Tracking the kinematics of fast-moving objects is an important diagnostic tool for science and engineering. Existing optical methods include high-speed CCD/CMOS imaging [1], streak cameras [2], lidar [3], serial time-encoded imaging [4] and sequentially timed all-optical mapping [5]. Here, we demonstrate an entirely new approach to positional and directional sensing based on the concept of classical entanglement [6][7][8] in vector beams of light. The measurement principle relies on the intrinsic correlations existing in such beams between transverse spatial modes and polarization. The latter can be determined from intensity measurements with only a few fast photodiodes, greatly outperforming the bandwidth of current CCD/CMOS devices. In this way, our setup enables two-dimensional real-time sensing with temporal resolution in the GHz range. We expect the concept to open up new directions in metrology and sensing.Vector beams of light with cylindrical, non-uniform polarization patterns [9] have found application in diverse areas of optics such as improved focusing [10], laser machining [11], plasmon excitation [12], metrology [13], optical trapping [14] and nano-optics [15][16][17]. Recently, vector beams have attracted attention [18][19][20][21][22] due to a simple but striking property: when viewed as a superposition of transverse electromagnetic modes with orthogonal linear polarizations, the nonseparable mode function of a radially polarized vector beam is mathematically equivalent to a maximally entangled Bell state of two qubits known from quantum mechanics. In contrast with the canonical Bell states in quantum optics, where two photons are entangled in polarization and exhibit non-local correlations when spatially separated, this "classical entanglement" in vector beams is necessarily local as it exists only between different degrees of freedom of one and the same physical system [23].However, these correlations have recently been shown to represent a valuable resource. Vector beams have been used to violate an analogue of Bell's inequality for spin-orbit modes [19,20] and have led to continuousvariable entanglement between different degrees of freedom [24]. In addition, vector beams have been used to implement classical counterparts of quantum protocols [25,26]. Promising proposals include an application to the study of quantum random walks [27] and realtime single-shot Mueller matrix measurements [28], and a scheme for measuring the depolarization strength of a material has been implemented [29]. In the present work, we demonstrate for the first time a fully operational application of classical entanglement to high-speed kinematic sensing. Several techniques are nowadays available for sensing the kinematics of fast-moving objects [1][2][3][4][5]. Each arXiv:1504.00697v2 [quant-ph]
Abstract:As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [1]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, −1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations, depending on the measurement scheme, are.
Abstract:We present an experimental method for the generation of amplitude squeezed high-order vector beams. The light is modified twice by a spatial light modulator such that the vector beam is created by means of a collinear interferometric technique. A major advantage of this approach is that it avoids systematic losses, which are detrimental as they cause decoherence in continuous-variable quantum systems. The utilisation of a spatial light modulator (SLM) gives the flexibility to switch between arbitrary mode orders. The conversion efficiency with our setup is only limited by the efficiency of the SLM. We show the experimental generation of Laguerre-Gauss (LG) modes with radial indices up to 1 and azimuthal indices up to 3 with complex polarization structures and a quantum noise reduction up to -0.9dB±0.1dB. The corresponding polarization structures are studied in detail by measuring the spatial distribution of the Stokes parameters.
Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2, 864 (2015)10.1364/OPTICA.2.000864]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.
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