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arXiv:1103.4733 · Optics Express

Quantum model for electro-optical amplitude modulation

J. Capmany, Carlos R. Fernández‐Pousa

Published Nov 17, 2010• 13 citations
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Abstract

We present a quantum model for electro-optic amplitude modulation, which is built upon quantum models of the main photonic components that constitute the modulator, that is, the guided-wave beamsplitter and the electro-optic phase modulator and accounts for all the different available modulator structures. General models are developed both for single and dual drive configurations and specific results are obtained for the most common configurations currently employed. Finally, the operation with two-photon input for the control of phase-modulated photons and the important topic of multicarrier modulation are also addressed.

DOI
10.1364/oe.18.025127

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We present a quantum model for electro-optic amplitude modulation, which is built upon quantum models of the main photonic components that constitute the modulator, that is, the guided-wave beamsplitter and the electro-optic phase modulator and accounts for all the different available modulator structures. General models are developed both for single and dual drive configurations and specific results are obtained for the most common configurations currently employed. Finally, the operation with two-photon input for the control of phase-modulated photons and the important topic of multicarrier modulation are also addressed.
Many components that are employed in quantum information and communication systems are well known photonic devices encountered in standard optical fiber communication systems, such as optical beamsplitters, waveguide couplers and junctions, electro-optic modulators and optical fiber links. The use of these photonic devices is becoming increasingly important especially in the context of their possible integration either in a specifically designed system or in an already deployed end-to-end fiber link. Whereas the behavior of these devices is well known under the classical regime, in some cases their operation under quantum conditions is less well understood. This paper reviews the salient features of the quantum scattering theory describing both the operation of the electro-optic phase and amplitude modulators in discrete and continuous-mode formalisms. This subject is timely and of importance in light of the increasing utilization of these devices in a variety of systems, including quantum key distribution and single-photon wavepacket measurement and conformation. In addition, the paper includes a tutorial development of the use of these models in selected but yet important applications, such as single and multi-tone modulation of photons, two-photon interference with phase-modulated light or the description of amplitude modulation as a quantum operation.
Abstract Many components that are employed in quantum information and communication systems are well known photonic devices encountered in standard optical fiber communication systems, such as optical beamsplitters, waveguide couplers and junctions, electro‐optic modulators and optical fiber links. The use of these photonic devices is becoming increasingly important especially in the context of their possible integration either in a specifically designed system or in an already deployed end‐to‐end fiber link. Whereas the behavior of these devices is well known under the classical regime, in some cases their operation under quantum conditions is less well understood. This paper reviews the salient features of the quantum scattering theory describing both the operation of the electro‐optic phase and amplitude modulators in discrete and continuous‐mode formalisms. This subject is timely and of importance in light of the increasing utilization of these devices in a variety of systems, including quantum key distribution and single‐photon wavepacket measurement and conformation. In addition, the paper includes a tutorial development of the use of these models in selected but yet important applications, such as single and multitone modulation of photons, two‐photon interference with phase‐modulated light or the description of amplitude modulation as a quantum operation.
We present a quantum mechanical model of dual parallel Mach Zehnder electro-optic modulators (DPMZMs), derived using the quantum scattering formalism [1,2]. We obtain the complete, unrestricted transformation of single-photon and coherent input states through the DPMZM architecture, including independent radiofrequency drive conditions on each internal modulator, and recover the symmetric push pull operating point as an exact special case. We numerically evaluate the resulting frequency comb structure, quantify the device sensitivity to bias error, modulation-index imbalance, and RF noise, and use the model to design a DP-MZM-based frequency-bin qubit source, reporting its fidelity as a function of these impairments.
We develop a quantum model of a traveling-wave electro-optical phase modulator by considering a parametric interaction of the optical and radiofrequency waves in the modulator medium by means of the electro-optic effect. The model includes a possible dispersion of the modulator medium in the optical domain. In the case of negligible dispersion, we derive a simple analytic expression for the evolution operator of the optical field, which has been proposed previously in the literature on the basis of an analogy to classical field transformation. We study by means of a perturbative approach the influence of small dispersion on the field evolution operator and formulate conditions of negligibility of modulator dispersion. We demonstrate the signature of dispersion in phase modulation: breaking the symmetry of sidebands with respect to the mean photon number. We obtain the law of transformation of a multimode coherent state by a phase modulator, which is important for understanding the structure of signal states in quantum cryptographic schemes utilizing phase modulation of coherent optical beams.
We present a detailed analysis of the quantum description of electro-optical phase modulation. The results define a black-box type model for this device, which may be especially useful in the engineering steps leading to the design of complex quantum information systems incorporating one or more of these devices. By constructing an explicit representation of the phase modulation scattering operator, it is shown that an approach based entirely on its classical description leads to unphysical modes associated to non-positive frequencies. After modifying this operator, phase modulation is described, for the first time to the best of our knowledge, in terms of a unitary scattering operator Ŝ defined over positive-frequency modes. The modifications introduced by Ŝ in the process of sideband generation by phase modulation are shown to be insignificant when the radiation belongs to optical bands, thus being consistent with the classical description. Finally, the model is employed to characterize the important case of multitone radio- frequency modulation of an optical signal.
High-fidelity quantum information processing with cascaded photonic integrated circuits demands precise phase control and minimal optical loss at every stage. Low-loss phase modulators therefore constitute a critical component, directly governing quantum coherence, interference visibility, and operational fidelity. In this perspective, we examine key strategies for achieving low-loss phase modulation in integrated photonic platforms. Recent advances are systematically categorized into thermo-optic, mechanical-optic, magneto-optic, and electro-optic approaches. We discuss the underlying physical mechanisms and performance trade-offs, and the advantages and limitations of each strategy in the context of quantum photonic applications. Finally, we outline future directions and emerging approaches for developing optical modulators tailored for large-scale, programmable quantum photonic systems.