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arXiv:2305.17125 · Optica Pura y Aplicada

Inspecting the use of SLMs for the control of photonic quantum states

Universidad de Buenos Aires, Sebastián Bordakevich

Published Jun 30, 2023• 1 citation
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Abstract

Spatial light modulators (SLMs) are widely used to coherently control quantum states of light.When carrying out these experiments, some assumptions are made.For instance, it is supposed that the position-momentum correlations between twin photon pairs are not affected by the use of a liquid crystal display (LCD) as a SLM.Furthermore, it is assumed that the characterization of such devices performed with an intense laser source, is still valid in the single photon regime.In this work, we show that such assumptions are acceptable, within the experimental uncertainties, for a liquid crystal on silicon (LCoS) display.This is especially important when considering the use of this kind of displays for the coherent control of quantum states based on twin photon sources.

DOI
10.7149/opa.56.2.51147

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Spatial light modulators (SLMs) are widely used to coherently control quantum states of light.When carrying out these experiments, some assumptions are made.For instance, it is supposed that the position-momentum correlations between twin photon pairs are not affected by the use of a liquid crystal display (LCD) as a SLM.Furthermore, it is assumed that the characterization of such devices performed with an intense laser source, is still valid in the single photon regime.In this work, we show that such assumptions are acceptable, within the experimental uncertainties, for a liquid crystal on silicon (LCoS) display.This is especially important when considering the use of this kind of displays for the coherent control of quantum states based on twin photon sources.
Spatial light modulators are versatile devices employed in a vast range of applications to modify the transverse phase or amplitude profile of an incident light beam. Most experiments are designed to use a specific polarization which renders optimal sensitivity for phase or amplitude modulation. Here we take a different approach and apply the formalism of quantum information to characterize how a phase modulator affects a general polarization state. In this context, the spatial modulators can be exploited as a resource to couple the polarization and the transverse spatial degrees of freedom. Using a quasimonochromatic single-photon beam obtained from a pair of twin photons generated by spontaneous parametric down conversion, we performed quantum process tomography in order to obtain a general analytic model for a quantum channel that describes the action of the device on the polarization qubits. We illustrate the application of these concepts by demonstrating the implementation of a controllable phase flip channel. This scheme can be applied in a straightforward manner to characterize the resulting polarization states of different types of phase or amplitude modulators and motivates the combined use of polarization and spatial degrees of freedom in innovative applications.
Abstract A conceptual framework for a quantum spectrometer is presented based on phase-controlled spatial light modulators (SLMs) and polarization-basis projection measurements, in which each SLM pixel functions as a macroscopic quantum eraser. Recently, macroscopic quantum erasers have been proposed and experimentally demonstrated using both single photons and continuous-wave laser light in the classical regime. Polarization-basis projection measurements, which are essential for realizing quantum erasers, are also widely employed in N00N-state-based quantum sensing. In this work, a pair of SLMs replaces bulky optical components, forming a pixelated array that enables precise polarization-basis control of quantum erasers. For potential applications of the SLM-based quantum spectrometer, intensity correlations between paired SLM pixels are numerically calculated, demonstrating resolution enhancement proportional to the number of pixels and surpassing that of conventional optical sensors.
Liquid crystal displays (LCDs) are devices capable of manipulating properties of an incident light beam, such as amplitude, phase, and polarization, based on the voltage applied to their molecules. In this work, we will experimentally characterize the effect of an LCD on light polarization, aiming at its use as a programmable spatial light modulator (SLM) in optics and quantum information experiments. In the first part, we will determine the Mueller matrix of the device and, from it, its polarimetric properties. We will show that the LCD acts only approximately as an ideal retarder plate since it introduces depolarization to the incident light. In the second part, we investigate the behavior of the LCD through the formalism of quantum operations, treating its action as an operation on polarization qubit states. Through process tomography, we determine the matrix characterizing the device's operation and show that it is non-unitary. Next, we derive a general expression for the process matrix of an SLM, given by the combination of the LCD with wave plates. This expression will allow us to implement programmable operations on the polarization states of light based on the configuration of the wave plates and the voltage on the LCD. As an application, we will quantify the fidelity of the actual operation implemented by the SLM with an ideal unitary operation of interest in quantum information protocols.
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.
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.