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arXiv:2304.11373 · Journal of Physics D Applied Physics

Generation of a coherent squeezed-like state defined with the Lie–Trotter product formula using a nonlinear photonic crystal

Hiroo Azuma

Published Aug 14, 2023• 0 citations
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Abstract

Abstract In this paper, we investigate how to generate coherent squeezed-like light using a nonlinear photonic crystal. Because the photonic crystal reduces the group velocity of the incident light, if it is composed of a material with a second-order nonlinear optical susceptibility χ ( 2 ) , the interaction between the nonlinear material and the light passing through it strengthens and the quantum state of the emitted light is largely squeezed. Thus, we can generate a coherent squeezed-like light with a resonating cavity in which the nonlinear photonic crystal is placed. This coherent squeezed-like state is defined with the Lie–Trotter product formula and its mathematical expression is different from those of conventional coherent squeezed states. We show that we can obtain this coherent squeezed-like state with a squeezing level 15.9 dB practically by adjusting the physical parameters for our proposed method. Feeding the squeezed light whose average number of photons is given by one or two into a beam splitter and splitting the flow of the squeezed light into a pair of entangled light beams, we estimate their entanglement quantitatively. This paper is a sequel to Azuma (2022 J. Phys. D: Appl. Phys. 55 315106).

DOI
10.1088/1361-6463/acefdc

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Abstract In this paper, we investigate how to generate coherent squeezed-like light using a nonlinear photonic crystal. Because the photonic crystal reduces the group velocity of the incident light, if it is composed of a material with a second-order nonlinear optical susceptibility χ ( 2 ) , the interaction between the nonlinear material and the light passing through it strengthens and the quantum state of the emitted light is largely squeezed. Thus, we can generate a coherent squeezed-like light with a resonating cavity in which the nonlinear photonic crystal is placed. This coherent squeezed-like state is defined with the Lie–Trotter product formula and its mathematical expression is different from those of conventional coherent squeezed states. We show that we can obtain this coherent squeezed-like state with a squeezing level 15.9 dB practically by adjusting the physical parameters for our proposed method. Feeding the squeezed light whose average number of photons is given by one or two into a beam splitter and splitting the flow of the squeezed light into a pair of entangled light beams, we estimate their entanglement quantitatively. This paper is a sequel to Azuma (2022 J. Phys. D: Appl. Phys. 55 315106).
Abstract We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility χ ( 2 ) . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of 4 × 10 − 6 . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Δ ν = 3.11 × 10 8 Hz for the signal light of ν = 3.23 × 10 14 Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.
Abstract We study implementing a heralded single-photon source with second-order nonlinear photonic crystals. Injecting pump and signal light beams into a one-dimensional photonic crystal composed of a material with a large second-order nonlinear optical susceptibility χ ( 2 ) , we can transform the coherent incident signal light into squeezed light. Preparing two squeezed light beams by this method and input them into two ports of a 50-50 beam splitter independently, we can transform them into a two-mode squeezed state. Because those two modes of photons share entanglement, a single photon of the one mode is emitted with a high probability on the condition of the single-photon detection of the other mode as a heralding signal. We evaluate the efficiency and the second-order intensity correlation function g ( 2 ) ( 0 ) for this heralded single-photon source. Moreover, we examine changes in the efficiency and g ( 2 ) ( 0 ) when we assume that the single-photon detector for the heralding signal is imperfect. For a specific concrete example, we consider a case where the nonlinear medium is lithium niobate LiNbO 3 and the frequency of the incident signal light is on the order of 1014 Hz.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
Entangled multi-mode squeezed states of light have a wide variety of applications in quantum information systems, particularly in the generation of non-Gaussian states of light, which are central to continuous-variable quantum computing. Although theoretical approaches exist to model the nonlinear generation of one- and two-mode entangled states of light in ring resonator systems, these approaches are difficult to implement in modeling more complicated many-cavity systems. In this work, we present an efficient and accurate theoretical approach to modeling the generation and propagation of quantum states of light in lossy coupled-cavity systems containing a two- or three-mode nonlinear resonant structure. Our approach is general and computationally viable even in systems with hundreds of modes. We apply our method to the design and modeling of a multimode photonic crystal coupled-cavity system for the generation of entangled squeezed states of light on-chip. The system consists of a three-mode resonant structure coupled to three coupled-resonator optical waveguides (CROWs) in a square lattice silicon photonic crystal slab. The computational speed of the method allows us to efficiently optimize the system such that the signal and idler light in the two output CROWs remains entangled even after propagating tens of cavities down the CROWs.
Quantum states of light, such as fixed photon number (Fock) states, entangled states, and squeezed states, offer important advantages with respect to classical states of light, such as coherent states and thermal states, in different areas: they enable secure communication and distribution of encryption keys, enable realization of sensors with higher sensitivity and resolution, and are considered candidates for quantum computing and simulation applications. To accommodate these applications, suitable methods for generating the quantum states are needed. Today, the quantum states are often produced by a spontaneous nonlinear process in a standard nonlinear material, followed by a series of optical elements necessary for encoding the desired state on the generated photons. In this review, we consider an alternative approach of structuring the nonlinearity of the crystal so that the desired quantum state will be generated directly at the crystal, without the need for additional elements. Our main focus here is on bulk crystals having structured second-order nonlinearity. The rising interest in these nonlinear metamaterials is fueled by advancements in the ability to efficiently simulate and design spontaneous parametric downconversion (SPDC) processes, as well as by new capabilities of structuring the nonlinearity of ferroelectric crystals, either by electric field poling or by laser-induced writing. As a result, nonlinear metamaterials were recently used to directly shape the spatial and spectral correlations of quantum light that is generated in SPDC. The paper covers the theoretical background and the design and fabrication methods of bulk nonlinear metamaterials for generating quantum light, as well as a series of demonstrations of the use of metamaterials in quantum optical applications.