Transverse Trapping Research Articles

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.

Abruptly autofocusing property and optical manipulation of circular Airy beams

By employing the angular spectrum representation, we successfully derive the partial-wave expansion coefficients of the circular Airy beams (CABs) with different polarizations, based on which the scattering of a spherical particle in the CABs is solved exactly. Special attention is focused on exploring the potential applications of the CABs in the abruptly autofocusing (AAF) property and optical manipulation of microparticle by optical force. It is found that both the linear and circular polarizations are the best candidates to implement the AAF property robustly against strong disturbance by a large-sized particle. In addition, although the CABs can be intensively focused to a small region, resulting in an abrupt increase of light intensity by two orders of magnitude at the focal point and enabling three-dimensional stable trapping of a Rayleigh particle near the focal point, the usual CABs fail to generate an optical force outweighing the Brownian force to achieve a stable transverse trapping in the region before the focal point. On the other hand, a Mie particle can be confined transversely in the primary ring and accelerated along the curved trajectory of CABs to the focal point, then pushed further all the way through the focal point rather than being trapped therein, and eventually accelerated further along a straight trajectory in the direction of light propagation over 100 wavelengths, due to the weak diffraction characteristic of a morphed Bessel-like beam of CABs. The exotic curved-straight trajectory transport of particles by the CABs may find applications in the case where the transport path is partly blocked.

Nonlinearities induced by parametric resonance in effectively 1D atomic Bose condensates

We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the system. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking, as is the similarity of techniques used to study them.

Experimental investigation on optical vortex tweezers for microbubble trapping

AbstractIn this paper, we investigated the microbubble trapping using optical vortex tweezers. It is shown that the microbubble can be trapped by the vortex optical tweezers, in which the trapping light beam is of vortex beam. We studied a relationship between the transverse capture gradient force and the topological charges of the illuminating vortex beam. For objective lenses with numerical aperture of 1.25 (100×), the force measurement was performed by the power spectral density (PSD) roll-off method. It was shown that transverse trapping forces of vortex optical tweezers increase with the increment of the laser power for fixed topological charge. Whereas, the increase in the topological charges of vortex beam for the same laser power results in the decrease of the transverse trapping forces. The experimental results demonstrated that the laser mode (topological charge) has significant influence on the lateral trapping force.

Trapping two types of particles using a focused partially coherent modified Bessel-Gaussian beam

Using the extended Huygens-Fresnel principle and Rayleigh scattering regime, the analytical expressions for the intensity and radiation forces of a focused partially coherent modified Bessel-Gaussian (MBG) beam have been derived, and used to study the optical trapping effect of the focused partially coherent MBG beams acting on dielectric sphere with different refractive indices. The results show that the focused partially coherent MBG beam with m = 0 cannot capture the low index of refraction particles, but can trap the high index of refraction particles. The focused partially coherent MBG beam with m ≥ 1 can trap the high index of refraction particles to a ring on the focal plane, and simultaneously capture the low index of refraction particles to z-axis. When the topological charge m increases, the radiation force decreases while the transverse trapping range increases for low and high index of refractive particles. Besides, larger the value of the spectral degree of coherence ξ is, the easier the two types of particles are trapped by the focused partially coherent MBG beam. Trapping stability is also analysed. The obtained results are useful for analysing the trapping efficiency of focused partially coherent MBG beam applied in micromanipulation and biotechnology.

Enhance of optical trapping efficiency by nonlinear optical tweezers

In this article, enhance of optical trapping efficiency by the nonlinear optical tweezers is investigated. The expressions described the longitudinal and transverse optical trapping efficiencies are theoretically derived. The influence of average laser power on the optical trapping efficiency is observed and discussed in comparison with that of linear optical tweezers. Remarkably, the optical trapping efficiency of nonlinear optical tweezers can be enhanced by using average laser power, and get several times higher than that of the linear optical ones having the same configuration.

Selectively transporting small chiral particles with circularly polarized Airy beams.

Based on the full wave simulation, we demonstrate that a circularly polarized vector Airy beam can selectively transport small chiral particles along a curved trajectory via the chirality-tailored optical forces. The transverse optical forces can draw the chiral particles with different particle chirality towards or away from the intensity maxima of the beam, leading to the selective trapping in the transverse plane. The transversely trapped chiral particles are then accelerated along a curved trajectory of the Airy beam by the chirality-tailored longitudinal scattering force, rendering an alternative way to sort and/or transport chiral particles with specified helicity. Finally, the underlying physics of the chirality induced transverse trap and de-trap phenomena are examined by the analytical theory within the dipole approximation.

Controlling steady-state bipartite entanglement and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one.

Multimode Bose-Hubbard model for quantum dipolar gases in confined geometries

We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons, they experience a periodic potential due to an optical lattice oriented along the wave guide and are polarised by an electric field orthogonal to the guide axis. The array is mechanically unstable by opening the transverse confinement in the direction orthogonal to the polarizing electric field and can undergo a transition to a double-chain (zigzag) structure. For this geometry we derive a multi-mode generalized Bose-Hubbard model for determining the quantum phases of the gas at the mechanical instability taking into account the quantum fluctuations in all directions of space. Our model limits the dimension of the numerically relevant Hilbert subspace by means of an appropriate decomposition of the field operator, which is obtained from a field theoretical model of the linear-zigzag instability. We determine the phase diagrams of small systems using exact diagonalization and find that, even for tight transverse confinement, the aspect ratio between the two transverse trap frequencies controls not only the classical but also the quantum properties of the ground state in a non-trivial way. Convergence tests at the linear-zigzag instability demonstrate that our multi-mode generalized Bose-Hubbard model can catch the essential features of the quantum phases of dipolar gases in confined geometries with a limited computational effort.

Optofluidic Chip for Single-Beam Optical Trapping of Particles Enabling Confocal Raman Measurements

We present an optofluidic chip in polymethyl methacrylate (PMMA) that combines optical trapping of single particles with confocal Raman spectroscopy. We introduce the design of the optofluidic chip and the ray-tracing simulations combined with mathematical calculations used to determine the optical forces exerted on the particles and to model the excitation and collection of Raman scattering. The optical trapping is done using a single-beam gradient trap realized by a high numerical aperture free-form reflector, monolithically embedded in the optofluidic chip. The focused beam functions both as the excitation beam as well as the trapping beam. The embedded free-form reflector is also used to collect the Raman scattered light generated from the trapped particle. We discuss the fabrication process for the prototyping of the chip, which consists of an ultraprecision diamond turning step and a sealing step. Finally, we demonstrate the functionality of the optofluidic chip in a proof-of-concept experimental setup and trap polystyrene beads with diameters from 6 to 15 $ \mu \text{m}$ . We characterize the maximal transverse optical trap strength in the sample flow direction using the drag force method, measuring average efficiencies that lie between 0.11 and 0.36, and perform confocal Raman measurements of these particles.

Using quaternions to analyze the trapping force of an ellipsoidal bead

In the ray-optics (RO) model of optical tweezers, tracing refractive and reflected rays with vectors play important roles in calculating the trapping forces. Traditional ray-tracing method with solid geometry, to some extent, is complicated in determining the orientations of those refractive and reflected rays according to spatial incident rays. It is difficult to calculate the trapping forces for irregular particles. In this paper, quaternion is proposed to rotate ray vectors for simplifying the traces of all kinds of spatial rays. Then, it is appropriate to calculate the trapping force of an ellipsoid bead. Based on the algorithm of quaternion and the convention between the interface normal and angular directions, the direction of normal always points from optically denser medium to thinner medium. The rotation axis is the cross product of the incident ray and the interface normal. And the positive angular direction can be determined by right-hand rule based on the orientation of the rotation axis. According to Snell' law, the rotation angle between the incident ray and refractive/reflected ray can be determined. The quaternion for rotation consists of rotation axis and angle. So the refractive and reflected rays are both determined by quaternions of incident ray and rotation based on rotation rules. Furthermore, the force on interface can also be calculated according to momentum changes of the photon before and after the interface refraction and reflection. The quaternion method is used to analyze the effects of coverslip position and deformation ratio on the trapping efficiency of ellipsoid particles. Our simulative results show that the lateral and axial trapping efficiencies are obviously affected by the deformation of the ellipsoid itself. No matter whether the bead deforms transversely or axially, the transverse and axial trapping efficiencies both become larger at a specific deformation. Meantime, the increase of the spherical aberration reduces the maximum axial trapping efficiency, and the equilibrium position of the bead becomes farther away from the center. Using quaternion method, the calculation of refractive lightvector can be simplified in comparison with by using the method of Euclidean geometry or transformation matrix. Theoretically, this quaternion can be used to trace rays on any irregular geometric surfaces. In conclusion, the method of quaternion can make ray tracing easier and extend the applications of RO model.

Noise-induced transport in the motion of trapped ions

The interplay of noise and quantum coherence in transport gives rise to rich dynamics relevant for a variety of systems. In this work, we put forward a proposal for an experiment testing noise-induced transport in the vibrational modes of a chain of trapped ions. We focus on the case of transverse modes, considering multiple-isotope chains and an "angle trap", where the transverse trapping varies along the chain. This variation induces localization of the motional modes and therefore suppresses transport. By suitably choosing the action of laser fields that couple to the internal and external degrees of freedom of the ions, we show how to implement effective local dephasing on the modes, broadening the vibrational resonances. This leads to an overlap of the local mode frequencies, giving rise to a pronounced increase in the transport of excitations along the chain. We propose an implementation and measurement scheme which require neither ground-state cooling nor low heating rates, and we illustrate our results with a simulation of the dynamics for a chain of three ions.

Buckling Transitions and Clock Order of Two-Dimensional Coulomb Crystals

Crystals of repulsively interacting ions in planar traps form hexagonal lattices, which undergo a buckling instability towards a multi-layer structure as the transverse trap frequency is reduced. Numerical and experimental results indicate that the new structure is composed of three planes, whose separation increases continuously from zero. We study the effects of thermal and quantum fluctuations by mapping this structural instability to the six-state clock model. A prominent implication of this mapping is that at finite temperature, fluctuations split the buckling instability into two thermal transitions, accompanied by the appearance of an intermediate critical phase. This phase is characterized by quasi-long-range order in the spatial tripartite pattern. It is manifested by broadened Bragg peaks at new wave vectors, whose line-shape provides a direct measurement of the temperature dependent exponent $\eta(T)$ characteristic of the power-law correlations in the critical phase. A quantum phase transition is found at the largest value of the critical transverse frequency: here the critical intermediate phase shrinks to zero. Moreover, within the ordered phase, we predict a crossover from classical to quantum behavior, signifying the emergence of an additional characteristic scale for clock order. We discuss experimental realizations with trapped ions and polarized dipolar gases, and propose that within accessible technology, such experiments can provide a direct probe of the rich phase diagram of the quantum clock model, not easily observable in condensed matter analogues. Therefore, this works highlights the potential for ionic and dipolar systems to serve as simulators for complex models in statistical mechanics and condensed matter physics.

Single fiber optical trapping of a liquid droplet and its application in microresonator

We propose and demonstrate an optical trapping of a liquid droplet and its application based on an annular core microstructured optical fiber. We grind and polish the annular core fiber tip to be a special frustum cone shape to make sure the optical force large enough to trap the liquid droplet non-intrusively. The axial and transverse optical trapping forces are simulated. In addition, we investigate the whispering gallery modes resonance characteristic of the trapped liquid droplet as the example of applications. The whispering gallery modes spectrum is sensitive to the size of the micro liquid droplet. Due to the simple construction and flexible manipulation, the fiber-based optical trapping technology for micro liquid droplets trapping, manipulating, and controlling has great application penitential in many fields, such as physics, biology, and interdisciplinary studies.

Vortex beams and radiation torque for kidney stone management

Our team previously developed an instrument to reposition kidney stones with acoustic radiation force. In a clinical trial, the technology was used to transcutaneously facilitate passage of small stones and to relieve pain by dislodging obstructing large stones. Acoustic trapping and manipulation of kidney stones in water has recently been investigated using both single element and sector arrays in the range of 0.3–1.5 MHz. Experimental holographic reconstruction of the transducer surface velocity confirmed the proper operation of each transducer. Human stones approximately 5 mm, as well as glass and aluminum beads, were placed on a flat tissue phantom in a water bath. During exposure, stones were drawn to the beam axis, and then controllably translated along the surface in any direction transverse to the beam. The phase between sector elements could be used to control the vortex size, as well as rate and direction of rotation of the trapped object. The trapping effect was disrupted at increased transducer output, possibly by generation of acoustic streaming. In conclusion, a method was tested for transverse acoustic trapping of kidney stones with vortex beams. [This work was supported by RBBR 14-02-00426, NIH NIDDK DK43881, DK104854, and DK092197, and NSBRI through NASA NCC 9-58.]

Near-field acoustic microbead trapping as remote anchor for single particle manipulation

We recently proposed an analytical model of a two-dimensional acoustic trapping of polystyrene beads in the ray acoustics regime, where a bead diameter is larger than the wavelength used. As its experimental validation, this paper demonstrates the transverse (or lateral) trapping of individual polystyrene beads in the near field of focused ultrasound. A 100 μm bead is immobilized on the central beam axis by a focused sound beam from a 30 MHz single element lithium niobate transducer, after being laterally displaced through hundreds of micrometers. Maximum displacement, a longest lateral distance at which a trapped bead can be directed towards the central axis, is thus measured over a discrete frequency range from 24 MHz to 36 MHz. The displacement data are found to be between 323.7 μm and 470.2 μm, depending on the transducer's driving frequency and input voltage amplitude. The experimental results are compared with their corresponding model values, and their relative errors lie between 0.9% and 3.9%. The results suggest that this remote maneuvering technique may be employed to manipulate individual cells through solid microbeads, provoking certain cellular reactions to localized mechanical disturbance without direct contact.

Highly Focused Conical Optical Field for Pico-Newton Scale Force Sensing

We propose to use a highly focused conical optical field generated by cone-frustum-shaped annular core fiber (ACF) tip for Pico-Newton scale force sensing. And we theoretically calculate the wave propagation in the ACF tip and its surrounding medium based on angular spectrum representation. The propagation properties and focusing effect of the highly focused conical optical field are also discussed and demonstrated experimentally. The ACF tip provides very strong focusing effect for the guided mode in the ACF. We show that there are stable three-dimensional trap-points for Rayleigh particles in the main lobe and every ring of the focused field with Bessel-like profile. And the transverse trapping forces are much greater (almost 30 times) than their corresponding longitudinal radiation forces so that a particle trapped by highly focused conical beam is only sensitive for disturbing force in longitudinal direction. Force sensitivities in longitudinal direction and the detection range are also discussed.

On-chip optical trapping and Raman spectroscopy using a TripleX dual-waveguide trap.

We present a new approach to the dual-beam geometry for on-chip optical trapping and Raman spectroscopy, using waveguides microfabricated in TripleX technology. Such waveguides are box shaped and consist of SiO2 and Si3N4, so as to provide a low index contrast with respect to the SiO2 claddings and low loss, while retaining the advantages of Si3N4. The waveguides enable both the trapping and Raman functionality with the same dual beams. Polystyrene beads of 1 μm diameter can be easily trapped with the device. In the axial direction discrete trapping positions occur, owing to the intensity pattern of the interfering beams. Trapping events are interpreted on the basis of simulated optical fields and calculated optical forces. The average transverse trap stiffness is 0.8 pN/nm/W, indicating that a strong trap is formed by the beams emitted by the waveguides. Finally, we measure Raman spectra of trapped beads for short integration times (down to 0.25 s), which is very promising for Raman spectroscopy of microbiological cells.

Determination of motility forces on isolated chromosomes with laser tweezers

Quantitative determination of the motility forces of chromosomes during cell division is fundamental to understanding a process that is universal among eukaryotic organisms. Using an optical tweezers system, isolated mammalian chromosomes were held in a 1064 nm laser trap. The minimum force required to move a single chromosome was determined to be ≈0.8–5 pN. The maximum transverse trapping efficiency of the isolated chromosomes was calculated as ≈0.01–0.02. These results confirm theoretical force calculations of ≈0.1–12 pN to move a chromosome on the mitotic or meiotic spindle. The verification of these results was carried out by calibration of the optical tweezers when trapping microspheres with a diameter of 4.5–15 µm in media with 1–7 cP viscosity. The results of the chromosome and microsphere trapping experiments agree with optical models developed to simulate trapping of cylindrical and spherical specimens.

Quantitative analysis of temperature dependent acoustic trapping characteristics by using concentric annular type dual element ultrasonic transducer

This paper presents the temperature dependence of lateral acoustic trapping capability by probing the speed of sound in individual lipid droplets at a given temperature of water and measuring its corresponding displacement, a value for quantitatively evaluating a spring-like behavior of the acoustic trap with certain strength. A 20/40MHz dual element LiNbO3 ultrasonic transducer is fabricated to simultaneously perform both transverse trapping and sound speed measurement for each droplet over a discrete temperature range from 20°C to 30°C. Time of flight method is employed for pulse tracking that determines the arrival time of an echo reflected back from either a trapped droplet or a mylar film.The estimated speeds of sound in water and droplets are 1484.8m/s and 1431.6m/s at 20°C, while 1506.0m/s and 1400.6m/s at 30°C, respectively. As the temperature rises, the sound speed in droplets decreases at an average rate of 3.1m/s/°C, and the speed in water increases at 2.1m/s/°C. The average displacement varies from 150.0μm to 179.0μm with an increasing rate of 2.9μm/°C, and its standard deviation is obtained between 1.0μm and 2.0μm over the same temperature range. Reduced sound speed as a function of rising temperature results in increased displacement, indicating that the trapping strength is adjustable by regulating ambient temperature in water as well as by changing transducer excitation parameters. Therefore, the results suggest that the temperature dependence of this trapping technique can be exploited for developing a remote manipulation tool of micron-sized particles in a thermally fluctuating environment. It is also shown that any deviated trapping strength caused by thermal disturbance near the trap can be restored to its desired level by compensating either temperature difference or trapping system condition.