Maps determined by rank- $$\varvec{s}$$ s matrices for relatively small $$\varvec{s}$$ s

Xu, Xiaofang; Li, Chen; Zhu, J.Z.

doi:10.1007/s00010-017-0469-8

Cited by 15 publications

(26 citation statements)

References 10 publications

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“…[]):

\begin{matrix} true \\ right \overset{H}{true} (t) = \overset{H}{true} + [{normalΩ}^{*} false(t false) \hat{σ} + Ω false(t false) {\overset{σ}{true}}^{†}] \end{matrix}

where

Ω (t)

is the “driving pulse” given by

\begin{matrix} true \\ right normalΩ (t) = g^{*} (ω_{E}) \int_{- \infty}^{\infty} α (ω) \exp (- i ω t) normald ω \end{matrix}

This driving term is similar to that obtained in a treatment of light–matter interaction in which the optical fields are treated classically. Addition of this driving term to the Hamiltonian allows us to solve a problem in which the loss channel is initially in the vacuum state—such a problem can be numerically analyzed within the master‐equation framework or the scattering matrix framework …”

Section: Fundamentalsmentioning

confidence: 99%

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

et al. 2019

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Sources of non‐classical light are of paramount importance for future applications in quantum science and technology such as quantum communication, quantum computation and simulation, quantum sensing, and quantum metrology. This Review is focused on the fundamentals and recent progress in the generation of single photons, entangled photon pairs, and photonic cluster states using semiconductor quantum dots. Specific fundamentals which are discussed are a detailed quantum description of light, properties of semiconductor quantum dots, and light–matter interactions. This includes a framework for the dynamic modeling of non‐classical light generation and two‐photon interference. Recent progress is discussed in the generation of non‐classical light for off‐chip applications as well as implementations for scalable on‐chip integration.

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“…[]):

\begin{matrix} true \\ right \overset{H}{true} (t) = \overset{H}{true} + [{normalΩ}^{*} false(t false) \hat{σ} + Ω false(t false) {\overset{σ}{true}}^{†}] \end{matrix}

where

Ω (t)

is the “driving pulse” given by

\begin{matrix} true \\ right normalΩ (t) = g^{*} (ω_{E}) \int_{- \infty}^{\infty} α (ω) \exp (- i ω t) normald ω \end{matrix}

Section: Fundamentalsmentioning

confidence: 99%

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

et al. 2019

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“…Note that the frequency domain scattering matrix doesn't have any connected parts [18] i.e. scattering of a K photon wave-packet from the linear optical device conserves the individual input frequencies.…”

Section: B Quantum Scattering Matrix Of the Point-coupling Hamiltonianmentioning

confidence: 99%

“…For a given frequency-independent classical scattering matrix implemented by the linear optical device, we provide a recipe to construct a point-coupling Hamiltonian describing the device. We formally integrate the Heisenberg equations of motion for the point-coupling Hamiltonian, and use the resulting solution to calculate its quantum scattering matrix [17][18][19]. It is shown that an application of the quantum scattering matrix on an incoming quantum state is equivalent to applying the inverse of the classical scattering matrix on the annihilation operators of the optical modes in the incoming quantum state, thereby reproducing the commonly used procedure for analyzing the quantum physics of linear-optical devices.…”

Section: Introductionmentioning

confidence: 99%

Point-coupling Hamiltonian for frequency-independent linear optical devices

et al. 2019

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We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering matrix, and show that an application of the quantum scattering matrix on an input state is equivalent to applying the inverse of classical scattering matrix on the annihilation operators describing the optical modes. We show how to construct the point-coupling Hamiltonian corresponding to a general linear optical device described by a classical scattering matrix, and provide examples of Hamiltonians for some commonly used linear optical devices. Finally, in order to demonstrate the practical utility of the point-coupling Hamiltonian, we use it to rigorously formulate a matrixproduct-state based simulation for time-delayed feedback systems wherein the feedback is provided by a linear optical device described by a scattering matrix as opposed to a hard boundary condition (e.g. a mirror with less than unity reflectivity).

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“…[16] for a modeling framework for systems with multiple inputs and Refs. [17][18][19] for non-linear S-matrix treatments of few-photon transport.) Second, although a general state of a single photon is a function of four quantum numbers, one related to the spectral degree of freedom, two related to the two transverse spatial degrees of freedom, and one related to the polarization or helicity degree of freedom, we will restrict ourselves to the spectral (or, equivalently, the temporal) degree of freedom.…”

Section: Introductionmentioning

confidence: 99%

Quantum networks for single photon detection

Propp

Enk

2019

Phys. Rev. A

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Single photon detection generally consists of several stages: the photon has to interact with one or more charged particles, its excitation energy will be converted into other forms of energy, and amplification to a macroscopic signal must occur, thus leading to a "click." We focus here on the part of the detection process before amplification (which we have studied in a separate publication). We discuss how networks consisting of coupled discrete quantum states and structured continua (e.g. band gaps) provide generic models for that first part of the detection process. The input to the network is a single continuum (a continuum of single-photon states), the output is again a single continuum describing the next irreversible step. The process of a single photon entering the network, its energy propagating through that network and finally exiting into another output continuum of modes can be described by a single dimensionless complex transmission amplitude, T (ω). We discuss how to obtain from T (ω) the photo detection efficiency, how to find sets of parameters that maximize this efficiency, as well as expressions for other input-independent quantities such as the frequencydependent group delay and spectral bandwidth. We then study a variety of networks and discuss how to engineer different transmission functions T (ω) amenable to photo detection.

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Maps determined by rank- $$\varvec{s}$$ s matrices for relatively small $$\varvec{s}$$ s

Cited by 15 publications

References 10 publications

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

Point-coupling Hamiltonian for frequency-independent linear optical devices

Quantum networks for single photon detection

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