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:1803.04648 · Physical Review A

Particle emission from open quantum systems

Kevin A. Fischer, Rahul Trivedi, Daniil M. Lukin

Published Aug 28, 2018• 18 citations
arXivHTMLPDF

Abstract

In this work, we discuss connections between different theoretical physics communities and their works, all related to systems that act as sources of particles such as photons, phonons, or electrons. Our interest is to understand how a low-dimensional quantum system driven by coherent fields, e.g., a two-level system, a Jaynes-Cummings system, or a photon pair source driven by a laser pulse, emits photons into a waveguide. Of particular relevance to solid-state sources is that we provide a way to include dissipation into the formalism for temporal-mode quantum optics. We will discuss the connections between temporal-mode quantum optics, scattering matrices, quantum stochastic calculus, continuous matrix product states and operators, and very traditional quantum optical concepts such as the Mandel photon counting formula and the Lindblad form of the quantum-optical master equation. We close with an example of how our formalism relates to single-photon sources with dephasing.

DOI
10.1103/physreva.98.023853

Related papers

Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system

Kevin A. Fischer, Rahul Trivedi, Vinay Ramasesh +2 more

We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.

arXiv:1710.02875•Quantum•May 28, 2018•70 citations

Open Quantum Systems, Decoherence, Atom-Field Coupling

Reinhold A. Bertlmann, Nicolai Friis

Abstract Chapter 22 investigates the dynamics of open quantum systems that interact with their environment. We discuss the time-evolution of the joint system in terms of a time-ordered exponential of an integral over the Hamiltonian and determine a similar formulation for a Liouvillian super-operator. Based on these ideas we develop the notion of dynamical maps and apply the Born-Markov approximation to arrive at a dynamical semi-group and general Markovian master equations. We then turn to a specific example of such an equation of motion for the density operator: the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation which captures both dissipative dynamics and decoherence using Lindblad operators. We employ the GKLS equation to model the absorption, and spontaneous as well as stimulated emission of radiation by a two-level atom. We then discuss the Jaynes-Cummings model that describes the interaction of such an atom with a single mode of the electromagnetic field in a cavity

•Sep 7, 2023•0 citations

Quantum interactions with pulses of radiation

Alexander Holm Kiilerich, Klaus Mølmer

This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free-space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave, and acoustic waves.

arXiv:2003.04573•Physical Review A•Aug 26, 2020•51 citations

Quantum emitters

Lukáš Novotný, Bert Hecht

The interaction of light with nanometer-sized structures is at the core of nano-optics. It is obvious that as the particles become smaller and smaller the laws of quantum mechanics will become apparent in their interaction with light. In this limit, continuous scattering and absorption of light will be supplemented or replaced by resonant interactions if the photon energy hits the energy difference of discrete internal (electronic) energy levels. In atoms, molecules and nanoparticles, like semiconductor nanocrystals and other “quantum confined” systems, these resonances are found at optical frequencies. Due to the resonant character, the light–matter interaction can often be approximated by treating the quantum system as an effective two-level system, i.e. by considering only those two (electronic) levels whose difference in energy is close to the interacting photon energy ħ ω 0 . In this chapter we consider single-quantum systems that are fixed in space, either by deposition to a surface or by being embedded into a solid matrix. The material to be covered should familiarize the reader with single-photon emitters and with concepts developed in the field of quantum optics. While various theoretical aspects related to the fields emitted by a quantum system have been discussed in Chapter 8, the current chapter focuses more on the nature of the quantum system itself. We adopt a rather practical perspective since more rigorous accounts can be found elsewhere (see e.g. [1–4]).

Cambridge University Press eBooks•Jun 1, 2006•0 citations

Quantum theory of the emission spectrum from quantum dots coupled to structured photonic reservoirs and acoustic phonons

Kaushik Roy‐Choudhury, Stephen Hughes

Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-$Q$ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.

arXiv:1504.03356•Physical Review B•Nov 4, 2015•58 citations

Quantum control of light and matter fields in the nonlinear regime

Nicolas L. Naumann

In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.

•Jan 1, 2017•0 citations
In this work, we discuss connections between different theoretical physics communities and their works, all related to systems that act as sources of particles such as photons, phonons, or electrons. Our interest is to understand how a low-dimensional quantum system driven by coherent fields, e.g., a two-level system, a Jaynes-Cummings system, or a photon pair source driven by a laser pulse, emits photons into a waveguide. Of particular relevance to solid-state sources is that we provide a way to include dissipation into the formalism for temporal-mode quantum optics. We will discuss the connections between temporal-mode quantum optics, scattering matrices, quantum stochastic calculus, continuous matrix product states and operators, and very traditional quantum optical concepts such as the Mandel photon counting formula and the Lindblad form of the quantum-optical master equation. We close with an example of how our formalism relates to single-photon sources with dephasing.
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.
Abstract Chapter 22 investigates the dynamics of open quantum systems that interact with their environment. We discuss the time-evolution of the joint system in terms of a time-ordered exponential of an integral over the Hamiltonian and determine a similar formulation for a Liouvillian super-operator. Based on these ideas we develop the notion of dynamical maps and apply the Born-Markov approximation to arrive at a dynamical semi-group and general Markovian master equations. We then turn to a specific example of such an equation of motion for the density operator: the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation which captures both dissipative dynamics and decoherence using Lindblad operators. We employ the GKLS equation to model the absorption, and spontaneous as well as stimulated emission of radiation by a two-level atom. We then discuss the Jaynes-Cummings model that describes the interaction of such an atom with a single mode of the electromagnetic field in a cavity
This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free-space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave, and acoustic waves.
The interaction of light with nanometer-sized structures is at the core of nano-optics. It is obvious that as the particles become smaller and smaller the laws of quantum mechanics will become apparent in their interaction with light. In this limit, continuous scattering and absorption of light will be supplemented or replaced by resonant interactions if the photon energy hits the energy difference of discrete internal (electronic) energy levels. In atoms, molecules and nanoparticles, like semiconductor nanocrystals and other “quantum confined” systems, these resonances are found at optical frequencies. Due to the resonant character, the light–matter interaction can often be approximated by treating the quantum system as an effective two-level system, i.e. by considering only those two (electronic) levels whose difference in energy is close to the interacting photon energy ħ ω 0 . In this chapter we consider single-quantum systems that are fixed in space, either by deposition to a surface or by being embedded into a solid matrix. The material to be covered should familiarize the reader with single-photon emitters and with concepts developed in the field of quantum optics. While various theoretical aspects related to the fields emitted by a quantum system have been discussed in Chapter 8, the current chapter focuses more on the nature of the quantum system itself. We adopt a rather practical perspective since more rigorous accounts can be found elsewhere (see e.g. [1–4]).
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.