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Scattering of coherent pulses on a two-level system

Joel Lindkvist, Göran Johansson

Published Jan 15, 2014• 1 citation
OpenAlex

Abstract

In this work, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line. Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate transmission lines, however, output fields with one-photon probabilities close to unity can be reached.

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Scattering of coherent pulses on a two-level system-single-photon generation

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In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached.

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In this work, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line. Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate transmission lines, however, output fields with one-photon probabilities close to unity can be reached.
In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached.
In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached.
In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached.
Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
In a preceding paper we introduced a formalism to study the scattering of low-intensity fields from a system of multilevel emitters embedded in a three-dimensional (3D3\mathrm{D}3D) dielectric medium. Here we show how this photon-scattering relation can be used to analyze the scattering of single photons and weak coherent states from any generic multilevel quantum emitter coupled to a one-dimensional (1D1\mathrm{D}1D) waveguide. The reduction of the photon-scattering relation to 1D1\mathrm{D}1D waveguides provides a direct solution of the scattering problem involving low-intensity fields in the waveguide QED regime. To show how our formalism works, we consider examples of multilevel emitters and evaluate the transmitted and reflected field amplitude. Furthermore, we extend our study to include the dynamical response of the emitters for scattering of a weak coherent photon pulse. As our photon-scattering relation is based on the Heisenberg picture, it is quite useful for problems involving photodetection in the waveguide architecture. We show this by considering a specific problem of state generation by photodetection in a multilevel emitter, where our formalism exhibits its full potential. Since the considered emitters are generic, the 1D1\mathrm{D}1D results apply to a plethora of physical systems such as atoms, ions, quantum dots, superconducting qubits, and nitrogen-vacancy centers coupled to a 1D1\mathrm{D}1D waveguide or transmission line.
We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multimode transmission line coupled to a two-level emitter. Using a recently developed scattering approach, we discuss transmission properties, the power spectrum, the full counting statistics, and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe the time evolution of the power spectrum and observe deviations from the Poissonian statistics for reflected and transmitted fields. In particular, the statistics of reflected photons can change from sub-Poissonian to super-Poissonian for increasing values of the detuning, while the statistics of transmitted photons is strictly super-Poissonian in all parametric regimes. We study the entanglement entropy of some spatial part of the scattered pulse and observe that it obeys the area laws and that it is bounded by the maximal entropy of the effective four-level system.