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arXiv:2312.15178 · Physical Review Research

Quantum state engineering and photon statistics at electromagnetic time interfaces

M. S. Mirmoosa, Tero Setälä, Andreas Norrman

Published Jan 31, 2025• 13 citations
arXivHTMLPDF

Abstract

Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different branches of electromagnetism and optics. However, compared with the research efforts and progresses that have taken place in the realm of classical electrodynamics, the quantum aspects of this emerging subject have been less explored. Here, through the lens of quantum optics, we study the scattering of electromagnetic fields from an isotropic and nondispersive material with a suddenly changing refractive index, creating a time interface. We revisit the transformation of the bosonic mode operators and corresponding quantum states due to this interface, governed by the two-mode squeeze operator. Building on this foundation, at the core of the investigation, our analysis focuses on the quantum state engineering and photon statistics of the scattered light. Notably, such an analysis reveals and connects various quantum optical phenomena and opportunities arising from the time interface, including photon-pair production and destruction, photon bunching and antibunching, vacuum generation, quantum state discrimination, and quantum state freezing. To bridge theory and experiment, we propose a possible circuit quantum electrodynamics approach for validating our theoretical predictions. We hope that our work inspires experimental investigations of such quantum state engineering and photon statistics phenomena, as well as further quantum optical explorations of electromagnetic field interaction with photonic time crystals or with dispersive time-varying materials.

DOI
10.1103/physrevresearch.7.013120

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Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different branches of electromagnetism and optics. However, compared with the research efforts and progresses that have taken place in the realm of classical electrodynamics, the quantum aspects of this emerging subject have been less explored. Here, through the lens of quantum optics, we study the scattering of electromagnetic fields from an isotropic and nondispersive material with a suddenly changing refractive index, creating a time interface. We revisit the transformation of the bosonic mode operators and corresponding quantum states due to this interface, governed by the two-mode squeeze operator. Building on this foundation, at the core of the investigation, our analysis focuses on the quantum state engineering and photon statistics of the scattered light. Notably, such an analysis reveals and connects various quantum optical phenomena and opportunities arising from the time interface, including photon-pair production and destruction, photon bunching and antibunching, vacuum generation, quantum state discrimination, and quantum state freezing. To bridge theory and experiment, we propose a possible circuit quantum electrodynamics approach for validating our theoretical predictions. We hope that our work inspires experimental investigations of such quantum state engineering and photon statistics phenomena, as well as further quantum optical explorations of electromagnetic field interaction with photonic time crystals or with dispersive time-varying materials.
In this presentation, we shed light on electromagnetic time interfaces using the principles of quantum optics. We begin by explaining the transformation of bosonic mode operators in response to a temporal discontinuity in the macroscopic parameters. Accordingly, our discussion extends to the general analysis of photon statistics and the degree of second-order coherence of the generated forward and backward modes. Focusing on input number states, we meticulously detail the quantum states produced after the time interface, elucidating the associated probability distributions. By virtue of this study, we specifically highlight the controllable nature of photon statistics of the output forward mode for particular input states. We show that this capability, in general, is not present for the backward mode generated through the time interface. Also, we reveal that photon-pair generation is a fundamental inherent feature of the time interface. By unveiling all these insights, we aim to pave the way for exploring photonic time crystals within the domain of quantum optics.
Photonic time crystals are exotic materials characterized by effective parameters that are uniform in space yet periodically vary over time. Recently, these materials have been the subject of extensive study from both theoretical and experimental perspectives. However, the quantum characteristics of light within photonic time crystals remain largely uncharted territory. In this presentation, we explore the interaction of light with these materials through the lens of quantum optics, addressing various topics ranging from mode operator transformation to the photon statistics of light in photonic time crystals.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.
Temporal modulation of materials offers unprecedented control over light, sparking recent interest in the quantum theory of light interaction with time-varying materials. In this presentation, through the lens of quantum optics, we evaluate the von Neumann entropy transformation induced by an electromagnetic time interface, in which the refractive index of an isotropic, homogeneous, nondispersive dielectric medium uniformly undergoes an abrupt change in time. We demonstrate that the entropy increases across such an interface, with the magnitude of the increase correlating positively with the refractive index contrast. Additionally, we analyze how photon population in the incident modes governs entropy evolution. We hope that our study advances both the fundamental physics of time interfaces and their potential applications in quantum information technology.
This presentation offers a fresh perspective on the quantum theory of electromagnetic time interfaces.Notably, by critically examining established assumptions, we uncover that, in addition to photon-pair production, photon-pair annihilation is also a salient feature of time interfaces.Our analysis reveals that this characteristic enables the generation of quantum vacuum states and facilitates quantum state discrimination.Thus, these findings not only expand our understanding of time interfaces, but also may open new avenues for applications in quantum optics.
Abstract The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation, and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we experimentally demonstrate that the manipulation of the quantum electromagnetic fluctuations of two-mode squeezed vacuum states leads to a family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on the use of conditional measurements to engineer the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. The experimental generation of nonclassical multiphoton states by means of photon subtraction unveils novel mechanisms to control fundamental properties of light. As a remarkable example, we demonstrate the engineering of a quantum state of light with up to ten photons, exhibiting nearly Poissonian photon statistics, that constitutes an important step towards the generation of entangled lasers. Our technique enables a robust protocol to prepare quantum states with multiple photons in high-dimensional spaces and, as such, it constitutes a novel platform for exploring quantum phenomena in mesoscopic systems.