Comparison of different concurrences characterizing photon pairs generated in the biexciton cascade in quantum dots coupled to microcavities

Abstract

We compare three different notions of concurrence to measure the polarization entanglement of two-photon states generated by the biexciton cascade in a quantum dot embedded in a microcavity. The focus of the paper lies on the often-discussed situation of a dot with finite biexciton binding energy in a cavity tuned to the two-photon resonance. Apart from the time-dependent concurrence, which can be assigned to the two-photon density matrix at any point in time, we study single-and double-time integrated concurrences commonly used in the literature that are based on different quantum state reconstruction schemes. In terms of the photons detected in coincidence measurements, we argue that the single-time integrated concurrence can be thought of as the concurrence of photons simultaneously emitted from the cavity without resolving the common emission time, while the more widely studied double-time integrated concurrence refers to photons that are neither filtered with respect to the emission time of the first photon nor with respect to the delay time between the two emitted photons. Analytic and numerical calculations reveal that the single-time integrated concurrence indeed agrees well with the typical value of the time-dependent concurrence at long times, even when the interaction between the quantum dot and longitudinal acoustic phonons is accounted for. Thus, the more easily measurable single-time integrated concurrence gives access to the physical information represented by the time-dependent concurrence. However, the doubletime integrated concurrence shows a different behavior with respect to changes in the exciton fine structure splitting and even displays a completely different trend when the ratio between the cavity loss rate and the fine structure splitting is varied while keeping their product constant. This implies the non-equivalence of the physical information contained in the time-dependent and single-time integrated concurrence on the one hand and the double-time integrated concurrence on the other hand.arXiv:1712.02584v3 [cond-mat.mes-hall] 9 May 2018

Phonon-Induced Enhancement of Photon Entanglement in Quantum Dot-Cavity Systems

“…In particular, phonons are known to provide a major source of decoherence [26][27][28][29][30][31][32][33][34][35], which led to the expectation that phonons should always degrade the entanglement. Indeed, recent simulations [24,36,37] are in line with this expectation.…”

“…This is realized, e.g., in the limit of weak biexciton binding and finite exciton or cavity mode splitting. In both cases, the phonon-induced enhancement is found in a finite range of binding energies and couplings g. Our studies are based on the Hamiltonian [24,37]:…”

Different Types of Photon Entanglement from a Constantly Driven Quantum Emitter Inside a Cavity

“…Experiments and theoretical studies in semiconductor quantum dots demonstrated the possibility to generate ΦBS entanglement. [ 3,16,29–50 ]…”

Distinctive characteristics of carrier-phonon interactions in optically driven semiconductor quantum dots

“…Even for degenerate excitons and cavity modes, multi-LOphonon coupling of the QD to the electronic continuum of wetting layer states can strongly reduce the entanglement for temperatures above 80 K [268]. Under fully symmetric conditions LA phonon-induced pure dephasing has been found to have no impact on the degree of polarization entanglement [269,270] since it affects the two competing pathways in exactly the same way. Indeed, current experiments come close to preparing maximally entangled states either by selecting QDs which naturally have a sufficiently small fine-structure splitting [263,266], by tuning the splitting with external fields [262,271,272], or by applying strain [273].…”