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Optics Express

Manipulation of continuous variable orbital angular momentum squeezing and entanglement by pump shaping

Zhi Li, Xulian Guo, Hengxin Sun, Kui Liu, Jiangrui Gao

Published Jan 10, 2023• 6 citations
Publisher

Abstract

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 G 0 + 1 mode and −5.3 dB for the L G 0 − 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 G 0 + 1 and L G 0 − 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.

DOI
10.1364/oe.479583

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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 G 0 + 1 mode and −5.3 dB for the L G 0 − 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 G 0 + 1 and L G 0 − 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.
We have generated a new quantum state of light composed of quadrature entangled Laguerre-Gaussian (LG) modes. For the generation we used an OPO operating in a new regime where all field parameters are degenerate except for its spatial degree of freedom for which it is two-fold degenerate. The entanglement is manifested in the squeezing of the rotated modes in the Hermite-Gauss (HG) basis, measured with a specially tailored local oscillator. The most promising application of CV orbital angular momentum (OAM) states is their compatibility with atoms, thus allowing for storage of CV quantum information.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincaré sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincaré sphere.
In the present dissertation we describe the generation of a Gaussian bipartite entangled state in which the two subsystems are multi-distinguishable thanks to the fact that they have different polarizations and carry an opposite amount of orbital angular momentum along the propagation direction. Polarization entangled states are produced by using an optical parametric oscillator as spontaneous parametric down conversion source. This is able to produce a bipartite state consisting of collinear thermal crossed polarized modes exhibiting entanglement. These two modes have the same frequency and constitute a continuous variable bipartite entangled system in which each of the modes can be labeled by the polarization degree of freedom. Once these two polarization entangled states are produced, the bipartite state is endowed with an additional degree of freedom constituted by orbital angular momentum, that makes possible to further distinguish between these two co-propagating modes. The two-dimensional Hilbert polarization space is mapped into the orbital angular momentum one by means of Gaussian operations i.e. physical trasformations that preserve Gaussianity. In order to achieve this task we used a liquid crystal optical device called q-plate. This device is able to couple polarization and orbital angular momentum degrees of freedom by making the passing through beam acquire orbital angular momentum that depends on the topological charge q of the device and on the polarization of the incoming beam. Moreover, the setup enginereed to achieve this task is also capable of generating squeezed vortex beams i.e. single mode states for which the quadrature noise is below the standard quantum limit. After producing the bipartite entangled state it enters the characterizaton stage. Its quantumness is investigated by witnessing both squeezing and non classical correlations via balanced optical homodyne, a phase sensitive detection method that permits, by measuring the electromagnetic field quadratures statistics, to reconstruct the state of the system. In order to retrieve the quantum state with a high fidelity, homodyne detector needs to be optimized. This, besides imposing stringent conditions on the optical components involved in the setup, forces to improve the mode matching between the signal and the local oscillator that plays a central role in determining the overall detector efficiency. Although homodyne is a consolidated detection scheme, herein it is proposed an innovative extension of this technique to structured modes that opens the doors for homodyning directly in the orbital angular momentum space. The very central role, in this detection method, is played by interference between the signal under investigation and a strong coherent reference beam called local oscillator. Besides behaving as an amplifier for the quadrature under scrutiny, local oscillator also acts as a spatial and frequency filter, selecting for the measure the part of the signal that shares with it the same spatio-temporal properties. Hence, in order to ensure interference, in case of a signal carrying orbital angular momentum a further effort is required. Indeed, also the local oscillator has to be in the same helical mode, in particular the two beams have to transport the same amount of orbital angular momentum along the propagation direction. So by suitably designing the overall experimental setup it is possible to homodyne the bipartite entangled state carrying orbital angular momentum directly in this degree of freedom Hilbert space. Once the covariance matrix of the bipartite Gaussian state has been reconstructed, thanks to Gaussianity, it is possible to assess entanglement between the vortex modes by means of entanglement criteria based on covariance matrix elements such as the Peres-Horodecki-Simon (PHS) and the Duan ones.
High-dimensional maximally entangled orbital angular momentum (OAM) states are a promising resource for enhancing information capacity and robustness in quantum communication. However, it still lacks an effective method to increase the state dimensionality. Here, we theoretically propose an efficient scheme to generate maximally entangled OAM states of ultrahigh dimensionality by manipulating the radial components of a Laguerre-Gaussian (LG) pump beam. By optimizing the complex amplitudes of multiple radial modes of the LG pump light, one can feasibly achieve 101-dimensional OAM-based maximally entangled states. Our scheme has potential applications in high capacity quantum communication networks.
We demonstrated that by using a pump field with nonzero orbital angular momentum (OAM) in the polarization self-rotation squeezing process it is possible to generate a squeezed vacuum optical field with the matching OAM. We found a similar level of maximum quantum noise reduction for a first-order Laguerre-Gaussian pump beam and a regular Gaussian pump beam, even though the optimal operational conditions differed in these two cases. Also, we investigated the effect of self-defocusing on the level of the vacuum squeezing by simultaneously monitoring the minimum quantum noise level and the output beam transverse profile at various pump laser powers and atomic densities and found no direct correlations between the increased beam size and the degree of measured squeezing.
High-dimensional quantum entanglement is an important resource for fundamental research and quantum technological application. Recently, the orbital angular momentum (OAM) of light has received much attention to realize high-dimensional quantum systems, and generating and manipulating the OAM entanglement has become an important topic. Here, we propose an inverse design technique to manipulate the OAM entanglement of the photon pair generated through spontaneous parametric down-conversion. The proposed technique directly tailors the OAM states of entangled photon pairs by shaping the incident pump beam. In particular, we construct a physics-informed model by leveraging the backpropagation algorithm and adhering to the overlap integral relation. Our model automatically optimizes diffractive masks, allowing the structured pump to quantitatively modulate the OAM distribution. The generation of maximally entangled states in different dimensions is demonstrated numerically and experimentally.