Trap Axis Research Articles

Stability, diffusion and interactions of nonlinear excitations in a many body system

When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.

Open microwave cavity for use in a Purcell enhancement cooling scheme.

A microwave cavity is described which can be used to cool lepton plasmas for potential use in synthesis of antihydrogen. The cooling scheme is an incarnation of the Purcell effect: when plasmas are coupled to a microwave cavity, the plasma cooling rate is resonantly enhanced through increased spontaneous emission of cyclotron radiation. The cavity forms a three electrode section of a Penning-Malmberg trap and has a bulged cylindrical geometry with open ends aligned with the magnetic trapping axis. This allows plasmas to be injected and removed from the cavity without the need for moving parts while maintaining high quality factors for resonant modes. The cavity includes unique surface preparations for adjusting the cavity quality factor and achieving anti-static shielding using thin layers of nichrome and colloidal graphite, respectively. Geometric design considerations for a cavity with strong cooling power and low equilibrium plasma temperatures are discussed. Cavities of this weak-bulge design will be applicable to many situations where an open geometry is required.

Integrated optical addressing of an ion qubit.

The long coherence times and strong Coulomb interactions afforded by trapped ion qubits have enabled realizations of the necessary primitives for quantum information processing and the highest-fidelity quantum operations in any qubit to date. Although light delivery to each individual ion in a system is essential for general quantum manipulations and readout, experiments so far have employed optical systems that are cumbersome to scale to even a few tens of qubits. Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing that are fully integrated within a surface-electrode ion trap chip. Ion qubits are addressed at multiple locations via focusing grating couplers emitting through openings in the trap electrodes to ions trapped 50 μm above the chip; using this light, we perform quantum coherent operations on the optical qubit transition in individual 88Sr+ ions. The grating focuses the beam to a diffraction-limited spot near the ion position with 2 μm 1/e2 radius along the trap axis, and we measure crosstalk errors between 10-2 and 4 × 10-4 at distances 7.5-15 μm from the beam centre. Owing to the scalability of the planar fabrication technique employed, together with the tight focusing and stable alignment afforded by the integration of the optics within the trap chip, this approach presents a path to creating the optical systems required for large-scale trapped-ion quantum information processing.

Photonic Torque Microscopy of the Nonconservative Force Field for Optically Trapped Silicon Nanowires.

We measure, by photonic torque microscopy, the nonconservative rotational motion arising from the transverse components of the radiation pressure on optically trapped, ultrathin silicon nanowires. Unlike spherical particles, we find that nonconservative effects have a significant influence on the nanowire dynamics in the trap. We show that the extreme shape of the trapped nanowires yields a transverse component of the radiation pressure that results in an orbital rotation of the nanowire about the trap axis. We study the resulting motion as a function of optical power and nanowire length, discussing its size-scaling behavior. These shape-dependent nonconservative effects have implications for optical force calibration and optomechanics with levitated nonspherical particles.

Tolerance in the Ramsey interference of a trapped nanodiamond

The scheme recently proposed in [M. Scala et al., Phys Rev Lett 111, 180403 (2013)], where a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle, provides a way to detect spatial quantum superpositions by means of spin measurements only. Here, the effect of unwanted coupling with other motional degrees of freedom is considered and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to misalignment between the quantization axis of the NV center spin and the trapping axis are shown not to change the qualitative behavior of the system, so that a proof-of- principle experiment can be neatly performed. Our analysis, which shows that the scheme retains the important features of not requiring ground state cooling and of being resistant to thermal fluctuations, can be useful for the several schemes which have been proposed recently for testing macroscopic superpositions in trapped microsystems.

Influence of the energy-band structure on ultracold reactive processes in lattices

We study theoretically ultracold collisions in quasi one-dimensional optical traps for bosonic and fermionic reactive molecules in the presence of a periodic potential along the trap axis. Elastic, reactive, and umklapp processes due to non-conservation of the center of mass motion are investigated for parameters of relevant experimental interest. The model naturally keeps into account the effect of excited energy bands and is particularly suited for being adapted to rigorous close-coupled calculations. Our formalism shows that a correct derivation of the parameters in tight-binding effective models must include the strong momentum dependence of the coupling constant we predict even for deep lattices.

Measuring the charge density of a tapered optical fiber using trapped microparticles.

We report the measurements of charge density of tapered optical fibers using charged particles confined in a linear Paul trap at ambient pressure. A tapered optical fiber is placed across the trap axis at a right angle, and polystyrene microparticles are trapped along the trap axis. The distance between the equilibrium position of a positively charged particle and the tapered fiber is used to estimate the amount of charge per unit length of the fiber without knowing the amount of charge of the trapped particle. The charge per unit length of a tapered fiber with a diameter of 1.6 μm was measured to be 2-1+3×10-11 C/m.

Trapped ion chain thermometry and mass spectrometry through imaging.

We demonstrate a spatial-imaging thermometry technique for ions in a one-dimensional Coulomb crystal by relating their imaged spatial extent along the linear radiofrequency ion trap axis to normal modes of vibration of coupled oscillators in a harmonic potential. We also use the thermal spatial spread of "bright" ions in the case of a two-species mixed chain to measure the center-of-mass resonance frequency of the entire chain and infer the molecular composition of the co-trapped "dark" ions. These non-destructive techniques create new possibilities for better understanding of sympathetic cooling in mixed-ion chains, improving few-ion mass spectrometry, and trapped-ion thermometry without requiring a scan of Doppler cooling parameters.

Phase-Stable Free-Space Optical Lattices for Trapped Ions.

We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the 157 μm range along the trap axis at accuracies of better than 6nm.

Planar Penning trap with combined resonance and top dynamics on quadratic algebra

We study the dynamics of a charge in the planar Penning trap in which the direction of the magnetic field does not coincide with the trap axis. Under a certain combined resonance condition on the deviation angle and magnitudes of magnetic and electric fields, the trajectories of a charge are near-periodic.We describe the reduction to a top-like system with one degree of freedom on the space with quadratic Poisson brackets and study the stability of the equilibrium points of this system.

Oscillons of Bose–Einstein condensate (A review)

The dynamics of localized structures of atomic Bose–Einstein condensate in traps with oscillating walls has been analyzed. The properties of these oscillons localized in the longitudinal and transverse directions with respect to the trap axis are compared with the properties of conservative and dissipative solitons.

The Features of Refraction of Electromagnetic Waves Near the Electron Cyclotron Resonance Surface in an Open Magnetic Trap

Some features of the electromagnetic wave propagation near the electron cyclotron resonance region in axisymmetric magnetic traps are studied both analytically and numerically. The ray paths are obtained with allowance for the plasma density inhomogeneities, magnetic field direction, and magnetic field strength. Criteria for the limiting cases of constructive refraction (the ray paths are attracted to the trap axis, where effective absorption takes place) and destructive refraction (the ray paths are expelled from the trap axis, and efficient heating of the central part of the plasma column is not possible) are found. It is shown that the inhomogeneities of the magnetic field direction and plasma density, which are typical of axisymmetric magnetic traps, as well as the spatial dispersion effects, can strongly affect the electromagnetic wave propagation near the electron cyclotron resonance surface.

Particle dynamics in damped nonlinear quadrupole ion traps

We examine the motions of particles in quadrupole ion traps as a function of damping and trapping forces, including cases where nonlinear damping or nonlinearities in the electric field geometry play significant roles. In the absence of nonlinearities, particles are either damped to the trap center or ejected, while their addition brings about a rich spectrum of stable closed particle trajectories. In three-dimensional (3D) quadrupole traps, the extended orbits are typically confined to the trap axis, and for this case we present a 1D analysis of the relevant equation of motion. We follow this with an analysis of 2D quadrupole traps that frequently show diamond-shaped closed orbits. For both the 1D and 2D cases, we present experimental observations of the calculated trajectories in microparticle ion traps. We also report the discovery of a new collective behavior in damped 2D microparticle ion traps, where particles spontaneously assemble into a remarkable knot of overlapping, corotating diamond orbits, self-stabilized by air currents arising from the particle motion.

Nonequilibrium dynamics of an ultracold dipolar gas

We study the relaxation and damping dynamics of an ultracold, but not quantum degenerate, gas consisting of dipolar particles. These simulations are performed using a direct simulation Monte Carlo method and employing the highly anisotropic differential cross section of dipoles in the Wigner threshold regime. We find that both cross-dimensional relaxation and damping of breathing modes occur at rates that are strongly dependent on the orientation of the dipole moments relative to the trap axis. The relaxation simulations are in excellent agreement with recent experimental results in erbium. The results direct our interest toward a less explored regime in dipolar gases where interactions are dominated by collision processes rather than mean-field interactions.

Diocotron modulation in an electron plasma through continuous radio-frequency excitation

The application of a radio-frequency (RF) excitation to any electrode of a Penning-Malmberg trap may result in significant electron heating and ionization of the residual gas with the formation of a plasma column when the RF frequency is of the order or larger than the typical axial bounce frequencies of few-eV electrons. The use of a quadrupolar excitation can induce additional phenomena, like formation of dense, narrow-cross section columns which exhibit an mθ=1 diocotron mode, i.e., a rotation of their center around the trap axis. A series of experiments is presented and discussed showing that the continuous application of such excitation causes a dramatic perturbation of the plasma equilibrium also involving continuous production and loss of particles in the trapping region. In particular, the growth of the first diocotron mode is suppressed even in the presence of ion resonance and resistive instability and the mode exhibits steady-state or underdamped amplitude and frequency modulations, typically in the Hertz range.

Dynamics and control of fast ion crystal splitting in segmented Paul traps

We theoretically investigate the process of splitting two-ion crystals in segmented Paul traps, i.e. the structural transition from two ions confined in a common well to ions confined in separate wells. The precise control of this process by application of suitable voltage ramps to the trap segments is non-trivial, as the harmonic confinement transiently vanishes during the process. This makes the ions strongly susceptible to background electric field noise, and to static offset fields in the direction of the trap axis. We analyze the reasons why large energy transfers can occur, which are impulsive acceleration, the presence of residual background fields and enhanced anomalous heating. For the impulsive acceleration, we identify the diabatic and adiabatic regimes, which are characterized by different scaling behavior of the energy transfer with respect to time. We propose a suitable control scheme based on experimentally accessible parameters. Simulations are used to verify both the high sensitivity of the splitting result and the performance of our control scheme. Finally, we analyze the impact of trap geometry parameters on the crystal splitting process.

A thin wire ion trap to study ion–atom collisions built within a Fabry–Perot cavity

We report on the implementation of a thin wire Paul trap with tungsten wire electrodes for trapping ions. The ion trap geometry, though compact, allows large optical access enabling a moderate finesse Fabry–Perot cavity to be built along the ion trap axis. The design allows a vapor-loaded magneto-optical trap of alkali atoms to be overlapped with trapped atomic or molecular ions. The construction and design of the trap are discussed, and its operating parameters are determined, both experimentally and numerically, for Rb+. The macromotion frequencies of the ion trap for 85Rb+ are determined to be f r = 43 kHz for the radial and f z = 54 kHz for the axial frequencies, for the experimentally determined optimal operating parameters. The destructive off axis ion extraction and detection by ion counting is demonstrated. Finally, evidence for the stabilization and cooling of trapped ions, due to ion–atom interactions, is presented by studying the ion-atom mixture as a function of interaction time. The utility and flexibility of the whole apparatus, for a variety of atomic physics experiments, are discussed in conclusion.

Spatially uniform single-qubit gate operations with near-field microwaves and composite pulse compensation

We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171Yb+ hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit π-rotations as fast as 1 μs with less than 6% variation in Rabi frequency over an 800 μm microwave interaction region. Fully compensating pulse sequences further improve the uniformity of X-gates across this interaction region.

Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation

Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled dc electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode frequencies, and adjust the orientation of trap axes. Microfabricated capacitors on dc electrodes suppress radio-frequency pickup and excess micromotion, while a top-level ground layer simplifies modeling of electric fields and protects trap structures underneath. A localized aperture in the substrate provides access to the trapping region from an oven below, permitting deterministic loading of particular isotopic/elemental sequences via species-selective photoionization. The shapes of the aperture and radio-frequency electrodes are optimized to minimize perturbation of the trapping pseudopotential. Laboratory experiments verify simulated potentials and characterize trapping lifetimes, stray electric fields, and ion heating rates, while measurement and cancellation of spatially-varying stray electric fields permits the formation of nearly-equally spaced ion chains.

Structural phase transitions in multipole traps

A small number of laser-cooled ions trapped in a linear radiofrequency multipole trap forms a hollow tube structure. We have studied, by means of molecular dynamics simulations, the structural transition from a double ring to a single ring of ions. We show that the single-ring configuration has the advantage to inhibit the thermal transfer from the rf-excited radial components of the motion to the axial component, allowing to reach the Doppler limit temperature along the direction of the trap axis. Once cooled in this particular configuration, the ions experience an angular dependency of the confinement if the local adiabaticity parameter exceeds the empirical limit. Bunching of the ion structures can then be observed and an analytic expression is proposed to take into account for this behaviour.