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Sculpting shadows : on the spatial structuring of fields & atoms : a tale of light and darkness

Thomas W. Clark

Published Jan 1, 2016• 2 citations
OpenAlex

Abstract

Whether in art or physics, two dimensions are better than one. And in this context, we consider the spatial shaping of optical fields and atomic polarisations. This work begins with a comprehensive review of how to accurately and arbitrarily modulate transverse beam profiles using six different methods. The methods are presented in the context of a general complex input beam and the shaping and measuring of the input beam with a single SLM is discussed and demonstrated. A simple setup is then considered that allows for the rapid switching between arbitrary profiles, using only a single holo- graphic component and an acousto-optical modulator (AOM). In this setup, a switching speed of approximately 10 kHz is demon- strated explicitly, limited by the current detection system, but where speeds of up to 20 MHz are estimated to be possible. The following discussion then concentrates on the spatial structure of atoms, reviewing the conceptual tools needed to measure and interpret an atomic cloud in the presence of a mag- netic field from fundamental concerns, both in theory and in practice: assuming a classical light field and a quantum atomic system. The specific implementation of both a magneto-optical trap and a holographically-shaped dynamic dark SpOT follows. The crux of the work then concerns how polarisation-structured light can be used to create spatial patterns of transparency (spa- tial EIT) within an atomic cloud. Beginning with a review of EIT in general, with particular focus on an F = 1 → F = 0 transition, the spatial modulation of absorption, dispersion, polarisation rotation and change in ellipticity is predicted for systems in the presence of a transverse magnetic field. The depth of this mag- netic field dependency is then explored in some detail, where the relationship between observed patterns and applied magnetic field suggests the possibility of a visual magnetometer. The final section then considers how linearly polarised light and a q-plate was used to demonstrate spatially dependent transparency in a real atomic cloud.

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Whether in art or physics, two dimensions are better than one. And in this context, we consider the spatial shaping of optical fields and atomic polarisations. This work begins with a comprehensive review of how to accurately and arbitrarily modulate transverse beam profiles using six different methods. The methods are presented in the context of a general complex input beam and the shaping and measuring of the input beam with a single SLM is discussed and demonstrated. A simple setup is then considered that allows for the rapid switching between arbitrary profiles, using only a single holo- graphic component and an acousto-optical modulator (AOM). In this setup, a switching speed of approximately 10 kHz is demon- strated explicitly, limited by the current detection system, but where speeds of up to 20 MHz are estimated to be possible. The following discussion then concentrates on the spatial structure of atoms, reviewing the conceptual tools needed to measure and interpret an atomic cloud in the presence of a mag- netic field from fundamental concerns, both in theory and in practice: assuming a classical light field and a quantum atomic system. The specific implementation of both a magneto-optical trap and a holographically-shaped dynamic dark SpOT follows. The crux of the work then concerns how polarisation-structured light can be used to create spatial patterns of transparency (spa- tial EIT) within an atomic cloud. Beginning with a review of EIT in general, with particular focus on an F = 1 → F = 0 transition, the spatial modulation of absorption, dispersion, polarisation rotation and change in ellipticity is predicted for systems in the presence of a transverse magnetic field. The depth of this mag- netic field dependency is then explored in some detail, where the relationship between observed patterns and applied magnetic field suggests the possibility of a visual magnetometer. The final section then considers how linearly polarised light and a q-plate was used to demonstrate spatially dependent transparency in a real atomic cloud.
In recent years great progress was made in the spatial control of light with dynamic phase and amplitude modulators such as spatial light modulators and digital micromirror devices. In this work we describe the theory and practice of light shaping with such devices, detailing the spatial control of amplitude, phase and polarisation of coherent laser beams. We use our expertise in generating and measuring light fields with spatially dependent polarisation structures to characterise the correlations between spatial modes and polarisation in such light fields. We do this by adapting concurrence, a quantum measure of entanglement, to these classical correlations. One of the most promising application of coherent laser light is in the control of atomic media via atom-light interactions. In this work we describe the construction of simple external cavity diode lasers designed for the generation of resonant light for atomic physics applications. We exploit these lasers and spatial light modulators to create and measure three-dimensional atomic population structures in a warm rubidium vapour. We also implement a magneto-optic and a dynamic dark spontaneous-force optical trap for rubidium. These traps produce dense (~ 10^11 cm^-3) and cold (~100 uK) clouds of rubidium atoms. We develop the theory of spatially dependent electromagnetically induced transparency in such traps using rate equations. We find that the absorption of linearly polarised light depends on the relative direction of a magnetic field and the light polarisation. We use the cold atom clouds to measure the direction of magnetic fields by using this dependence and laser beams with structured polarisation.
Recent years have seen vast progress in the generation and detection of structured light, with potential applications in high capacity optical data storage and continuous variable quantum technologies. Here we measure the transmission of structured light through cold rubidium atoms and observe regions of electromagnetically induced transparency (EIT), using the phase profile as control parameter for the atomic opacity. With q plates we generate a probe beam with azimuthally varying phase and polarization structure, and its right and left circular polarization components provide the probe and control of an EIT transition. We observe an azimuthal modulation of the absorption profile that is dictated by the phase and polarization structure of the probe laser. Conventional EIT systems do not exhibit phase sensitivity. We show, however, that a weak transverse magnetic field closes the EIT transitions, thereby generating phase-dependent dark states which in turn lead to phase-dependent transparency, in agreement with our measurements.
Sculpted light refers to the generation of custom designed light fields. These light fileds can be applied in many diverse fields ranging from interrogating single atoms or atom assembly to using these fields for optical micromanipulation and optical tweezers as well as creating new quantum devices and sensors. We consider here the study and application of light with structured intensity, polarization and phase. We can create custom fields in multiple planes using dynamic and geometric phase control. As an example, the use of sculpted light in imaging has led to superresolution microscopy developed by Betzig, Hell and Moerner (2014 Nobel prize in Chemistry). Sculpted light can be generated using several technologies. These are spatial light modulators (SLM) and Digital Micromirror Devices (DMD) that enable the production of configurable and flexible confining potentials at the nano and micron-scale. Sculpted light can also be produced using time averaged methods such as Acousto-Optics Modulators (AOM), enabling production of highly configurable time-averaged traps. All these methods achieve dynamical and flexible sculpted light fields and enable imaging of the amplitude patterns, phase and polarization. Using these sculpted light we can produce novel optical potentials which can be used for intricate studies of light -matter interactions in a variety of environments. We will describe their use ranging from studies such as quantum thermodynamics using ultra cold atoms to trapping and manipulating nano and micron-size objects or even making measurements in-vivo inside biological cells.
A structured-light-based approach to magneto-optical rotation (MOR) magnetometry is proposed, in which magnetically induced polarization rotation is converted into a directly observable spatial displacement. A radially polarized Laguerre--Gaussian beam propagating through cold 87Rb^{87}\mathrm{Rb}87Rb atoms in the presence of a longitudinal magnetic field experiences circular birefringence, which induces a relative phase shift between the σ+σ_+σ+​ and σ−σ_-σ−​ polarization components. This phase shift manifests itself as the angular rotation of a petal-shaped interference pattern, enabling the MOR angle to be determined directly from the spatial intensity distribution. Unlike conventional MOR detection techniques based on balanced polarimetry or Stokes-parameter reconstruction, the proposed method requires only a fixed-axis polarization projection and avoids computationally intensive polarization analysis. By translating polarization rotation into a topology-dependent spatial observable, the scheme enables direct and spatially resolved magnetic-field measurements. Furthermore, the use of electromagnetically induced transparency (EIT) allows low-loss operation while preserving high sensitivity. These characteristics make the proposed technique a promising platform for optical magnetometry and structured-light-based quantum sensing.
Abstract The ultimate challenge for shaping technology is how to control the light field with a single optical element in a high-speed manner, wherein the spatial distribution of amplitude, phase or polarization are manipulated. Here we describe the use of the magneto optic effect to achieve the rapidly shaping of vector beams in real time using atomic ensemble. Firstly, the Faraday-rotation effect of vector beams is shown. On this basis, dynamically modulate the polarization of a vector beams on each point is implemented, and the polarization state of the manipulated beam is characterized with spatially resolved Stokes parameters measurements. The response time of this manipulation is about 40 μ s. The magnetic field high-speed switching and the dynamic manipulation capabilities of this method will be particularly useful for controlling light propagation through complex media and speed up the measurement of the properties of media.
The interaction between cylindrical vector beams and atoms under a weak magnetic field induces spatially dependent electromagnetically induced transparency (EIT). Based on this coherence effect, we investigated the relationship between the magnitude and orientation of the transverse magnetic field (TMF) and the spatial intensity distribution of cylindrical vector beams passing through a thermal atom ensemble, which is intuitively manifested in polarization selection absorption. The radially polarized beam exhibits a spatial axisymmetric polarization structure. When a TMF is applied, transparent regions in the transmitted beam strongly correlate with the beam’s polarization distribution. Variations in the TMF magnitude alter the absorption of specific polarization components by the atomic system, thereby affecting the local transmittance. This enables the TMF magnitude to be inferred from the single transmittance of the intensity pattern. The alignment of the TMF orientation is reflected in the rotation of the petal-shaped transmission patterns aligned with the mirror axis. Theoretical solutions using optical Bloch equations reveal this specific spatially dependent EIT is closely related to the transverse relaxation rate between the ground state energy levels. Experimental data align perfectly with the theoretical results, suggesting potential applications in light field manipulation and magnetic field measurement.