Laser frequency stabilization in the 10 -14 range via optimized modulation transfer spectroscopy on the 87Rb D2 line.

We present a high-performance laser frequency stabilization method using modulation transfer spectroscopy (MTS) on the rubidium 87D2 transition line. A substantial improvement of the laser frequency stability was achieved by searching for the optimal diameter and intensity settings of the probe and pump beam. The frequency instability measured from the beat frequency of two locked external cavity diode lasers (ECDLs) reached a short-term stability of 4.5×10-14/τ and did not exceed 2 × 10-12 until 105 s, which is the best performance reported thus far with a D2 transition. The long-term stability is limited by the offset fluctuations of the baseline induced by the residual amplitude modulation (RAM), which can be further improved by reducing the current temperature variation of about 0.2 K by means of temperature stabilization or through a further reduction of the RAM.

Magnetic-field enhanced modulation transfer spectroscopy: theory and experiment.

We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S1/2 (F = 1) → 5P3/2 (F' = 0, 1, and 2) transitions of 87Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F' = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F' = 1 transition are also examined.

Bifurcation-enhanced ultrahigh sensitivity of a buckled cantilever.

Buckling, first introduced by Euler in 1744 [Euler L (1744) Opera Omnia I 24:231], a sudden mechanical sideways deflection of a structural member under compressive stress, represents a bifurcation in the solution to the equations of static equilibrium. Although it has been investigated in diverse research areas, such a common nonlinear phenomenon may be useful to devise a unique mechanical sensor that addresses the still-challenging features, such as the enhanced sensitivity and polarization-dependent detection capability. We demonstrate the bifurcation-enhanced sensitive measurement of mechanical vibrations using the nonlinear buckled cantilever tip in ambient conditions. The cantilever, initially buckled with its tip pinned, flips its buckling near the bifurcation point (BP), where the buckled tip becomes softened. The enhanced mechanical sensitivity results from the increasing fluctuations, unlike the typical linear sensors, which facilitate the noise-induced buckling-to-flipping transition of the softened cantilever. This allows the in situ continuous or repeated single-shot detection of the surface acoustic waves of different polarizations without any noticeable wear of the tip. We obtained the sensitivity above 106 V(m/s)-1, a 1,000-fold enhancement over the conventional seismometers. Our results lead to development of mechanical sensors of high sensitivity, reproducibility, and durability, which may be applied to detect, e.g., the directional surface waves on the laboratory as well as the geological scale.

Linewidth in saturated absorption spectroscopy for two-level atoms: an empirical formula.

We present an empirical formula for linewidth in saturated absorption spectroscopy for two-level atoms with cycling transition lines, taking the coherence term in the Doppler-broadened limit into account. The full width at half-maximum is obtained as (1+(1+as0)b)γt, where s0 is the on-resonance saturation parameter, γt is the transverse decay rate, and a and b are the parameters that depend on γt. We find that as γt increases, a and b approach 1 and 1/2, respectively. These are the typical values in the case without the coherence term.

Buckling-Based Non-Linear Mechanical Sensor.

Mechanical sensors provide core keys for high-end research in quantitative understanding of fundamental phenomena and practical applications such as the force or pressure sensor, accelerometer and gyroscope. In particular, in situ sensitive and reliable detection is essential for measurements of the mechanical vibration and displacement forces in inertial sensors or seismometers. However, enhancing sensitivity, reducing response time and equipping sensors with a measurement capability of bidirectional mechanical perturbations remains challenging. Here, we demonstrate the buckling cantilever-based non-linear dynamic mechanical sensor which addresses intrinsic limitations associated with high sensitivity, reliability and durability. The cantilever is attached on to a high-Q tuning fork and initially buckled by being pressed against a solid surface while a flexural stress is applied. Then, buckling instability occurs near the bifurcation region due to lateral movement, which allows high-sensitive detection of the lateral and perpendicular surface acoustic waves with bandwidth-limited temporal response of less than 1 ms.

High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms.

We have designed, built, and characterized a high-resolution objective lens that is compatible with an ultrahigh vacuum environment. The lens system exploits the principle of the Weierstrass sphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 µm. Our two-lens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning near-field optical microscopy, to measure the point spread function (PSF) of a high NA optical system. From the PSF, we infer the wavefront aberration for the entire field of view of about 75 µm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technologies such as quantum control of atoms in optical microtraps with an unprecedented spatial resolution and photon collection efficiency.

Polarization-selective four-wave mixing in a degenerate multi-level system.

This paper describes the first observation of polarization-selective four-wave mixing signals in conventional coupling-probe spectroscopy, specifically, saturation absorption spectroscopy in 85Rb atoms. The four-wave mixing signal is induced by two counter-propagating laser beams in a degenerate multi-level atomic system, involving the F g = 3 → F e = 2 , 3 , and 4 transitions of the 85Rb D2 line. Consequently, the four-wave mixing signals copropagating along the probe beam induce polarization rotation of a linearly polarized probe beam. To distinguish these four-wave mixing signals from the resulting probe beam, we detect the polarization components orthogonal to the polarization direction of the input probe beam, depending on the linear polarization angles between the probe and coupling beams. The experimental findings demonstrate excellent agreement with theoretical results.

Enhanced formation of a confined nano-water meniscus using a 780 nm laser with a quartz tuning fork-atomic force microscope.

Demonstrated herein is the optical-field-induced enhancement of the formation of a confined nanowater meniscus using a distance-regulated quartz tuning fork-atomic force microscope (QTF-AFM) with a 780 nm laser. While a pulled optical fiber tip approaches the surface, the laser is suddenly turned on and focuses on the front spot of the tip by the shape of the pulled optical fiber, which plays the role of an objective lens and induces the gathering effect of the water molecules directed to the electromagnetic-field gradient in air. This phenomenon facilitates a new boundary condition to form a long-range confined nano-scale liquid bridge between the tip and the surface. After the pulling of the optical fiber, 20-nm-thick gold was sputtered on the apex (diameter: approximately 100 nm) of the tip to guide and focus the beam on the spot. The critical power of the laser to overcome the barrier for the formation of a new boundary is 100 microW at the distance of 22 nm from the substrate.

Dynamic polarization response of polarization-maintaining fibers by periodic thermal cycling method.

We report a periodic thermal cycling method to investigate the dynamic response of the polarization of a laser propagating through polarization-maintaining (PM) optical fiber, driven by periodic weak temperature modulation. Consequently, temperature modulation on the surface of the coating material of the PM fiber was found to cause a continuous periodic change in the polarization state of the output laser without approaching the steady state of the resulting dynamic polarization response. Additionally, the response was found to depend on the temperature-modulation frequency and amplitude. These experimental results are qualitatively in good agreement with that of the simple theoretical model. Our research would be applied not only to the method of measuring properties of a PM optical fiber by utilizing the continuous modulation of the differential refractive index with a wide modulation-frequency range but also to various applications of the dynamic control of the periodic refractive index in materials.

Shear-stress function approach of hydration layer based on the Green-Kubo formula.

We present the analytic expression of the stress correlation (SC) function for the ubiquitous hydration water layer (HWL) using the Green-Kubo equation and the shear modulus of HWL. The SC function is then experimentally obtained by measuring the viscoelastic properties of HWL using shear-mode dynamic force spectroscopy. Interestingly, the SC changes sign from positive to negative as the HWL thickness increases, where the shear stresses acting on the HWLs bound to two nearby surfaces are out of phase. We also suggest that the repulsive hydration force originates from the SC of HWL. Our results provide the first demonstration of the microscopic understanding of the HWL viscoelasticity and may allow a deeper insight on the HWL dynamics as well as the complex liquids.

Note: Ultra-low birefringence dodecagonal vacuum glass cell.

We report on an ultra-low birefringence dodecagonal glass cell for ultra-high vacuum applications. The epoxy-bonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stress-induced birefringence. We characterize the birefringence Δn of each window with the cell under vacuum conditions, obtaining values around 10(-8). After baking the cell at 150 °C, we reach a pressure below 10(-10) mbar. In addition, each window is antireflection coated on both sides, which is highly desirable for quantum optics experiments and precision measurements.

Relaxation of an unstable state in parametrically excited cold atoms.

We investigate the scaling behavior of the relaxation process for an unstable state near a subcritical Hopf bifurcation point. When the parametric modulation is applied to a magneto-optical trap, the atomic cloud becomes unstable and decays to the dynamic bistable states. Near the subcritical Hopf bifurcation point, we experimentally show that the relaxation process exhibits the scaling behavior; the relaxation time shows a scaling exponent of -1.002 (±0.024). We also present the passage time distribution for the statistical interpretation of the escape process associated with the relaxation of the unstable state. We compare the experimental results to the numerical and analytic results, demonstrating the good agreement between them.

Ideal mean-field transition in a modulated cold atom system.

We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. We describe experimental observations and develop a full microscopic theory of the observed critical phenomena. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The observations, including anomalous fluctuations in the symmetry broken phase, are fully described by the theory.