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Two-photon purification of quantum light emission via quantum feedback

Leon Droenner, Nicolas L. Naumann, Andreas Knorr, Alexander Carmele

Published Jan 10, 2018• 0 citations
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Abstract

A single two-level system acts as a single photon source under a $\pi$-pulse excitation. Increasing the pulse area such that the pulse induces a full Rabi-oscillation of the two-level system, a two-photon emission process becomes more probable. We propose a quantum feedback protocol to either choose preferable single or two-photon emission at a $2\pi$-pulse excitation. By simulating the feedback reservoir as a matrix-product state within the quantum stochastic Schr\odinger picture and by going beyond the common Euler-like expansion, we are able to efficiently deal with light emission in a non-Markovian environment under external time-dependent excitation. Our findings propose quantum interference induced by quantum feedback as an additional control parameter to purify the light emission statistics on demand.

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A single two-level system acts as a single photon source under a π\piπ-pulse excitation. Increasing the pulse area such that the pulse induces a full Rabi-oscillation of the two-level system, a two-photon emission process becomes more probable. We propose a quantum feedback protocol to either choose preferable single or two-photon emission at a 2π2\pi2π-pulse excitation. By simulating the feedback reservoir as a matrix-product state within the quantum stochastic Schr\odinger picture and by going beyond the common Euler-like expansion, we are able to efficiently deal with light emission in a non-Markovian environment under external time-dependent excitation. Our findings propose quantum interference induced by quantum feedback as an additional control parameter to purify the light emission statistics on demand.
Due to their excellent optical properties, quantum dots are promising for applications in photonic quantum technologies. For on-demand single-photon generation, a two-level system given by an excitonic transition is typically excited with a resonant laser pulse of area π. This prepares the two-level system in its excited state from where it spontaneously emits a single photon. However, emission that occurs already during the presence of the laser pulse allows for re-excitation and, thus, multi-photon emission which limits the single-photon purity [1]. In contrast, when exciting the system with a pulse of area 2π, the system is expected to be returned to the ground state. However, in this case emission during the presence of the pulse is most likely to occur when the system is in its excited state – exactly after an area of π has been absorbed. This restarts the Rabi oscillation with a pulse area of π remaining in the pulse which leads to re-excitation with near-unity probability and the emission of a second photon within the excited state lifetime [2,3]. Finally, we present the generation of single photons with ultra-low multi-photon probability [4]. Using two-photon excitation of the bi-exciton suppresses re-excitation and improves the single photon purity by several orders of magnitude for short pulses. [1] K. A. Fischer, et al., New J. Phys. 18, 113053 (2016) [2] K. A. Fischer, et al., Nature Physics 13, 649-654 (2017) [3] K. A. Fischer, et al., Quantum Sci. Technol. 3, 014006 (2017) [4] L. Hanschke et al., arxiv: 1801.01672 (2018)
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multiphoton pulses can yield a significantly higher steady-state excitation than possible with an initially excited emitter since the stimulated emission process can enhance the trapping probability in comparison to the spontaneous decay of an initially excited emitter.
We numerically show that time-delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows us to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As an exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased for a given set of parameters in orders of magnitude due to intrinsically and externally controllable quantum interferences. Our modeling is based on a fully non-Markovian quantum simulation of a structured photon continuum. We show that an approximative method in the Schr\"odinger picture allows a very good estimate for quantum feedback induced features for low pump rates.
The Area Theorem states that when a short optical pulse drives a quantum two-level system, it undergoes Rabi oscillations in the probability of scattering a single photon. In this work, we investigate the breakdown of the Area Theorem as both the pulse length becomes non-negligible and for certain pulse areas. Using simple quantum trajectories, we provide an analytic approximation to the photon emission dynamics of a two-level system. Our model provides an intuitive way to understand re-excitation, which elucidates the mechanism behind the two-photon emission events that can spoil single-photon emission. We experimentally measure the emission statistics from a semiconductor quantum dot, acting as a two-level system, and show good agreement with our simple model for short pulses. Additionally, the model clearly explains our recent results [K. Fischer and L. Hanschke, et al., Nature Physics (2017)] showing dominant two-photon emission from a two-level system for pulses with interaction areas equal to an even multiple of π\piπ.
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the formation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses. In the latter case, we find that for certain feedback delay times, multi-photon pulses yield a significantly higher steady-state excitation than possible with an initially excited emitter. In the system we consider, we find an increase of around 90 percent. Thus, the quantum optical initialization is found to be more efficient due to the self-consistent inclusion of emerging quantum noise. Furthermore, we propose a recursive Heisenberg ansatz which shows good qualitative agreement with the numerically expensive matrix product state method and requires only numerical resources growing quadratically with the number of excitations.
Summary form only given. On-demand single-photon sources that produce a single photon as a response to a deterministic input are widely regarded as critical light sources for quantum key distribution, quantum repeaters, and quantum information science generally [1]. The wavepackets from such a source must have low probability to contain more than one photon, exist in a pure state so they may interfere with one another, and have a spatio-temporal profile that is appropriate for their application [2]. A very popular source for generating high quality single-photon wavepackets is the quantum two-level system, an artificial atom with one ground and one excited state, often implemented using solid-state quantum dots embedded within microcavities [3]. The two-level system is excited with a short resonant pulse of width τFWHM that prepares the system in its excited state, called a π-pulse, where it subsequently decays and emits a single photon with almost unity probability. Because the typical pulse lengths are orders of magnitude shorter than the lifetime of the system, it is often not appreciated that there is finite chance for an ideal two-level system to emit more than one photon at a time.