Phonon effects in quantum dot single-photon sources

Abstract

Semiconductor quantum dots are inevitably coupled to the vibrational modes of their host lattice. This interaction reduces the efficiency and the indistinguishability of singlephotons emitted from semiconductor quantum dots. While the adverse effects of phonons can be significantly reduced by embedding the quantum dot in a photonic cavity, phonon-induced signatures in the emitted photons cannot be completely suppressed and constitute a fundamental limit to the ultimate performance of single-photon sources based on quantum dots. In this paper, we present a self-consistent theoretical description of phonon effects in such sources and describe their influence on the figures of merit. IntroductionSources of single indistinguishable photons are key components in optical quantum information processing [1], and deterministic single-photon sources based on self-assembled semiconductor quantum dots (QDs) have developed significantly over the past few years. QDs can be grown with excellent optical properties, and advances in fabrication of photonic nanostructures have led to demonstrations of bright and coherent single-photon sources [2][3][4][5]. However, the inevitable coupling of the QD to the vibrational phonon modes of the host lattice constitutes a significant challenge [6], which will only be increasingly important as the performance of the sources is pushed from the current state-of-the-art towards the high level necessary for realising large-scale optical quantum computation.There are several figures of merit that characterise the performance of a single photon source. Naturally, the photon number statistics of the emitted light is important. The Hanbury Brown and Twiss second-order correlation function, g (2) (τ), quantifies the probability of simultaneously detecting two photons when evaluated at τ = 0 [8]. Multiphoton components in the emitted light leads to a non-zero value of g (2) (0), which can stem from the excitation process [9][10][11]. Similarly, the efficiency of the source is the probability of sending a single photon into the detection channel when the source is triggered [7]. Another important feature, which characterises the coherence properties of the source, is the indistinguishability of the emitted photons, which is a measure of the degree to which two photons can interfere. The indistinguishability is measured by sending the two photons into the two input ports of a beamsplitter. If the two photons are completely indistinguishable, the Hong-Ou-Mandel effect results in the photons leaving the beamsplitter in the same output port [12]. This effect is a fundamental necessity for linear quantum computing schemes, forming the basis for two-photon gates [13]. Alternatively, the quantum dot can be operated by exciting a biexciton, thereby emitting a polarisation-entangled photon pair [4,14,15]. In this scenario, the entanglement fidelity of the emitted photon pair constitutes an additional figure of merit of the source. Suppressing phonon-assisted photon emission in these pair-sources requires indivi...

Optical signatures of electron-phonon decoupling due to strong light-matter interactions

“…where n B (ν) = [e −ν/(k B T ) − 1] −1 is the Bose distribution and μ together with the overall electron-phonon coupling α quantifies the strength of the virtual scattering process. For a typical GaAs quantum dot, we find μ = 0.023 ps 2 [47], which together with α = 0.025 ps 2 and ξ = 2.2 ps −1 correspond to γ * (4 K) = 6.7×10 −6 ps −1 and γ * (150 K) = 0.08 ps −1 .…”

Micropillar single-photon source design for simultaneous near-unity efficiency and indistinguishability

“…While our simulations identify geometrical parameters leading to predicted performance significantly beyond state-of-the-art, the exact performance obtained experimentally will depend on unknown experimental parameters. Even though the exciton-phonon coupling strength α and the cutoff frequency ν c are QD-dependent, previous investigations have revealed that the optimum cavity linewidth for maximum indistinguishability is independent of the QD size in the 10-40 nm range 41 . Futhermore, the magnitude of the Markovian noise term as well as the unavoidable fabrication imperfections influence the performance.…”

“…with α being exciton-phonon coupling strength and ν c = √ 2v c /L denoting the cutoff frequency 40 , where v c and L are the speed of sound and the size of the QD, respectively. Here, the exciton-phonon coupling strength α depends on the QD material and on the cutoff frequency ν c , which itself is related to the size of the QD 41 . The Franck-Condon factor, B 2 , can be written compactly in terms of this function as B 2 = e −ϕ(0) .…”

Non-Markovian perturbation theories for phonon effects in strong-coupling cavity quantum electrodynamics

“…The model we consider in this paper consists of a localized exciton state |X that couples with a cavity mode with annihilation (creation) operator a (a † ) through the Jaynes-Cummings model [32,43]:…”

“…The polariton-polaron approach is found to be the most accurate method in the strong-coupling regime, where phonons manifest themselves as sidebands on the polariton peaks [14,15]. The variational approach is, on the other hand, found to be precise in the Purcell regime, where the zero-phonon line acquires a phonon sideband [2,43].…”