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arXiv:1912.10153

High-dimensional states of light with full control of transverse path and OAM degrees of freedom

D. O. Pabón, Silvia Adriana Ledesma, Lorena Rebón

Published Dec 21, 2019• 0 citations
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Abstract

We present here a compact scheme for the generation of high-dimensional states of light encoded in the transverse path variable of photons that carry orbital angular momentum. We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup we are able to control, independently, the relative phases and amplitudes of the path superposition in addition to the topological charge of each path. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions $d\times m$. Experimental results from the characterization of different generated states of dimensions up to $9\times 5$ are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above $95\%$.

DOI
10.48550/arxiv.1912.10153

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We present here a compact scheme for the generation of high-dimensional states of light encoded in the transverse path variable of photons that carry orbital angular momentum. We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup we are able to control, independently, the relative phases and amplitudes of the path superposition in addition to the topological charge of each path. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions d×md\times md×m. Experimental results from the characterization of different generated states of dimensions up to 9×59\times 59×5 are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above 95%95\%95%.
We present a compact scheme for the generation of high-dimensional states of light encoded in the transverse linear momentum of photons that carry orbital angular momentum (OAM). We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup, we are able to control, independently, the relative phases and amplitudes of the spatial superposition in addition to the topological charge of the OAM. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions d × m . Experimental results from the characterization of different generated states of dimensions up to 9 × 5 are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above 95%.
We present here a compact scheme for the generation of high-dimensional states of light encoded in the path variable of photons that carry orbital angular momentum. Our method uses a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. This setup allows us to independently control the relative phases and amplitudes of the path superposition, in addition to the topological charge of each path. Experimental results from the characterization of different generated states up to dimension 45, are in excellent agreement with the numerical simulations, and fidelities with respect to the target state are all above 95%95\%95%.
The experimental realization of multidimensional quantum states may lead to unexplored and interesting physics, as well as advanced quantum communication protocols. The orbital angular momentum of photons is a well suitable discrete degree of freedom for implementing high-dimensional quantum systems. The standard method to generate and manipulate such photon modes is to use bulk and fixed optics. Here the authors demonstrate the utilization of a spatial light modulator to manipulate the orbital angular momentum of entangled photons generated in spontaneous parametric downconversion. They show that their setup allows them to realize photonic entanglement of up to 21 dimensions, which in principle can be extended to even larger dimensions.
We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional (Dgeqslant2D\\geqslant 2Dgeqslant2) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D. The amplitude information was codified by introducing phase gratings inside each slit, and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process, we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried out. In this scheme, the amplitudes are set by appropriate phase gratings addressed at the SLM, while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete $2\\pi $ modulation is obtained by shifting the grating by one period; hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analyses are performed for qudits with D = 3 and D = 7.
High-dimensional quantum computing has emerged as a recent alternative to conventional qubit-based approaches, offering advantages such as an increased information density and enhanced robustness against noise. In this work, we explore the use of the orbital angular momentum (OAM) of light as a degree of freedom in which high-dimensional quantum gates can be implemented. We present a theoretical and experimental study of structured light beams carrying OAM, with emphasis on Laguerre–Gauss modes, as a natural basis for high-dimensional quantum computing. We then describe the generation of OAM beams using computer-generated holograms and spatial light modulators, detailing practical methods for encoding arbitrary phase profiles. Building on this framework, we analyze the implementation of high-dimensional quantum logic gates, focusing on the generalized Pauli Z_d and X_d operations. Optical setups based on Dove prisms, Sagnac interferometers, spiral phase plates, and parity sorters are proposed and theoretically validated. Finally, we report experimental results demonstrating the generation of Laguerre–Gauss beams, the transformation properties of Dove prisms, and the operation of a parity sorter, which constitutes a building block for realizing high-dimensional quantum gates. These results establish a solid foundation for future implementations of high-dimensional quantum information processing using the orbital angular momentum of light.
We present a method for preparing arbitrary pure states of spatial qudits, namely, D -dimensional ( ) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D . The amplitude information was codified by introducing phase gratings inside each slit, and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process, we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried out. In this scheme, the amplitudes are set by appropriate phase gratings addressed at the SLM, while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete modulation is obtained by shifting the grating by one period; hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analyses are performed for qudits with D = 3 and D = 7.