Jonathan Leach

Quantum correlations in optical angle-orbital angular momentum variables

Entanglement in a Twist The strong correlations observed in quantum mechanically entangled particles, such as photons, offer potential for secure communication and quantum information processing. Leach et al. (p. 662) now show such strong quantum correlations between the complementary variables—angular position and orbital angular momentum—of two photons created during the parametric down-conversion process in a nonlinear crystal. This demonstration of entanglement in an angular basis establishes that angles are genuine quantum observables and can therefore be considered a resource for quantum information processing, capable of secure, high-dimension, key distribution. Strong quantum correlations are induced between the angular position and angular momentum of two photons. Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.

Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities

Bell’s theorem experiments, which test the completeness of quantum mechanics, have a number of loopholes. However, one type—detection loopholes—becomes smaller when the measurement has more possible outcomes. Bell’s inequality is now violated in tests with as many as 11 different results.

Observation of the vortex structure of a non-integer vortex beam

An optical beam with an eil phase structure carries an orbital angular momentum of l per photon. For integer l values, the phase fronts of such beams form perfect helices with a single screw-phase dislocation, or vortex, on the beam axis. For non-integer l values, Berry (2004 J. Opt. A: Pure Appl. Opt. 6 259) predicts a complex-phase structure comprising many vortices at differing positions within the beam cross-section. Using a spatial light modulator we produce eil beams with varying l. We examine the phase structure of such beams after propagation through an interference-based phase-measurement technique. As predicted, we observe that for half-integer l values, a line of alternating charge vortices is formed near the radial dislocation.

Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy

We assess the performance of a CMOS camera for the measurement of particle position within optical tweezers and the associated autocorrelation function and power spectrum. Measurement of the displacement of the particle from the trap center can also be related to the applied force. By considering the Allan variance of these measurements, we show that such cameras are capable of reaching the thermal limits of nanometer and femtonewton accuracies, and hence are suitable for many of the applications that traditionally use quadrant photodiodes. As an example of a multi-particle measurement we show the hydrodynamic coupling between two particles.

Interactive approach to optical tweezers control

We have developed software with an interactive user interface that can be used to generate phase holograms for use with spatial light modulators. The program utilizes different hologram design techniques, allowing the user to select an appropriate algorithm. The program can be used to generate multiple beams and can be used for beam steering. We see a major application of the program to be in optical tweezers to control the position, number, and type of optical traps.

Vortex knots in light

Optical vortices generically arise when optical beams are combined. Recently, we reported how several laser beams containing optical vortices could be combined to form optical vortex loops, links and knots embedded in a light beam (Leach et al 2004 Nature 432 165). Here, we describe in detail the experiments in which vortex loops form these structures. The experimental construction follows a theoretical model originally proposed by Berry and Dennis, and the beams are synthesized using a programmable spatial light modulator and imaged using a CCD camera.

3D manipulation of particles into crystal structures using holographic optical tweezers

We have developed holographic optical tweezers that can manipulate many particles simultaneously in three dimensions in order to create micro-crystal structures that extend over many tens of microns. The technique uses specific hologram-design algorithms to create structures that can be dynamically scaled or rotated about arbitrary axes. We believe the generation and control of pre-determined crystal-like structures have significant potential in fields as diverse as photonic-crystal construction, seeding of biological tissue growth and creation of metrological standards within nanotechnology.

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.

Optically controlled three-dimensional rotation of microscopic objects

We demonstrate that microscopic objects held in optical tweezers can be set into controlled rotation about any axis of choice. Our approach relies on the use of a spatial light modulator to create a pair of closely separated optical traps holding different parts of the same object. The pair of traps can be made to revolve around each other in any plane, rotating the trapped object with them. This technique overcomes the previous restriction on the orientation of the rotation axis to be parallel to the beam axis, and extends the versatility of optical tweezers as micromanipulation tools.

Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping.

Phase-hologram patterns that can shape the intensity distribution of a light beam in several planes simultaneously can be calculated with an iterative Gerchberg-Saxton algorithm [T. Haist et al., Opt. Commun. 140, 299 (1997)]. We apply this algorithm in holographic optical tweezers. This allows us to simultaneously trap several objects in individually controllable arbitrary 3-dimensional positions. We demonstrate the interactive use of our approach by trapping microscopic spheres and moving them into an arbitrary 3-dimensional configuration.