Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

Group velocity of light in internal conical refraction

We calculated the group velocity of light in internal conical refraction in a biaxial crystal as a function of the direction of the electric displacement vector, or the vibration direction, of its carrier wave. Our method represents group velocity through the electromagnetic fields of light, rather than its wave normal or ray direction. The travel time of a light pulse traversing a parallel plate biaxial crystal in internal conical refraction is found to vary as a sinusoidal function of twice the vibration angle of the light wave. Our method distinguishes the four directions of the two optic axes in monoclinic and triclinic crystals. Numerical examples are given for K N b O 3 at the wavelength of 400 nm, and for S n 2 P 2 S 6 at the wavelength of 550 nm.

Non-circularly shaped conical diffraction

Waves with tailored shape and vectorial non-homogeneous polarization are of much interest due to the many prospects for relevant applications in the classical and quantum domains. Such vector beams can be generated naturally via conical diffraction in optically biaxial crystals. The recent strongly revived attention to this phenomenon is motivated by modern applications such as optical trapping, polarimetry or super-resolution imaging, partly enabled by new configurations increasing the beam complexity, like those with several crystals in cascade. However, up to now all beams generated by conical diffraction conserve at their sharpest plane the underlying circular shape connected with the planar section of light cones. Here we show that a proper manipulation in wave-vector space within a conical diffraction cascade produces vector beams with highly peculiar non-circular forms, leading to an interesting and reconfigurable platform for easily shaping all structured wave properties, increasing complexity and information content. The experimental observations are confirmed by numerical integration of a paraxial model incorporating the effects of the wave-vector space manipulation.

Polarization-dependent group velocity of light pulses traveling in the optic ray axis directions of a biaxial crystal

We theoretically prove that the group velocity of a light pulse traveling in an optic ray axis direction of a biaxial crystal depends on the polarization state of the light. Our calculation shows that the group index varies as a sinusoidal function of twice the polarization angle of the light pulse. For monoclinic and triclinic crystals, in general the four directions of the two optic ray axes need to be distinguished. Numerical examples show that in KNbO₃ the group velocity varies by 2.7% at 400 nm wavelength, and in Sn₂P₂S₆ it varies by 3.9% at 550 nm wavelength, when the polarization state of the light is changing.

Modeling Atom Interferometry Experiments with Bose–Einstein Condensates in Power-Law Potentials

Recent atom interferometry (AI) experiments involving Bose–Einstein condensates (BECs) have been conducted under extreme conditions of volume and interrogation time. Numerical solution of the rotating-frame Gross–Pitaevskii equation (RFGPE), which is the standard mean-field theory applied to these experiments, is impractical due to the excessive computation time and memory required. We present a variational model that provides approximate solutions of the RFGPE for a power-law potential on a practical time scale. This model is well-suited to the design and analysis of AI experiments involving BECs that are split and later recombined to form an interference pattern. We derive the equations of motion of the variational parameters for this model and illustrate how the model can be applied to the sequence of steps in a recent AI experiment where BECs were used to implement a dual-Sagnac atom interferometer rotation sensor. We use this model to investigate the impact of finite-size and interaction effects on the single-Sagnac-interferometer phase shift.

Atomtronic Matter-Wave Lensing

In this Letter, we demonstrate magnetogravitational matter-wave lensing as a novel tool in atom-optics in atomtronic waveguides. We collimate and focus matter waves originating from Bose-Einstein condensates and ultracold thermal atoms in ring-shaped time-averaged adiabatic potentials. We demonstrate "delta-kick cooling" of Bose-Einstein condensates, reducing their expansion energies by a factor of 46 down to 800 pK. The atomtronic waveguide ring has a diameter of less than one millimeter, compared to other state-of-the-art experiments requiring zero gravity or free-flight distances of ten meters and more. This level of control with extremely reduced spatial requirements is an important step toward atomtronic quantum sensors.

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.

Conical refraction mode of an optical resonator

The fundamental mode of a conical refraction resonator, i.e., an optical cavity where light experiences conical refraction (CR) from a biaxial crystal, is experimentally demonstrated in the plano-concave cavity configuration. We have discovered that the fundamental CR mode is characterized by the polarization and intensity structures of CR beams between the plane mirror and CR crystal, and it resembles the fundamental Gaussian mode with homogeneous polarization between the crystal and concave mirror. We theoretically explained this fundamental CR mode using the dual cone model and symmetry of the CR phenomenon and confirmed this explanation by numerical simulations.

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum

Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

Partial Fermionization: Spectral Universality in 1D Repulsive Bose Gases

Because of the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few and up to many particles share the same underlying spectral features. In our derivation we supplement quantum cluster expansions with short-time dynamical information. Our nonperturbative analytical results are in excellent agreement with numerics for systems of experimental relevance in cold atom physics, such as interacting bosons on a ring (Lieb-Liniger model) or subject to harmonic confinement. Our method provides predictions for excitation spectra that enable access to finite-temperature thermodynamics in large parameter ranges.

Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases

We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.

Complex beam shaping by cascaded conical diffraction with intercalated polarization transforming elements

Cascaded conical diffraction where optical elements modifying the local polarization state are intercalated between the aligned biaxial crystals is analyzed theoretically in the framework of paraxial diffraction theory. The obtained expressions are verified and confirmed experimentally for the case of a two-crystal cascade intercalated by a polarizer or a wave plate. The present approach can be used to realize a variety of vector beams with complex beam shapes composed of concentric rings with strongly modulated azimuthal intensity distribution. A potentially very fast switching of the overall beam shape is possible if the intercalated elements are electro-optically tunable retarders.

Dual polarization split lenses

We report the realization of polarization sensitive split lens configurations. While split lenses can be used to easily generate different types of controlled structured light patterns, their realization has been limited so far to scalar beams. Here we propose and experimentally demonstrate their generalization to vectorial split lenses, leading to light patterns with customized intensity and state of polarization. We demonstrate how these polarization split lenses can be experimentally implemented by means of an optical system using two liquid crystal spatial light modulators, each one phase modulating one orthogonal polarization component. As a result, we demonstrate the experimental generation of vectorial beams with different shapes generated with these dual polarization split lenses. Excellent experimental results are provided in each case. The proposed technique is a simple method to generate structured light beams with polarization diversity, with potential applications in polarimetry, customized illuminators or quantum optics.

Extreme Ultraviolet Fractional Orbital Angular Momentum Beams from High Harmonic Generation

We investigate theoretically the generation of extreme-ultraviolet (EUV) beams carrying fractional orbital angular momentum. To this end, we drive high-order harmonic generation with infrared conical refraction (CR) beams. We show that the high-order harmonic beams emitted in the EUV/soft x-ray regime preserve the characteristic signatures of the driving beam, namely ringlike transverse intensity profile and CR-like polarization distribution. As a result, through orbital and spin angular momentum conservation, harmonic beams are emitted with fractional orbital angular momentum, and they can be synthesized into structured attosecond helical beams –or “structured attosecond light springs”– with rotating linear polarization along the azimuth. Our proposal overcomes the state of the art limitations for the generation of light beams far from the visible domain carrying non-integer orbital angular momentum and could be applied in fields such as diffraction imaging, EUV lithography, particle trapping, and super-resolution imaging.

High efficiency, low cost holographic optical elements for ultracold atom trapping

We demonstrate a method of creating high efficiency, high fidelity, holographic optical elements for the generation of complex optical fields, in a low cost photopolymer, Bayfol HX. The desired optical field profile is generated by a spatial light modulator and written into an optically addressable photopolymer as a volume hologram. We demonstrate the utility of this approach by trapping a Bose-Einstein condensate of rubidium-87 atoms in the nodal plane of an HG_0,1 mode generated by one of these holographic optical elements. We also extend this method to the generation holograms with twice the angular momentum per photon than can be generated with a given spatial light modulator.

Fifteen years of cold matter on the atom chip: promise, realizations, and prospects

Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.

Implementation and performance of an in-line incomplete Stokes polarimeter based on a single biaxial crystal

Due to the increasing interest of polarimetric information in numerous applications, different Stokes polarimeter designs are provided in the literature for the measure of light beam polarization. Recently, the concept of polarimeters based on the conical refraction (CR) phenomenon, occurring in biaxial crystals, was proposed. CR polarimeters are snapshot polarimeters that allow controlling the volume of data redundancy without an increase in the acquisition time. We present the implementation, calibration, and analysis of an incomplete CR-polarimeter optimized for the measure of linear polarizations. A simpler and cheaper experimental configuration is achieved, if compared with other polarimeters proposed in the literature. The suitability of the polarimeter is experimentally demonstrated and some of its benefits, such as its performance in low-intensity conditions, are discussed.

Interferometric characterization of the structured polarized light beam produced by the conical refraction phenomenon

The interest on the conical refraction (CR) phenomenon in biaxial crystals has revived in the last years due to its prospective for generating structured polarized light beams, i.e. vector beams. While the intensity and the polarization structure of the CR beams are well known, an accurate experimental study of their phase structure has not been yet carried out. We investigate the phase structure of the CR rings by means of a Mach-Zehnder interferometer while applying the phase-shifting interferometric technique to measure the phase at the focal plane. In general the two beams interfering correspond to different states of polarization (SOP) which locally vary. To distinguish if there is an additional phase added to the geometrical one we have derived the appropriate theoretical expressions using the Jones matrix formalism. We demonstrate that the phase of the CR rings is equivalent to that one introduced by an azimuthally segmented polarizer with CR-like polarization distribution. Additionally, we obtain direct evidence that the Poggendorff dark ring is an annular singularity, with a π phase change between the inner and outer bright rings.

Transformation of vector beams with radial and azimuthal polarizations in biaxial crystals

We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, this node being found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e., that every two diametrically opposite points of the light ring are linearly orthogonally polarized.

Focus issue introduction: optical cooling and trapping

The year 2015 is an auspicious year for optical science, as it is being celebrated as the International Year of Light and Light-Based Technologies. This Focus Issue of the journals Optics Express and Journal of the Optical Society of America B has been organized by the OSA Technical Group on Optical Cooling and Trapping to mark this occasion, and to highlight the most recent and exciting developments in the topics covered by the group. Together this joint Focus Issue features 32 papers, including both experimental and theoretical works, which span this wide range of activities.

On the dual-cone nature of the conical refraction phenomenon

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones.