One-dimensional Trap Research Articles

Single-nanoparticle electrophoretic mobility determination and trapping using active-feedback 3D tracking.

Nanoparticles (NP) are versatile materials with widespread applications across medicine and engineering. Despite rapid incorporation into drug delivery, therapeutics, and many more areas of research and development, there is a lack of robust characterization methods. Light scattering techniques such as dynamic light scattering (DLS) and electrophoretic light scattering (ELS) use an ensemble-averaged approach to the characterization of nanoparticle size and electrophoretic mobility (EM), leading to inaccuracies when applied to polydisperse or heterogeneous populations. To address this lack of single-nanoparticle characterization, this work applies 3D Single-Molecule Active Real-time Tracking (3D-SMART) to simultaneously determine NP size and EM on a per-particle basis. Single-nanoparticle EM is determined by using active feedback to "lock on" to a single particle and apply an oscillating electric field along one axis. A maximum likelihood approach is applied to extract the single-particle EM from the oscillating nanoparticle position along the field-actuated axis, while mean squared displacement is used along the non-actuated axes to determine size. Unfunctionalized and carboxyl-functionalized polystyrene NPs are found to have unique EM based on their individual size and surface characteristics, and it is demonstrated that single-nanoparticle EM is a more precise tool for distinguishing unique NP preparations than diffusion alone, able to determine the charge number of individual NPs to an uncertainty of less than 30. This method also explored individual nanoparticle EM in various ionic strengths (0.25-5 mM) and found decreased EM as a function of increasing ionic strength, in agreement with results determined via bulk characterization methods. Finally, it is demonstrated that the electric field can be manipulated in real time in response to particle position, resulting in one-dimensional electrokinetic trapping. Critically, this new single-nanoparticle EM determination and trapping method does not require microfluidics, opening the possibility for the exploration of single-nanoparticle EM in live tissue and more comprehensive characterization of nanoparticles in biologically relevant environments.

Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model

We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful analysis of the volume growth of the invariant measure of the process under study. As for the quantitative homogenization results, these include both quenched and annealed Berry–Esseen-type theorems, as well as a quantitative quenched local limit theorem. Whilst the model we study here is a particularly simple example of a random walk in a random environment, we believe the roadmap we provide for establishing the latter result in particular will be useful for deriving quantitative local limit theorems in other, more challenging, settings.

New topological rainbow trapping approach for phononic beam-foundation systems

Rainbow trapping is of great significance for frequency-based wave splitting and broadband wave attenuation. By recognizing the deficiency of prevailing gradient rainbow reflection devices in terms of energy concentration and broadband vibration isolation, we design a new topological rainbow trapping device by introducing a topological protected interface mode (TPIM) into the prevailing gradient rainbow device. Therefore, a topological rainbow trapping beam composed of a homogenous beam rested on an alternate and gradient foundation is constructed. Using theoretical and numerical analysis, we perform a unit-cell band structure analysis. The dependence of bandgap region and group velocity on the reference foundation stiffness is investigated. With the help of the topological phase transition and Zak phase analysis, we successfully predict and demonstrate TPIM. A quantitative evaluation of the advancement of topological rainbow devices upon the prevailing gradient device in vibration amplification and broadband wave attenuation is also presented. We believe that the robust one-dimensional topological rainbow trapping beam will be useful in many applications, such as energy harvesting, wave splitting, and vibration control.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces.

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Correction: Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

Correction: Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

We analyze a system of fermions in a one dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two fermion pairs numerically using the so-called "coboson formalism" as an alternative to techniques which are based on the single-particle basis. This allows us to explore the strongly bound regime, approaching the limit of infinite attraction in which the composite particles behave as hard-core bosons. Our procedure is computationally inexpensive and illustrates how the coboson toolbox is useful for ultracold atom systems even in absence of condensation.

Suppression of laser beam’s polarization and intensity fluctuation via a Mach–Zehnder interferometer with proper feedback

Long ground-Rydberg coherence lifetime is interesting for implementing high-fidelity quantum logic gates, many-body physics, and other quantum information protocols. However, the potential well formed by a conventional far-off-resonance red-detuned optical-dipole trap that is attractive for ground-state cold atoms is usually repulsive for Rydberg atoms, which will result in the rapid loss of atoms and low repetition rate of the experimental sequence. Moreover, the coherence time will be sharply shortened due to the residual thermal motion of cold atoms. These issues can be addressed by a one-dimensional magic lattice trap, which can form a deeper potential trap than the traveling wave optical dipole trap when the output power is limited. In addition, these common techniques for atomic confinement generally have certain requirements for the polarization and intensity stability of the laser. Here, we demonstrated a method to suppress both the polarization drift and power fluctuation only based on the phase management of the Mach–Zehnder interferometer for a one-dimensional magic lattice trap. With the combination of three wave plates and the interferometer, we used the instrument to collect data in the time domain, analyzed the fluctuation of laser intensity, and calculated the noise power spectral density. We found that the total intensity fluctuation comprising laser power fluctuation and polarization drift was significantly suppressed, and the noise power spectral density after closed-loop locking with a typical bandwidth of 1–3000 Hz was significantly lower than that under the free running of the laser system. Typically, at 1000 Hz, the noise power spectral density after locking was about 10 dB lower than that under the free running of a master oscillator power amplifier system. The intensity–polarization control technique provides potential applications for atomic confinement protocols that demand fixed polarization and intensity.

Quench dynamics of two interacting atoms in a one-dimensional anharmonic trap

A temporal response of two interacting particles to a quench of the coupling strength in one-dimensional harmonic and anharmonic traps is explored. The coupling strength is changed from repulsive to attractive interactions and vice versa. The time evolution of the fidelity, wave packet, one-body reduced density matrix and momentum distributions is analyzed in details. It was found that impacts of the pre- and postquench states interchange during the dynamics. In the case of the anharmonic trap additional contribution of the center-of-mass excited states comes into play and the whole evolution becomes significantly altered. Yet the impact of the pre- and postquench states in some cases still could be identified. The quench dynamics of the ground and excited states are considered.

Erratum: “Two and three particles interacting in a one-dimensional trap” [Am. J. Phys. 85, 769 (2017)

Erratum: “Two and three particles interacting in a one-dimensional trap” [Am. J. Phys. <b>85</b>, 769 (2017)

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Formation Dynamics of Black- and White-Hole Horizons in an Analogue Gravity Model

We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks–Girardeau gas), we show that by switching on a step potential, either a sonic, black-hole-like horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated white-hole horizon, although a stable stationary solution of the dynamical equations with those properties is analytically found. Moreover, we show that the semiclassical dynamics, based on the Gross–Pitaevskii equation, conforms to the exact solution only in the case of fully subsonic flows while a stationary solution exhibiting a supersonic transition is never reached dynamically.

Generating a nonequilibrium stationary state from a ground-state condensate through an almost adiabatic cycle

It is shown that the ground state of weakly interacting Bose particles in a quasi one-dimensional box trap can be converted into an excited stationary state by an adiabatic cyclic operation that involves a quench of interaction strength: A sharp impurity potential is applied and its strength is varied during the cycle, which induces a nonequilibrium stationary state exhibiting the inversion of population. This process is robust in the sense that the resultant stationary state is almost independent of the details of the cycle, such as the position of the impurity as long as the cycle is far enough from critical regions. The case of the failure of the population inversion due to the strong interparticle interactions is also examined.

Sawtooth-wave adiabatic passage in a magneto-optical trap

We investigate theoretically the application of sawtooth-wave adiabatic passage (SWAP) in a one-dimensional (1D) magneto-optical trap (MOT). As opposed to related methods that have been previously discussed, our approach utilizes repeated cycles of stimulated absorption and emission processes to achieve both trapping and cooling, thereby reducing the adverse effects that arise from photon scattering. Specifically, we demonstrate this method's ability to cool, slow, and trap particles with fewer spontaneously emitted photons, with higher forces, and in less time when compared to a traditional MOT scheme that utilizes the same narrow linewidth transition. We calculate the phase-space compression that is achievable and characterize the resulting system equilibrium cloud size and temperature.

Inhomogeneity of a one-dimensional Yukawa system in a trap

A system of like charges interacting with a weak repulsive Yukawa potential and confined in a one-dimensional parabolic electrostatic trap is under consideration. It is shown that inter-particle distance in this system grows from the center of the structure to its periphery. The same effect takes place for the mean square displacement of particles from their equilibrium positions, which corresponds to the amplitude of thermal oscillations, and for the value of Lindemann parameter. This leads to different degrees of order for particles located at different distances from the center of the structure. This result might be important for the study of phase transitions in dusty, colloidal and one-component plasmas.

Crossover of Quasiparticles and Statistics of Bose-Einstein Condensate with Increasing Interaction: from an Ideal Gas to a Thomas-Fermi Regime. The Case of a One-Dimensional Flat Trap

A change-over of the quasiparticle wave functions and spectrum under a variation in an interparticle interaction in a Bose-Einstein condensed gas of bosons confined in a one-dimensional trap with a flat potential and impermeable walls is studied analytically and numerically. An efficient approximate method of analysis is developed. It yields a solution to the self-consistent Bogoliubov and Gross-Pitaevskii equations for quasiparticles and the condensate that describes a crossover from the regime of a gas of noninteracting bosons to the regime of a gas with the interaction being strong enough to reach a Thomas-Fermi asymptotics. As a result, the characteristic function of the total number of noncondensed particles is found which, for the first time, allows one to figure out how the quantum statistics of fluctuations of the number of particles in the condensate depends on its inhomogeneity and the interparticle interaction in the case of the flat trap. The qualitative features of this dependence as well as a possibility of an experimental observation of the predicted effects in the actual traps are discussed.

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900 (2006)], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.

Parafermionic behavior of Bose-Einstein condensates

Bright solitons of 7Li atoms in a quasi one-dimensional optical trap, formed in a stable Bose–Einstein condensate in which the interactions have been magnetically tuned from repulsive to attractive, have been seen to exhibit repulsive interactions among them when set in motion by offsetting the optical potential. Solving first the Gross–Pitaevskii equation for the special conditions corresponding to the experiment, we show then that this system can be described in terms of generalized parafermionic oscillators, the order of the parafermions being related to the strength of the interaction among the atoms and being a measure of the bosonic behavior vs. the fermionic behavior of the system.

First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate.

First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here, we study the interplay between these two strategies, for a diffusing particle in a one-dimensional trapping potential V(x), being randomly reset at a constant rate r. Stochastic resetting has been of great interest as it is known to provide an "optimal rate" (r_{*}) at which the mean first passage time is a minimum. On the other hand, an attractive potential also assists in the first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e., r_{*}→0). We derive a condition for this optimal resetting rate vanishing transition, which is continuous. We study this problem for various functional forms of V(x), some analytically, and the rest numerically. We find that the optimal rate r_{*} vanishes with a deviation from the critical strength of the potential as a power law with an exponent β which appears to be universal.

Review of one-dimensional few-body systems in ultracold atomic physics

We review some recent theoretical and experimental developments of one-dimensional few-body problems in ultracold atomic system. The experiments have so far realized the deterministic loading of few atoms in the ground state of a potential well, the observation of tunneling dynamics out of the metastable trap controlled by a magnetic gradient for a repulsively or attractively interacting system, the preparation of two fermionic atoms in an isolated double-well potential with a full control over the quantum state of the system, the formation of a Fermi sea by studying quasi-one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions, and the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These achievements make the ultracold atoms an ideal platform to study many-body physics in a bottom-up approach, i.e., one starts from the fundamental building block of the system and observes the emergence of many-body effects by adding atoms one by one into the system. Corresponding theoretical models have been developed to explain the experimental data, to tackle the crossover boundary between few and many particles, and even explore the solvability and integrability of the models, especially the energy spectrum of interacting few atoms such as two atoms in a harmonic trap, two heteronuclear atoms of unequal mass in a ring trap, and two atoms in a &lt;inline-formula&gt;&lt;tex-math id="M6000"&gt;\begin{document}$\delta$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181993_M6000.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181993_M6000.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;-barrier split double well potential. After a brief review of Bethe-Ansatz method, a theory for the tunneling of one atom out of a trap containing two interacting cold atoms is developed based on the calculation of the quasiparticle wave function, and the tunneling dynamics of two atoms starting from the NOON state is explored from the exactly solved model of &lt;inline-formula&gt;&lt;tex-math id="M6001"&gt;\begin{document}$\delta$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181993_M6001.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181993_M6001.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;-barrier split double well based on a Bethe ansatz type hypothesis of the wave functions. It was shown that the spectroscopy and spin dynamics for strongly interacting few atoms of spin-1/2 and spin-1 can be described by effective spin chain Hamiltonians, which serves as a useful and efficient tool to study the quantum magnetism with clod atoms.

Experimental realization of Feynman’s ratchet

Feynman’s ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures TA and TB, that was proposed by Richard Feynman to illustrate the second law of thermodynamics. In equilibrium (TA = TB), thermal fluctuations prevent the ratchet from generating directed motion. When the ratchet is maintained away from equilibrium by a temperature difference (), it can operate as a heat engine, rectifying thermal fluctuations to perform work. While it has attracted much interest, the operation of Feynman’s ratchet as a heat engine has not been realized experimentally, due to technical challenges. In this work, we realize Feynman’s ratchet with a colloidal particle in a one-dimensional optical trap in contact with two heat reservoirs: one is the surrounding water, while the effect of the other reservoir is generated by a novel feedback mechanism, using the Metropolis algorithm to impose detailed balance. We verify that the system does not produce work when TA = TB, and that it becomes a microscopic heat engine when . We analyze work, heat and entropy production as functions of the temperature difference and external load. Our experimental realization of Feynman’s ratchet and the Metropolis algorithm can also be used to study the thermodynamics of feedback control and information processing, the working mechanism of molecular motors, and controllable particle transportation.