of normalized ground state solutions for problem (0.2) is stable under the associated flow. Finally, to connect case (i) and case (ii), we analyze the asymptotic behavior of the two solutions to problem (0.2) obtained in case (ii) as the trapping frequency a vanishes.

Towards a transportable aluminium ion quantum logic optical clock.

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=-0.4-0.3 +0.4×10-18 and the black-body radiation shift is δνBBR/ν = (-4.0 ± 0.4) × 10-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.

Effect of heating rate on thermoluminescence characteristics of Y2O3 nanoparticles

The present paper reports the results of heating rate dependencies of thermoluminescence (TL) peaks observed for Y2O3 nanoparticles in the below room temperature region. TL glow curve presented six peaks around 62.5, 91.3, 114.5, 162.7, 196.0 and 214.9 K for heating rate of 0.4 K/s. The increase of heating rate resulted in increase in peak maximum temperature and decrease in peak maximum intensity as expected according to theoretical information. Peak maximum temperature-heating rate dependencies of observed peaks were analysed according to exponential dependency relation. Curve fit and initial rise methods were applied on thermally cleaned individual peaks and activation energies of associated trap centers, frequency factors and order of kinetics were obtained from the analyses. Activation energy values of the revealed trapping centers found from both methods were in good agreement with each other. Moreover, lattice parameters, crystalline size and micro-strain of nanoparticles were investigated by means of x-ray diffraction measurements.

Operation of a Microfabricated Planar Ion‐Trap for Studies of a Yb+–Rb Hybrid Quantum System

In order to study interactions of atomic ions with ultracold neutral atoms, it is important to have sub‐µm control over positioning ion crystals. Serving for this purpose, a microfabricated planar ion trap featuring 21 DC electrodes is introduced. The ion trap is controlled by a home‐made FPGA voltage source providing independently variable voltages to each of the DC electrodes. To assure stable positioning of ion crystals with respect to trapped neutral atoms, the authors integrate into the overall design a compact mirror magneto optical chip trap (mMOT) for cooling and confining neutral 87Rb atoms. The trapped atoms will be transferred into an also integrated chip‐based Ioffe‐Pritchard trap potential formed by a Z‐shaped wire and an external bias magnetic field. The authors introduce the hybrid atom–ion chip, the microfabricated planar ion trap, and use trapped ion crystals to determine ion lifetimes, trap frequencies, positioning ions, and the accuracy of the compensation of micromotion.