Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0911.0657 · Journal of the Optical Society of America B

Quantum model for electro-optical phase modulation

J. Capmany, Carlos R. Fernández‐Pousa

Published Apr 29, 2010• 48 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.27.00a119

Related papers

Quantum Blackbox Model for Electro-Optical Phase Modulation

J. Capmany, Carlos R. Fernández‐Pousa

We present, for the first time, a blackbox model characterizing the quantum optical phase modulation operation in terms of a unitary scattering operator which excludes the unphysical negative frequencies.

National Fiber Optic Engineers Conference (NFOEC)•Jan 1, 2010•0 citations

Quantum Modelling of Electro-Optic Modulators

J. Capmany, Carlos R. Fernández‐Pousa

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.

arXiv:1103.4747•Mar 24, 2011•0 citations

Spectral decomposition of single-tone-driven quantum phase modulation

J. Capmany, Carlos R. Fernández‐Pousa

[EN] Electro-optic phase modulators driven by a single radio-frequency tone ¿ can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of h¿. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F 1, the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F1 is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation. © 2011 IOP Publishing Ltd.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 18, 2011•8 citations

Quantum modelling of electro‐optic modulators

J. Capmany, Carlos R. Fernández‐Pousa

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.

Laser & Photonics Review•Apr 18, 2011•37 citations

Evolution of Quantum States in an Electro-Optic Phase Modulator

Pradeep K Kumar, Anil Prabhakar

We present a quantum mechanical model to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.

IEEE Journal of Quantum Electronics•Dec 17, 2008•22 citations

Performance evaluation of a non-resonant electro-optic phase modulator using quantum interference

Arpan Adak, Ayan Ray

Phase modulation of light plays a key role in modern-day optical communication and processing systems. For this purpose, electro-optic phase modulators are indispensable because of their unique operational flexibility in manipulating the output light signal and providing a large modulation bandwidth. We propose a characterization of the performance of a non-resonant electro-optic phase modulator using what we believe to be a novel quantum-interference-based method. The evaluation is done to study (i) sideband generation, (ii) V π voltage, (iii) modulation parameter, and (iv) capability to introduce controlled phase noise in the system. Electromagnetically induced absorption, a product of constructive quantum interference, is used to study the above-mentioned aspects. These results are compared with those obtained from scanning Fabry–Perot Etalon fringes. In the case of a non-resonant modulator, the efficiency of analysis based on electromagnetically induced absorption is proved to be better than that of Etalon fringe analysis. The result of the noise through the phase modulator in the atom-field system is cross-verified with the resulting heterodyne beat signal obtained between two similar external cavity lasers (free-running, passive stabilization using an extra layer of thermal and vibrational isolation), where one of them is quieter than the other and experiences the introduction of noise through the electro-optic phase modulator.

Journal of the Optical Society of America B•Jul 13, 2026•0 citations
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.
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.
[EN] Electro-optic phase modulators driven by a single radio-frequency tone ¿ can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of h¿. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F 1, the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F1 is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation. © 2011 IOP Publishing Ltd.
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 to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.
Phase modulation of light plays a key role in modern-day optical communication and processing systems. For this purpose, electro-optic phase modulators are indispensable because of their unique operational flexibility in manipulating the output light signal and providing a large modulation bandwidth. We propose a characterization of the performance of a non-resonant electro-optic phase modulator using what we believe to be a novel quantum-interference-based method. The evaluation is done to study (i) sideband generation, (ii) V π voltage, (iii) modulation parameter, and (iv) capability to introduce controlled phase noise in the system. Electromagnetically induced absorption, a product of constructive quantum interference, is used to study the above-mentioned aspects. These results are compared with those obtained from scanning Fabry–Perot Etalon fringes. In the case of a non-resonant modulator, the efficiency of analysis based on electromagnetically induced absorption is proved to be better than that of Etalon fringe analysis. The result of the noise through the phase modulator in the atom-field system is cross-verified with the resulting heterodyne beat signal obtained between two similar external cavity lasers (free-running, passive stabilization using an extra layer of thermal and vibrational isolation), where one of them is quieter than the other and experiences the introduction of noise through the electro-optic phase modulator.