Trap Frequency Research Articles

Robust polarization gradient cooling of trapped ions

We implement three-dimensional polarization gradient cooling (PGC) of trapped ions. Counter-propagating laser beams near 393 nm impinge in lin ⊥ lin configuration, at a frequency below the S1/2 to P3/2 resonance in 40Ca+. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number and works continuously in the crossover from regular Doppler cooling to detunings of tens of linewidths. It is thus robust against heating events and also works well for an initial ion motion far out of the Lamb–Dicke regime. We show that PGC performance strongly depends on residual micromotion (MM) and find PGC working for a MM modulation index β ⩽ 0.1. Still, we find that the spectral impurity of the laser field affects both, cooling rates and cooling limits. Thus, a Fabry–Pérot cavity filter is employed to efficiently suppress amplified spontaneous emission of the diode laser. We demonstrate mean phonon numbers for a single ion of 5.4(4) at a trap frequency of 2π × 285 kHz and 3.3(4) at 2π × 480 kHz, in the axial and radial directions, respectively.

Thermoluminescence kinetic parameters of yttrium niobate

Yttrium niobate (YNbO4) phosphorus produced using the solid-state technique by sintering at 1200 °C investigated for thermoluminescence (TL) kinetics after irradiated with ultraviolet radiation (UV). The TL glow curve of UV irradiated yttrium niobate phosphorus recorded with a heating rate of 2 Ks−1 exhibited glow peaks at 366 and 424 K. The TL kinetic parameters belonging to main glow peak (424 K) of yttrium niobate phosphor, namely trap energy (E), frequency factor (s) and kinetic order (b) were investigated using Various Heating Rates (VHR), Computerized Glow Curve Deconvolution (CGCD), and Chen's Peak Shape (PS) methods after exposure to UV radiation. Trap energies of the phosphor by all methods were calculated as 1.09 eV. The frequency factors of the phosphor by CGCD, VHR and Chen’s PS methods were obtained as 0.96 × 1012 s−1, 1.38 × 1012 s−1 and 0.98 × 1012 s−1, respectively. The results attained by all methods are discussed and compared.

Supersolid-like square- and honeycomb-lattice crystallization of droplets in a dipolar condensate

We demonstrate a supersolid-like spatially-periodic square- and honeycomb-lattice crystallization of droplets, in addition to the commonly-studied triangular-lattice crystallization, in a cylindrically-symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interactions and the same trap frequencies. The energy $E$ of all three crystallization as a function of number $N$ of atoms satisfy the universal scaling relation $E\sim N^{0.4}$ indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed $N$, constitute two quasi-degenerate ground states while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.

Trapping effects in quantum atomic arrays

Quantum emitters, particularly atomic arrays with subwavelength lattice constant, have been proposed to be an ideal platform for studying the interplay between photons and electric dipoles. In this work, motivated by the recent experiment [1], we develop a microscopic quantum treatment using annihilation and creation operator of atoms in deep optical lattices. Using a diagrammatic approach on the Keldysh contour, we derive the cooperative scattering of the light and obtain the general formula for the S matrix. We apply our method to study the trapping effect, which is beyond previous treatment with spin operators. If the optical lattices are formed by light fields with magical wavelength, the result matches previous results using spin operators. When there is a mismatch between the trapping potentials for atoms in the ground state and the excited state, atomic mirrors become imperfect, with multiple resonances in the optical response. We further study the effect of recoil for large but finite trapping frequency. Our results are consistent with existing experiments.

Atom recoil in collectively interacting dipoles using quantized vibrational states

The recoil of atoms in dense ensembles during light matter interactions is studied using quantized vibrational states for the atomic motion. The recoil resulting from the forces due to the near-field collective dipole interactions and far-field laser and decay interactions are explored. The contributions to the recoil and the dependence on the trap frequency of the different terms of the Hamiltonian and Lindbladian are studied. These calculations are compared with previous results using the impulse model in the slow oscillation approximation. Calculations in highly subradiant systems show enhanced recoil indicating that recoil effects cannot be ignored in such cases.

Manipulating and measuring single atoms in the Maltese cross geometry.

Background: Optical microtraps at the focus of high numerical aperture (high-NA) imaging systems enable efficient collection, trapping, detection and manipulation of individual neutral atoms for quantum technology and studies of optical physics associated with super- and sub-radiant states. The recently developed "Maltese cross" geometry (MCG) atom trap uses four in-vacuum lenses to achieve four-directional high-NA optical coupling to single trapped atoms and small atomic arrays. This article presents the first extensive characterisation of atomic behaviour in a MCG atom trap. Methods: We employ a MCG system optimised for high coupling efficiency and characterise the resulting properties of the trap and trapped atoms. Using current best practices, we measure occupancy, loading rate, lifetime, temperature, fluorescence anti-bunching and trap frequencies. We also use the four-directional access to implement a new method to map the spatial distribution of collection efficiency from high-NA optics: we use the two on-trap-axis lenses to produce a 1D optical lattice, the sites of which are stochastically filled and emptied by the trap loading process. The two off-trap-axis lenses are used for imaging and single-mode collection. Correlations of single-mode and imaging fluorescence signals are then used to map the single-mode collection efficiency. Results:We observe trap characteristics comparable to what has been reported for single-atom traps with one- or two-lens optical systems. The collection efficiency distribution in the axial and transverse directions is directly observed to be in agreement with expected collection efficiency distribution from Gaussian beam optics. Conclusions: The multi-directional high-NA access provided by the Maltese cross geometry enables complex manipulations and measurements not possible in geometries with fewer directions of access, and can be achieved while preserving other trap characteristics such as lifetime, temperature, and trap size.

Rotating Bose gas dynamically entering the lowest Landau level

Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wavefunction. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states.

Nanotrappy: An open-source versatile package for cold-atom trapping close to nanostructures

Trapping cold neutral atoms in close proximity to nanostructures has raised a large interest in recent years, pushing the frontiers of cavity-QED and boosting the emergence of the waveguide-QED field of research. The design of efficient dipole trapping schemes in evanescent fields is a crucial requirement and a difficult task. Here we present an open-source Python package for calculating optical trapping potentials for neutral atoms, especially in the vicinity of nanostructures. Given field distributions and for a variety of trap configurations, nanotrappy computes the three-dimensional trapping potentials as well as the trap properties, ranging from trap positions to trap frequencies and state-dependent light shifts. We demonstrate the versatility for various seminal structures in the field, e.g., optical nanofiber, alligator slow-mode photonic-crystal waveguide, and microtoroid. This versatile package facilitates the systematic design of structures and provides a full characterization of trapping potentials with applications to the coherent manipulation of atoms and quantum information science.

Dynamic vortex evolution of harmonically trapped coupled Bose–Einstein condensate with quintic nonlinearity

In this study, we investigate the evolution of vortex in harmonically trapped two-component coupled Bose–Einstein condensate with quintic-order nonlinearity. We derive the vortex solution of this two-component system based on the coupled quintic-order Gross–Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state. The radius of vortex soliton shrinks and expands with time, resulting in periodic breathing oscillation, and the angular frequency of the breathing oscillation is twice the value of the harmonic trapping frequency under infinitesimal nonlinear strength. At the same time, it is also found that the higher-order nonlinear term has a quantitative effect rather than a qualitative impact on the oscillation period. With practical experimental setting, we identify the quasi-stable oscillation of the derived vortex evolution mode and illustrated its features graphically. The theoretical results developed in this work can be used to guide the experimental observation of the vortex phenomenon in ultracold coupled atomic systems with quintic-order nonlinearity.

Thermodynamic contacts and breathing-mode physics of one-dimensional p -wave Fermi gases in the high-temperature limit

An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to occur at twice the harmonic trapping frequency when the interactions are scale invariant. When the interactions are not scale invariant, the frequency of the breathing mode will deviate from twice the trap frequency. The deviation itself depends on the thermodynamic contacts, which describe how the energy changes with the interactions. In this work I examine how the thermodynamic contacts and the breathing mode frequency of a spin-polarized one-dimensional (1D) p-wave Fermi gas depend on the 1D scattering volume, $\ell$, and the effective range, $r$, in the high temperature limit. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depend on interactions with a finite effective range.

Effective scaling approach to frictionless quantum quenches in trapped Bose gases

We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.

Extended Bose-Hubbard models with Rydberg macrodimer dressing

Extended Hubbard models have proven to bear novel phases of matter, but their experimental realization remains challenging. In this work we propose to use bosonic quantum gases dressed with molecular bound states in Rydberg interaction potentials for the observation of these quantum states. We study the molecular Rabi coupling with respect to the effective principal quantum number and trapping frequency of the ground-state atoms for various molecular potentials of rubidium and potassium, and the hereby resulting dressed interaction strength. Additionally, we propose a two-color excitation scheme which significantly increases the dressed interaction and cancels otherwise-limiting ac Stark shifts. We study the various equilibrium phases of the corresponding extended Bose-Hubbard model by means of the cluster Gutzwiller approach and perform time evolution simulations via the Lindblad master equation. We find a supersolid phase by slowly ramping the molecular Rabi coupling of an initially prepared superfluid and discuss the role of dissipation.

Bias Dependence Model of Peak Frequency of GaN Trap in GaN HEMTs Using Low-Frequency Y₂₂ Parameters

A model for the peak frequency in the imaginary part of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}_{{22}}$ </tex-math></inline-formula> (Im( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}_{{22}}{))}$ </tex-math></inline-formula> based on the bias for gallium nitride (GaN) high electron mobility transistors (HEMTs) is investigated while considering both self-heating (SH) and Poole–Frenkel (PF) (electric field) effects. The peak frequency of Im( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}_{{22}}{)}$ </tex-math></inline-formula> corresponds to the emission time constant of the trap in the GaN layer. In this study, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}_{{22}}$ </tex-math></inline-formula> for GaN HEMTs were measured for low frequencies at which the traps respond by significantly changing not only drain voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {DS}}{)}$ </tex-math></inline-formula> but also gate voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {GS}}{)}$ </tex-math></inline-formula> . Because the vector network analyzer used ac with an extremely small power of −20 dBm as a signal for sensing the trap, the trap properties can be measured at a fixed dc bias. In this model, the SH effect is introduced to replace the ambient temperature in the conventional Arrhenius equation by simulating the lattice temperature. The PF effect introduces the apparent activation energy, based on the simulated electric field at the channel under the gate field edge of the drain side. The electric field is related to the voltage between the gate and drain. This model is consistent with the experimental data for a wide range of transistor biases, i.e., from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {GS}}$ </tex-math></inline-formula> near the pinch-off voltage to the ON-state condition, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {DS}}$ </tex-math></inline-formula> in the saturation region at ambient temperatures between 23 °C and 160 °C. Furthermore, using this model, we confirmed that the PF effect dominates at a low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {GS}}$ </tex-math></inline-formula> of −2 V near the pinch-off.

On-chip optical levitation with a metalens in vacuum

Optical levitation of dielectric particles in vacuum is a powerful technique for precision measurements, testing fundamental physics, and quantum information science. Conventional optical tweezers require bulky optical components for trapping and detection. Here, we design and fabricate an ultrathin dielectric metalens with a high numerical aperture of 0.88 at 1064 nm in vacuum. It consists of 500-nm-thick silicon nano-antennas, which are compatible with an ultrahigh vacuum. We demonstrate optical levitation of nanoparticles in vacuum with a single metalens. The trapping frequency can be tuned by changing the laser power and polarization. We also transfer a levitated nanoparticle between two separated optical tweezers. Optical levitation with an ultrathin metalens in vacuum provides opportunities for a wide range of applications including on-chip sensing. Such metalenses will also be useful for trapping ultracold atoms and molecules.

Determination of the oscillation frequency in a strongly damped dipole trap by control of spin current

We present experimental and theoretical results on the measurements of the oscillation frequency in a dipole trap based on the spin current in a sodium spinor Bose–Einstein condensate. The spin current is induced under different magnetic field intensities. The oscillation of the spin components in the dipole trap is strongly enhanced by a radio frequency pulse. Both theoretical analysis and experimental results demonstrate that this method can be used to efficiently measure the trap frequencies. Since this mechanism is independent of atomic species, this study is promising to be extended to rubidium and other optical-trappable quantum gases.

40Ca+ optical clocks in China

In this review, the improvements made in the past two decades for 40Ca+ optical clocks in China are presented. Uncertainty of below 1.3×10−17 was achieved by applying the “magic” RF trapping frequency and introducing a generalized Ramsey excitation scheme. The stability of 40Ca+ optical clocks has been improved to 2.5×10−15/τ with an uptime rate of 93.8% by implementing two ameliorated lock algorithms in the Ramsey excitation scheme. A long-term clock frequency comparison shows a clock stability of 6.3 × 10−18 in an averaging time of 524 000 s. A robust and transportable clock installed in an air-conditioned car trailer can achieve almost the same performance of laboratory clocks. A height difference between transportable and laboratory clocks was measured with an uncertainty of 0.33 m and the absolute frequency of 40Ca+ optical clock transitions was remeasured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of 5.6×10−16 based on a Cs fountain clock in the National Institute of Metrology after the transportable clock was transported from Wuhan to Beijing. The author predicts that transportable single-ion optical clocks especially based on the 40Ca+ will make a significant contribution to the construction of a world-wide optical clock network and the redefinition of the unit of time in the future.

Investigation of solvent microparticle formation in spray ionization–quadrupole ion trap–mass spectrometry

AbstractIn the present study, a new method has been developed for the real‐time analysis of insource created solvent particles based on spray ionization–quadrupole ion trap–mass spectrometry (SI‐QIT‐MS). This is the first work in the literature reporting the formation of different solvent particles during solvent spray in mass spectrometry. The solvent particles formed from the solvent droplets are detected by a charge detector. Our ion trap system allows the measurement of a wide range particle masses. Various solvents and solvent mixtures such as water, methanol, acetone, toluene, n‐butanol, water‐methanol, and water‐ethanol were sprayed through a cone system, and the mass of the particles was monitored by different trap frequencies and voltages. While polar molecules produce larger and more diverse particles due to their strong intermolecular forces, apolar solvents generally do not produce a significant number of particles. We obtained results using a homemade ion trap mass spectrometer capable of determining the mass of micro‐sized solvent and solvent mixture particles weighing up to 1015 (Da). The instrument uses a charge detector connected to the exit of the ion trap. Simultaneous acquisition of particle mass spectra and measurement of the amount of charge in each particle allow mass assignment of each particle. Sprayed solvent particles were examined at various trap frequencies and voltages to find the best instrumental parameters for the highest trapping efficiency. The custom SI‐QIT‐MS instrument allows the measurement of the mass distribution of charged particles from the solvent spray.

Particle creation in the spin modes of a dynamically oscillating two-component Bose-Einstein condensate

We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, triggered by the dynamical evolution of the condensate density. We first make use of a Thomas-Fermi approximation to develop a tractable theoretical model of the quantum dynamics of the Bogoliubov excitations in a harmonically trapped condensate with a time-dependent trapping frequency. The predictions of this model are then compared to an ab-initio numerical study of the correlation functions of density and spin fluctuations for general spatially inhomogeneous configurations. Results are shown for the two cases of expanding and oscillating condensates: while the quantum excitation of spin modes remains weak and relatively featureless in the case of an expanding condensate, clear and experimentally promising signatures of particle creation are anticipated for the oscillating case under suitable resonance conditions between the density and the spin modes.

Faraday waves in strongly interacting superfluids

We report on the observation of Faraday waves in a cigar-shaped Fermi superfluid of 6Li parametrically excited by modulating the radial trap frequency. We characterize the phenomenon as a function of the interaction parameter employing a Feshbach resonance. Starting from the BEC side of the resonance, we observe a reduction of visibility of the Faraday pattern as we approach unitarity, possibly due to the increased incompressibility of the system. We probe the superfluid excitation spectrum by extracting an effective 1D speed of sound for different values of the interaction parameter, in good agreement with numerical simulations. We also discuss the effects introduced by the finite size of the sample. Finally, we introduce a novel model based on Floquet theory that we employ to perform a stability analysis in the parameter space, showing the emergence of the Faraday waves as unstable solutions to a Mathieu-like equation.

Transparent qubit manipulations with spin-orbit coupled two-electron nanowire quantum dot

We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba–Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.