Micro-fabricated components for cold atom sensors.

Laser cooled atoms have proven transformative for precision metrology, playing a pivotal role in state-of-the-art clocks and interferometers and having the potential to provide a step-change in our modern technological capabilities. To successfully explore their full potential, laser cooling platforms must be translated from the laboratory environment and into portable, compact quantum sensors for deployment in practical applications. This transition requires the amalgamation of a wide range of components and expertise if an unambiguously chip-scale cold atom sensor is to be realized. We present recent developments in cold-atom sensor miniaturization, focusing on key components that enable laser cooling on the chip-scale. The design, fabrication, and impact of the components on sensor scalability and performance will be discussed with an outlook to the next generation of chip-scale cold atom devices.

Optical characterisation of micro-fabricated Fresnel zone plates for atomic waveguides.

We optically assess Fresnel zone plates (FZPs) that are designed to guide cold atoms. Imaging of various ring patterns produced by the FZPs gives an average RMS error in the brightest part of the ring of 3% with respect to trap depth. This residue is attributed to the imaging system, incident beam shape and FZP manufacturing tolerances. Axial propagation of the potentials is presented experimentally and through numerical simulations, illustrating prospects for atom guiding without requiring light sheets.

Cold-atom clock based on a diffractive optic.

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects 107 87Rb atoms, which are subsequently cooled to 20 µK in optical molasses. We optically probe the microwave atomic ground-state splitting using lin⊥lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only 0.5 mm, the measured short-term fractional frequency stability is 2×10-11/τ.

High-precision control of static magnetic field magnitude, orientation, and gradient using optically pumped vapour cell magnetometry.

An integrated system of hardware and software allowing precise definition of arbitrarily oriented magnetic fields up to |B| = 1 µT within a five-layer Mumetal shield is described. The system is calibrated with reference to magnetic resonance observed between Zeeman states of the 6S1/2 F = 4 133Cs ground state. Magnetic field definition over the full 4π solid angle is demonstrated with one-sigma tolerances in magnitude, orientation, and gradient of δ|B| = 0.94 nT, δθ = 5.9 mrad, and δ|∇B|=13.0 pT/mm, respectively. This field control is used to empirically map Mx magnetometer signal amplitude as a function of the static field (B0) orientation.

Design and fabrication of diffractive atom chips for laser cooling and trapping.

It has recently been shown that optical reflection gratings fabricated directly into an atom chip provide a simple and effective way to trap and cool substantial clouds of atoms (Nshii et al. in Nat Nanotechnol 8:321-324, 2013; McGilligan et al. in Opt Express 23(7):8948-8959, 2015). In this article, we describe how the gratings are designed and microfabricated and we characterise their optical properties, which determine their effectiveness as a cold atom source. We use simple scalar diffraction theory to understand how the morphology of the gratings determines the power in the diffracted beams.

Phase-space properties of magneto-optical traps utilising micro-fabricated gratings.

We have used diffraction gratings to simplify the fabrication, and dramatically increase the atomic collection efficiency, of magneto-optical traps using micro-fabricated optics. The atom number enhancement was mainly due to the increased beam capture volume, afforded by the large area (4cm(2)) shallow etch (~ 200nm) binary grating chips. Here we provide a detailed theoretical and experimental investigation of the on-chip magneto-optical trap temperature and density in four different chip geometries using (87)Rb, whilst studying effects due to MOT radiation pressure imbalance. With optimal initial MOTs on two of the chips we obtain both large atom number (2×10(7)) and sub-Doppler temperatures (50 µK) after optical molasses.

A surface-patterned chip as a strong source of ultracold atoms for quantum technologies.

Laser-cooled atoms are central to modern precision measurements. They are also increasingly important as an enabling technology for experimental cavity quantum electrodynamics, quantum information processing and matter-wave interferometry. Although significant progress has been made in miniaturizing atomic metrological devices, these are limited in accuracy by their use of hot atomic ensembles and buffer gases. Advances have also been made in producing portable apparatus that benefits from the advantages of atoms in the microkelvin regime. However, simplifying atomic cooling and loading using microfabrication technology has proved difficult. In this Letter we address this problem, realizing an atom chip that enables the integration of laser cooling and trapping into a compact apparatus. Our source delivers ten thousand times more atoms than previous magneto-optical traps with microfabricated optics and, for the first time, can reach sub-Doppler temperatures. Moreover, the same chip design offers a simple way to form stable optical lattices. These features, combined with simplicity of fabrication and ease of operation, make these new traps a key advance in the development of cold-atom technology for high-accuracy, portable measurement devices.

Trans-spectral orbital angular momentum transfer via four-wave mixing in Rb vapor.

We report the transfer of phase structure and, in particular, of orbital angular momentum from near-infrared pump light to blue light generated in a four-wave-mixing process in 85Rb vapor. The intensity and phase profile of the two pump lasers at 780 and 776 nm, shaped by a spatial light modulator, influences the phase and intensity profile of light at 420 nm, which is generated in a subsequent coherent cascade. In particular, we observe that the phase profile associated with orbital angular momentum is transferred entirely from the pump light to the blue. Pumping with more complicated light profiles results in the excitation of spatial modes in the blue that depend strongly on phase matching, thus demonstrating the parametric nature of the mode transfer. These results have implications on the inscription and storage of phase information in atomic gases.

Enhanced frequency up-conversion in Rb vapor.

We demonstrate highly efficient generation of coherent 420 nm light via up-conversion of near-infrared lasers in a hot rubidium vapor cell. By optimizing pump polarizations and frequencies we achieve a single-pass conversion efficiency of 260% per Watt, significantly higher than in previous experiments. A full exploration of the coherent light generation and fluorescence as a function of both pump frequencies reveals that coherent blue light is generated close to (85)Rb two-photon resonances, as predicted by theory, but at high vapor pressure is suppressed in spectral regions that do not support phase matching or exhibit single-photon Kerr refraction. Favorable scaling of our current 1 mW blue beam power with additional pump power is predicted.

Optical ferris wheel for ultracold atoms.

We propose a versatile optical ring lattice suitable for trapping cold and quantum degenerate atomic samples. We demonstrate the realisation of intensity patterns from pairs of Laguerre-Gauss (exp(i??) modes with different ? indices. These patterns can be rotated by introducing a frequency shift between the modes. We can generate bright ring lattices for trapping atoms in red-detuned light, and dark ring lattices suitable for trapping atoms with minimal heating in the optical vortices of blue-detuned light. The lattice sites can be joined to form a uniform ring trap, making it ideal for studying persistent currents and the Mott insulator transition in a ring geometry.

Evaluation of a deformable musculoskeletal model for estimating muscle-tendon lengths during crouch gait.

The hamstrings and psoas muscles are often lengthened surgically in an attempt to correct crouch gait in persons with cerebral palsy. The purpose of this study was to determine if, and under what conditions, medial hamstrings and psoas lengths estimated with a "deformable" musculoskeletal model accurately characterize the lengths of the muscles during walking in individuals with crouch gait. Computer models of four subjects with crouch gait were developed from magnetic resonance (MR) images. These models were used in conjunction with the subjects' measured gait kinematics to calculate the muscle-tendon lengths at the body positions corresponding to walking. The lengths calculated with the MR-based models were normalized and were compared to the lengths estimated using a deformable generic model. The deformable model was either left undeformed and unscaled, or was deformed or scaled to more closely approximate the femoral geometry or bone dimensions of each subject. In most cases, differences between the normalized lengths of the medial hamstrings computed with the deformable and MR-based models were less than 5 mm. Differences in the psoas lengths computed with the deformable and MR-based models were also small (<3 mm) when the deformable model was adjusted to represent the femoral geometry of each subject. This work demonstrates that a deformable musculoskeletal model, in combination with a few subject-specific parameters and simple normalization techniques, can provide rapid and accurate estimates of medial hamstrings and psoas lengths in persons with neuromuscular disorders.

Rotational moment arms of the medial hamstrings and adductors vary with femoral geometry and limb position: implications for the treatment of internally rotated gait.

Persons with cerebral palsy frequently walk with a crouched, internally rotated gait. Spastic medial hamstrings or adductors are presumed to contribute to excessive hip internal rotation in some patients; however, the capacity of these muscles to produce internal rotation has not been adequately investigated. The purpose of this study was to determine the hip rotation moment arms of the medial hamstrings and adductors in persons with femoral anteversion deformities who walk with a crouched, internally rotated gait. A musculoskeletal model with a "deformable" femur was developed. This model was used, in conjunction with kinematic data obtained from gait analysis, to calculate the muscle moment arms for combinations of joint angles and anteversion deformities exhibited by 21 subjects with cerebral palsy and excessive hip internal rotation. We found that the semimembranosus, semitendinosus, and gracilis muscles in our model had negligible or external rotation moment arms when the hip was internally rotated or the knee was flexed -- the body positions assumed by the subjects during walking. When the femur was excessively anteverted, the rotational moment arms of the adductor brevis, adductor longus, pectineus, and proximal compartments of the adductor magnus in our model shifted toward external rotation. These results suggest that neither the medial hamstrings nor the adductors are likely to contribute substantially to excessive internal rotation of the hip and that other causes of internal rotation should be considered when planning treatments for these patients.

Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity.

OBJECTIVE: Biomechanical models that compute the lengths and moment arms of soft tissues are broadly applicable to the treatment of movement abnormalities and the planning of orthopaedic surgical procedures. The goals of this study were to: (i) develop methods to construct subject-specific biomechanical models from magnetic resonance (MR) images, (ii) create models of three lower-extremity cadaveric specimens, and (iii) quantify the accuracy of muscle-tendon lengths and moment arms estimated using these models. MATERIALS AND METHODS: Models describing the paths of the medial hamstrings and psoas muscles for a wide range of body positions were developed from MR images in one joint configuration by defining kinematic models of the hip and knee, and by specifying "wrapping surfaces" that simulate interactions between the muscles and underlying structures. Our methods for constructing these models were evaluated by comparing hip and knee flexion moment arms estimated from models of three specimens to the moment arms determined experimentally on the same specimens. Because a muscle's moment arm determines its change in length with joint rotation, these comparisons also tested the accuracy with which the models could estimate muscle-tendon lengths over a range of hip and knee motions. RESULTS: Errors in the moment arms calculated with the models, averaged over functional ranges of hip and knee flexion, were less than 4 mm (within 10% of experimental values). CONCLUSION: The combination of MR imaging and graphics-based musculoskeletal modeling provides an accurate and efficient means of estimating muscle-tendon lengths and moment arms in vivo.

Do the hamstrings and adductors contribute to excessive internal rotation of the hip in persons with cerebral palsy?

Children with cerebral palsy frequently walk with excessive internal rotation of the hip. Spastic medial hamstrings or adductors are presumed to contribute to the excessive internal rotation in some patients; however, the capacity of these muscles to produce internal rotation during walking in individuals with cerebral palsy has not been adequately investigated. The purpose of this study was to determine the hip rotation moment arms of the medial hamstrings and adductors in persons who walk with a crouched, internally-rotated gait. Highly accurate computer models of three subjects with cerebral palsy were created from magnetic resonance images. These subject-specific models were used in conjunction with joint kinematics obtained from gait analysis to calculate the rotational moment arms of the muscles at body positions corresponding to each subject's internally-rotated gait. Analysis of the models revealed that the medial hamstrings, adductor brevis, and gracilis had negligible or external rotation moment arms throughout the gait cycle in all three subjects. The adductor longus had an internal rotation moment arm in two of the subjects, but the moment arm was small (<4 mm) in each case. These findings indicate that neither the medial hamstrings nor the adductor brevis, adductor longus, or gracilis are likely to be important contributors to excessive internal rotation of the hip. This suggests that these muscles should not be lengthened to treat excessive internal rotation of the hip and that other factors are more likely to cause internally-rotated gait in these patients.

Length changes of the hamstrings and adductors resulting from derotational osteotomies of the femur.

Derotational osteotomies of the femur are frequently performed to treat persons with cerebral palsy who walk with excessive internal rotation of the hip. However, whether these procedures stretch or slacken the surrounding muscles appreciably is unknown. Determination of how muscle lengths are altered by derotational osteotomies is difficult because the length changes depend not only on the osteotomy site and the degree of derotation, but also on the anteversion angle of the femur and the rotational position of the hip. We have developed a three-dimensional computer simulation of derotational osteotomies, tested by anatomical experiments, to examine how femoral anteversion, hip internal rotation, and derotation affect the lengths of the semitendinosus, semimembranosus, biceps femoris long head, adductor longus, adductor brevis, and gracilis muscles. Simulation of derotational osteotomies at the intertrochanteric, subtrochanteric, or supracondylar levels decreased the origin-to-insertion lengths of the hamstrings and gracilis in our model by less than 8 mm (1.8%). Hence, the lengths of the hamstrings and gracilis are not likely to be altered substantially by these procedures. The origin-to-insertion lengths of the adductor longus and adductor brevis decreased less than 4 mm (1.9%) with subtrochanteric correction in our model, but the length of adductor brevis increased 8 mm (6.3%) with 60 degrees of intertrochanteric derotation. These muscles are also unlikely to be affected by derotational osteotomies, unless a large degree of intertrochanteric derotation is performed.

Internal rotation gait: a compensatory mechanism to restore abduction capacity decreased by bone deformity.

Children with excessive femoral anteversion frequently walk with abnormal internal rotation of the hip. The authors hypothesized that excessive anteversion decreases the abduction moment arm of the gluteus medius and that this moment arm is restored with internal rotation; hence internal rotation may be a compensatory mechanism to preserve abduction capacity. To test this hypothesis a three-dimensional computer model of an adult lower limb was developed to determine how changes in femoral anteversion angle, neck-shaft angle, and hip internal rotation angle affect the abduction moment arm of the gluteus medius. Analysis of the model revealed that anteversion and valgus deformities of the femur can decrease the abduction moment arm of the gluteus medius substantially. In particular, increasing the anteversion angle of the model by 30 to 40 degrees caused a 40 to 50% decrease in the abduction moment arm of the gluteus medius - enough to impair walking. Internal rotation of the hip by 30 degrees restored the abduction moment arm of the gluteus medius to within 5% of the moment arm of the model in its normal, undeformed state. These results support the authors' hypothesis and are consistent with the theory that internal rotation may be a compensatory mechanism adopted by children with femoral deformities to achieve the abduction moment arm needed for walking.

Hamstrings and psoas lengths during normal and crouch gait: implications for muscle-tendon surgery.

Crouch gait, one of the most common movement abnormalities among children with cerebral palsy, is characterized by persistent flexion of the knee during the stance phase. Short hamstrings are thought to be the cause of crouch gait; thus, crouch gait is often treated by surgical lengthening of the hamstrings. In this study, a graphics-based model of the lower extremity was used in conjunction with three-dimensional kinematic data obtained from gait analysis to estimate the lengths of the hamstrings and psoas muscles during normal and crouch gaits. Only three of 14 subjects with crouch gait (four of 20 limbs with knee flexion of 20 degrees or more throughout stance) had hamstrings that were shorter than normal by more than 1 SD during walking. Most (80%) of the subjects with crouch gait had hamstrings of normal length or longer, despite persistent knee flexion during stance. This occurred because the excessive knee flexion was typically accompanied by excessive hip flexion throughout the gait cycle. All of the subjects with crouch gait had a psoas that was shorter than normal by more than 1 SD during walking. These results emphasize the need to consider the geometry and kinematics of multiple joints before performing surgical procedures aimed at correcting crouch gait.

Design of a controlled-energy-dissipation orthosis (CEDO) for functional suppression of intention tremors.

Conventional neurological practice is generally not successful in restoring independent upper extremity function to people with disabiling tremors. The authors have been investigating an orthotic approach, the application of energy-dissipating loads to affected limbs, to allow voluntary intent to be expressed while attenuating tremor. CEDO 1 is a prototype Controlled-Energy-Dissipation Orthosis, which permits the 3 degrees of freedom (dof) needed for table-top activities. It mounts to the user's chair or table and applies velocity-proportional resistance to his/her forearm by means of computer-controlled magnetic particle brakes. The design incorporates a stiff linkage transmission to the elbow brake of the orthosis, allowing it to be fixed in the frame of reference. This eliminates its inertia from the moving linkage and provides virtually direct drive in all 3 dof. Initial experimental results show selective clinically significant tremor reduction during experimental tracking tasks.

Assessment of a method to estimate muscle attachments from surface landmarks: a 3D computer graphics approach.

A method for estimating the locations of muscle origins and insertions from the measurement of surface landmarks was evaluated using two indirect accuracy tests and a three-dimensional computer graphics program. For each of four lower extremity anatomical segments, a least-squares technique was used to map the measured locations of three landmark targets to their anatomically based locations. The residual errors, obtained from the applications of the least squares, supplied the first indirect accuracy test. These residual errors were between 6 and 12 mm for the four anatomical segments when averaged over ten subjects. The second indirect accuracy test was conducted by comparing the predicted locations of end points on two adjacent segments forming a joint. Errors in aligning adjacent end points were between 12 and 29 mm for three anatomical joints when averaged over ten subjects. A three-dimensional computer graphics program was developed by the authors and demonstrated that the static testing techniques alone were insufficient to evaluate the quality of the muscle origin and insertion estimates. Any evaluation of muscle lengths, velocities and lines-of-action from surface landmarks should examine the estimates made from motion data, and should address both the ability of the model to fit the subjects as well as model's ability to represent the geometry of the musculoskeletal system.