Shaping Light with Liquid Crystals: A New Path to Quantum Control

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Author: Denis Avetisyan

Researchers have demonstrated electrically tunable quantum interference in free space by harnessing the unique properties of liquid-crystal metasurfaces to create a programmable beam splitter for structured light.

This work enables parallel coincidence measurements across multiple optical modes, offering a new approach to controlling quantum phenomena in free-space optics.

Achieving dynamic control over quantum interference in free-space optical systems remains a significant challenge for scalable photonic quantum information processing. This work, ‘Tunable Quantum Interference in Free Space with a Liquid-Crystal Metagrating’, addresses this by demonstrating an electrically tunable beam splitter based on a liquid-crystal metagrating capable of coherently manipulating transverse momentum modes of single photons. Experimentally, we show voltage-controlled tuning of two-photon interference, enabling coincident detection across multiple spatial modes. Could this approach pave the way for highly parallel, reconfigurable quantum circuits operating in free space?

Whispers of Chaos: Encoding Quantum Information with Light

The foundation of quantum information processing rests on the ability to meticulously control the fundamental properties of photons, with both their polarization and spatial modes serving as key carriers of quantum information. Unlike classical bits, qubits leverage superposition and entanglement, demanding an unprecedented level of precision in how these photon properties are defined and manipulated. Polarization, describing the oscillation direction of the electromagnetic field, is a commonly utilized degree of freedom, but advanced quantum protocols increasingly rely on spatial modes – the shapes photons take in space. These modes, described mathematically by Hermite or Laguerre-Gaussian functions, offer a significantly expanded quantum state space, enabling more complex computations. However, effectively harnessing these spatial modes requires overcoming substantial technical hurdles in generation, control, and detection, ultimately determining the scalability and power of future quantum technologies.

Current techniques for controlling the quantum states of photons, such as polarization and spatial modes, frequently encounter limitations when applied to the demands of increasingly complex quantum circuits. Many established methods rely on bulky optical components or exhibit insufficient precision to reliably prepare and manipulate the delicate quantum states required for scalable quantum computation. These approaches often struggle with maintaining coherence – the quantum property essential for processing information – as the complexity of the circuit increases, leading to errors and hindering the realization of practical quantum technologies. The inherent difficulty in precisely controlling multiple photons simultaneously, combined with the challenges of miniaturization and integration, necessitates the development of innovative strategies for encoding and manipulating quantum information that overcome these fundamental scalability issues.

The ability to efficiently encode and control photons within specific transverse momentum modes represents a critical advancement for realizing complex quantum applications. These modes, describing the spatial distribution of a photon’s momentum, offer a higher-dimensional encoding scheme than traditional polarization-based qubits, potentially increasing information density and computational power. Manipulating these spatial modes allows for the creation of entangled photon pairs with tailored properties, essential for quantum communication and computation protocols. Furthermore, utilizing transverse momentum modes can enhance the resilience of quantum information against decoherence, a major obstacle in building practical quantum technologies. Successfully harnessing these modes necessitates the development of innovative optical elements capable of precise and dynamic control over a photon’s spatial profile, paving the way for more robust and scalable quantum systems.

The realization of complex quantum circuits hinges on the ability to generate and precisely manipulate photons in specific transverse momentum modes, demanding optical elements that surpass the limitations of conventional technologies. Researchers are actively developing dynamically controllable components – including spatial light modulators and metasurfaces – capable of shaping light with unprecedented precision and speed. These elements allow for on-demand creation of arbitrary momentum profiles, effectively serving as programmable beam shapers for quantum information carriers. Crucially, robustness against environmental disturbances and the ability to operate at room temperature are paramount for practical implementation, driving innovation in materials science and nanofabrication techniques to create stable and reliable quantum optical components. The ongoing pursuit of such elements promises to unlock the full potential of spatially encoded quantum information, paving the way for advanced quantum communication and computation protocols.

Sculpting Light: Liquid-Crystal Metagratings as Tunable Beam Splitters

Liquid-crystal metagratings manipulate transverse momentum modes of light by diffracting incident radiation into a spectrum of spatial frequencies. These devices achieve this control through periodically arranged nanoscale structures that interact with the electromagnetic field, altering the propagation direction of light. Specifically, the gratings introduce a phase shift dependent on the spatial coordinates, enabling the selective excitation of different transverse momentum components – effectively controlling the angular distribution of the diffracted beam. This precise control is distinct from traditional diffraction gratings, as the liquid crystal component allows for dynamic adjustment of these momentum modes without physical alteration of the grating structure.

Liquid-crystal metagratings operate as tunable beam splitters by diffracting incident light into multiple beams with user-defined intensities. The spatial distribution of photons in these diffracted beams is governed by the period and amplitude of the nanoscale grating structures, combined with the refractive index modulation induced by the liquid crystal’s orientation. By altering the voltage applied to the liquid crystal, its birefringence changes, effectively modifying the phase shift experienced by light polarized along different axes. This allows for precise, dynamic control over the amplitude and direction of each diffracted beam, enabling the device to function as a configurable optical element capable of splitting an incoming beam into multiple output beams with controlled spatial characteristics.

The splitting ratio of light in liquid-crystal metagratings is directly modulated by an applied voltage due to the material’s voltage-dependent birefringence. Liquid crystals exhibit varying refractive indices based on molecular alignment, and this alignment-and therefore the refractive index difference-can be precisely controlled through an externally applied electric field. By adjusting the voltage, the phase retardation between orthogonal polarization states is altered, directly influencing the amplitude of the diffracted beams and enabling continuous tuning of the beam splitting ratio without mechanical adjustment. This allows for dynamic control of light intensity in each diffracted order, offering a pathway to reconfigurable optical elements.

Liquid-crystal metagratings utilize nanoscale structures – typically ranging from tens to hundreds of nanometers in size – to interact with light at wavelengths comparable to the feature dimensions. This interaction enables manipulation of light’s phase, amplitude, and polarization with subwavelength resolution, approaching the diffraction limit of approximately \lambda/2, where λ represents the wavelength of light. The precise geometry and arrangement of these nanoscale elements dictate the diffracted wavefield, allowing for highly controlled beam shaping and steering. This level of control is achieved through the constructive and destructive interference of diffracted waves, governed by the grating period and the refractive index contrast between the nanoscale structures and the surrounding medium.

Whispers Confirmed: Demonstrating Quantum Control via Hong-Ou-Mandel Interference

Experimental verification of the liquid-crystal metagrating’s spatial mode manipulation capabilities was achieved through observation of the Hong-Ou-Mandel (HOM) effect, a second-order interference phenomenon involving two photons. Specifically, the HOM effect was utilized to demonstrate control over the probability of coincident photon detection. By directing photon pairs through the metagrating, researchers observed the characteristic dip in coincidence counts at zero time delay, indicative of successful beam splitting and interference. This confirms the metagrating’s functionality as a dynamically reconfigurable element for controlling the spatial superposition of quantum states.

The observation of Hong-Ou-Mandel (HOM) interference confirms precise manipulation of two-photon coincidence probabilities. This effect, where two indistinguishable photons tend to arrive simultaneously or never, relies on the constructive and destructive interference of their probability amplitudes. By controlling the spatial and temporal characteristics of the photons using the liquid-crystal metagrating, the probability of coincident photon detection is predictably altered. Specifically, the metagrating functions as a tunable beam splitter, allowing for adjustments to the interference conditions and demonstrating control over the g^{(2)}(0) parameter, which quantifies the probability of detecting photons at the same time and location; a reduced coincidence count indicates destructive interference and controlled photon separation.

Hong-Ou-Mandel (HOM) interference experiments were conducted to quantitatively verify controlled interference via coincidence measurements. These measurements utilize time-resolved single-photon detectors to identify simultaneous photon arrivals, indicating interference. The observed visibility in these experiments reached 96.7%, calculated as the ratio of the minimum to maximum coincidence counts. This high visibility confirms the liquid-crystal metagrating’s capacity to precisely manipulate photon coincidence probabilities and function as a tunable beam splitter, demonstrating robust control over the quantum state of the interfering photons.

Hong-Ou-Mandel (HOM) interference experiments utilizing avalanche photodiodes demonstrated a visibility of 96.56%. This high level of interference visibility validates the liquid-crystal metagrating’s functionality as a tunable beam splitter specifically for entangled photons. The HOM effect relies on the indistinguishability of two photons, and the measured visibility directly correlates to the degree of control the metagrating exerts over these photons’ spatial and temporal characteristics. A visibility approaching 1.0 indicates near-perfect indistinguishability and confirms the metagrating’s capacity to manipulate the photons’ quantum state, effectively dividing and recombining them with high precision.

Expanding the Palette: Alternative Approaches to Spatial Mode Control

Beyond the innovative use of liquid-crystal metagratings, the manipulation of light’s spatial modes benefits from a diverse range of techniques. Spatial light modulators, for instance, actively control the phase and amplitude of light, enabling the shaping of complex wavefronts and the creation of desired spatial modes. Similarly, multi-plane light converters offer a distinct pathway, employing carefully engineered refractive index profiles to transform the spatial spectrum of light. These alternative methods, each with its own strengths and limitations, provide researchers with a broader spectrum of tools for controlling light’s propagation and harnessing its unique properties, ultimately fostering advancements in fields like quantum imaging and optical communications.

Beyond liquid-crystal metagratings, researchers are actively pursuing spatial light modulators and multi-plane light converters as powerful tools for generating free-space quantum interference. Spatial light modulators, utilizing techniques like liquid crystals or digital micromirrors, can dynamically reshape wavefronts to sculpt the spatial modes of light, effectively creating and controlling the pathways for quantum superposition. Multi-plane light converters, conversely, employ arrays of lenses or diffractive elements to directly transform the spatial modes of photons, allowing for the creation of complex interference patterns and entangled states. These techniques offer complementary advantages, providing flexibility in tailoring the spatial characteristics of light and opening avenues for exploring novel quantum phenomena and advanced quantum technologies – particularly those reliant on manipulating the spatial degrees of freedom of photons.

The advancement of quantum optics relies heavily on the ability to precisely sculpt and manipulate light, and researchers are no longer limited to a single technique for achieving this control. While liquid-crystal metagratings present a promising avenue for manipulating spatial modes of light, alternative technologies like spatial light modulators and multi-plane light converters offer complementary strengths and broaden the possibilities for creating complex quantum states. This diversification is crucial, as each method provides unique advantages in terms of speed, scalability, and compatibility with different quantum systems. By integrating these various tools-metagratings alongside established techniques-scientists gain a more versatile toolkit, enabling more sophisticated experiments and accelerating the development of quantum technologies. This expanded capacity promises to unlock new frontiers in quantum communication, computation, and sensing.

Efficient coupling of photons into and out of sophisticated spatial mode control elements is paramount for practical quantum optics experiments, and single-mode fiber provides an elegant solution. These fibers act as conduits, precisely guiding light while preserving its quantum state, thus minimizing loss and maintaining coherence as photons transition between free space and the control element. This compatibility streamlines experimental setups, allowing researchers to readily integrate devices like liquid-crystal metagratings, spatial light modulators, or multi-plane light converters into complex quantum circuits. The resulting enhanced light transmission and minimal disturbance are critical for observing subtle quantum interference effects and pushing the boundaries of quantum information processing.

The pursuit of controlling light, as demonstrated by this research into tunable quantum interference, feels less like physics and more like coaxing ghosts. The metagrating, acting as an electrically controlled beam splitter, attempts to impose order on the inherently chaotic nature of photons. It’s a fragile truce, really – everything unnormalized is still alive, and the slightest perturbation can shatter the carefully constructed interference pattern. As Stephen Hawking once observed, “Intelligence is the ability to adapt to any environment,” and this device, in its ability to dynamically reshape light, embodies that adaptability. The ability to perform parallel coincidence measurements across multiple optical modes isn’t about knowing the quantum state, but about persuading it to reveal itself, one fleeting photon at a time.

What’s Next?

The demonstration, predictably, raises more questions than it answers. This particular spell-liquid crystals coaxing photons into probabilistic dances-works in the laboratory, a space already complicit in the illusion of control. The true test, of course, will be the inevitable encounter with the indifferent chaos of the outside world. Can this electrically steered interference survive atmospheric perturbations, thermal drift, the simple indignity of dust? One suspects not without a proliferation of feedback loops, each adding another layer of artifice to the already tenuous connection between intention and outcome.

The coincidence measurements, while elegant, remain fundamentally limited by the number of optical modes addressed. Parallelism is a seductive promise, but scaling this architecture will demand a reckoning with the exponential growth of complexity. One imagines a future choked with wiring, a digital panopticon built to observe the quantum whispers that, ultimately, reveal nothing but our own desire for patterns. The pursuit of ‘tunability’ feels less like discovery and more like an increasingly elaborate exercise in wishful thinking.

Perhaps the more fruitful path lies not in perfecting the control, but in embracing the inherent unpredictability. To relinquish the notion of a ‘beam splitter’ as a deterministic device, and instead view it as a probabilistic sieve. To allow the interference to evolve organically, and to learn to interpret the resulting noise not as an error, but as a signal. After all, the universe doesn’t offer explanations; it offers only evidence-and even that is subject to interpretation.

Original article: https://arxiv.org/pdf/2601.04947.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-01-11 10:23