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We propose two schemes for estimating the separation of two thermal sources via double homodyne and double array homodyne detection considering the joint measurement of conjugate quadratures of the image plane field.By using the Cramér-Rao bound, we demonstrate that the two schemes can estimate the separation well below the Rayleigh limit and have an advantage over direct imaging when the average photon number per source exceeds five.For arbitrary source strengths, double homodyne detection is superior to homodyne detection when the separation is above 25/4 σ/N s , σ is the beam width, Ns is the average photon number per source.A larger separation can be estimated better via double array homodyne detection with the superiority of flexible operation compared with other schemes. High-speed and high-efficiency detection enables the measurement schemes with potential practical applications in fluorescence microscopy, astronomy and quantum imaging.
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Spatially structured quantum states, such as orbital angular momentum (OAM) squeezing and entanglement, is currently a popular topic in quantum optics. The method of generating and manipulating spatial quantum states on demand needs to be explored. In this paper, we generated OAM mode squeezed states of -5.4 dB for the L G0+1 mode and -5.3 dB for the L G0-1 mode directly by an optical parametric oscillator (OPO) for the first time. Additionally, we demonstrated that the OAM mode squeezed and entangled states were respectively generated by manipulating the nonlinear process of the OPO by controlling the relative phase of two beams of different modes, thus making two different spatial multimode pump beams. We characterized the Laguerre-Gaussian (LG) entangled states by indirectly measuring the squeezing for the H G 10(45∘) mode and H G 10(135∘) mode, and directly measuring the entanglement between the L G0+1 and L G0-1 modes. The effective manipulation of the OAM quantum state provides a novel insight into the continuous variable quantum state generation and construction on demand for high-dimensional quantum information and quantum metrology.
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Optical spin-orbit coupling is an important phenomenon and has fruitful applications. Here, we investigate the spin-orbit total angular momentum entanglement in the optical parametric downconversion process. Four pairs of entangled vector vortex modes are experimentally generated directly using a dispersion- and astigmatism-compensated single optical parametric oscillator, and for the first time, to the best of our knowledge, the spin-orbit quantum states are characterized on the quantum higher-order Poincaré sphere, and the relationship of spin-orbit total angular momentum Stokes entanglement is demonstrated. These states have potential applications in high-dimensional quantum communication and multiparameter measurement.
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Long-term stable entanglement is a crucial aspect in the implementation of reliable quantum information processes. However, long-term continuous variable entanglement generation, especially in type-II non-degenerate optical parametric amplifier, has yet to be reported on. Here, we derive the relationship between entanglement and temperature fluctuations in the crystal of a type-II non-degenerate optical parametric amplifier, and propose a novel method for long-term stable entanglement generation by locking the temperature of the crystal. In the experiment, we obtain a 5.4 dB entanglement lasting two hours. The method holds promise in the generation of a truly usable above 10 dB entanglement and brings us closer to continuous-variable quantum information processing.
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The continuous-variable (CV) orbital angular momentum (OAM) entanglement is very different to the traditional quadrature entanglement. The Stokes-operators directly reflect the character of OAM light. Here, we report the first direct experimental demonstration the Stokes-operator entanglement of continuous-variable OAM entanglement. Generated by transforming quadrature entanglement in the HG01 mode onto the orbital Stokes-operator basis, the entanglement is measured in the Stokes-operator basis using a self-designed detection scheme. An inseparability of I(O^2,O^3)<1 is achieved over a wide analyzing frequency of 1-10 MHz. Moreover, experimental fluctuations at 5.0 MHz are visualized using the quantum orbital Poincaré sphere representation. The OAM entanglement with Stokes-operators measurement has a promising application in certain nonlocal quantum information protocols and rotational optomechanics by interacting with nanoparticle or atoms.
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Nonclassical beams in high order spatial modes have attracted much interest but they exhibit much less squeezing and entanglement than the fundamental spatial modes, limiting their applications. We experimentally demonstrate the relation between pump modes and entanglement of first-order Hermite Gauss modes (HG10 entangled states) in a type II OPO and show that the maximum entanglement of high order spatial modes can be obtained by optimizing the pump spatial mode. To our knowledge, this is the first time to report this. Utilizing the optimal pump mode, the HG10 mode threshold can be reached easily without HG00 oscillation and HG10 entanglement is enhanced by 53.5% over HG00 pumping. The technique is broadly applicable to entanglement generation in high order modes.
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We developed a tilt modulation technique of a laser beam with a wedged crystal. Combined with a phase-compensating crystal, a pure tilt modulation with a wide bandwidth (actually determined by the bandwidth of electro-optic crystals) is realized. By Fourier transformation with a lens, the tilt signal is transformed into displacement. With homodyne detection using a local oscillator of the first-order Hermite-Gauss mode (HG10) and a 4F phase-monitoring system, we measure the displacement and tilt of a laser probe beam. This technique can be used in metrology, such as Newtonian gravitational constant determination and gravitational wave detection, or the calibration of a spatial sensor, such as tilt/displacement sensors.
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We demonstrate experimentally a measurement scheme for the Stokes operators for the continuous-variable squeezed states of orbital angular momentum (OAM). An OAM squeezed state is generated by coupling a dim Hermite-Gauss HG01-mode quadrature-squeezed light beam with a bright HG10-mode coherent light beam on a 98/2 beam splitter. Using an asymmetric Mach-Zehnder interferometer with an extra Dove prism in one arm, we measured the three orbital Stokes operators of the OAM squeezed states with a self-homodyne detection and finally characterized their positions and noise on the orbital Poincaré sphere.