Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model

Abstract

We theoretically study electro-optic light modulation based on a quantum model where the linear electrooptic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. In contrast to the limiting case of infinitely large number of interacting modes, when the number of interacting modes is finite, the sideband intensities reveal strongly nonmonotonic behavior supplemented with asymmetry of the intensity distribution provided the pumped mode is not central. We also analyze different regimes of two-modulator transmission and establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field.

Generation of frequency sidebands on single photons with indistinguishability from quantum dots

“…In this Rapid Communication, we build on the work above and use single photons from an isolated InGaAs quantum dot to show agreement with the quantum analysis [19] when an electro-optic phase modulator is used to produced frequency sidebands centered around the emission frequency of the dot. A HOM interferometer is used to demonstrate preservation of quantum coherence in the resulting quantum coherent superposition state.…”

“…The work by Kolchin et al [20] lays an experimental foundation for the pulse shaping at a single-photon level and has motivated several works on the topic [21][22][23][24][25]. The timeliness for a demonstration is highlighted by the recent publication of papers that use a phase modulator as a quantum optics device that preserves quantum coherence [26][27][28][29][30].In this Rapid Communication, we build on the work above and use single photons from an isolated InGaAs quantum dot to show agreement with the quantum analysis [19] when an electro-optic phase modulator is used to produced frequency sidebands centered around the emission frequency of the dot. A HOM interferometer is used to demonstrate preservation of quantum coherence in the resulting quantum coherent superposition state.…”

“…The state vector of a single photon becomes modified with additional frequency modes that were previously unoccupied. The new frequency components are separated by the harmonics of the microwave field with amplitudes determined by the microwave field modes coupling with the optical field [19]. For a monochromatic input field (|ψ in = |1 ω 0 ) of the single photon centered at ω 0 , at the limit that a large number of microwave modes are coupled with the optical field, the output state can be expanded as an infinite sum of the Bessel coefficients of the first kind [19,47],…”

Transformations properties of quantum optical signals in phase modulator

“…There are some difficulties with unitarity which appears form straightforward generalization of existing classical model of electro-optical phase modulation process [3]. In [4] we suggest an algebraic model of EOPM based of effective Hamiltonian approach describing multimode quantum parametric process including arbitrary, but finite number of interacting modes. From that we obtain transformation of each frequency mode operator ( ) following from temporal evolution of signal inside phase modulator [4]:…”

“…In [4] we suggest an algebraic model of EOPM based of effective Hamiltonian approach describing multimode quantum parametric process including arbitrary, but finite number of interacting modes. From that we obtain transformation of each frequency mode operator ( ) following from temporal evolution of signal inside phase modulator [4]:…”