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arXiv:1106.5521 · Physical Review B

Entangled photon pair generation in hybrid superconductor–semiconductor quantum dot devices

Milad Khoshnegar, A. Hamed Majedi

Published Sep 8, 2011• 23 citations
arXivHTMLPDF

Abstract

We investigate the effect of Cooper pair injection in shifting the biexciton energy level of low-symmetry (${C}_{2v}$) quantum dots (QDs) exhibiting nontrivial fine structure splitting. Coupling QDs to the superconducting coherent state forms extra fine structures by intermixing the ground and biexcitonic states where spectroscopic separation of neutral exciton and biexciton can be diminished, yielding a system to be utilized in the time reordering scheme. The separability of exciton and biexciton energy levels is ascribed to the corresponding direct, exchange, and correlation energies calculated here through the configuration interaction method. We demonstrate the possibility of enhancing photon entanglement concurrence via providing an energy coincidence for biexciton-exciton ($XX$ \ensuremath{\rightarrow} $X$) and exciton-ground ($X$ \ensuremath{\rightarrow} 0) emissions within the weak coupling regime.

DOI
10.1103/physrevb.84.104504

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We investigate the effect of Cooper pair injection in shifting the biexciton energy level of low-symmetry (C2v{C}_{2v}C2v​) quantum dots (QDs) exhibiting nontrivial fine structure splitting. Coupling QDs to the superconducting coherent state forms extra fine structures by intermixing the ground and biexcitonic states where spectroscopic separation of neutral exciton and biexciton can be diminished, yielding a system to be utilized in the time reordering scheme. The separability of exciton and biexciton energy levels is ascribed to the corresponding direct, exchange, and correlation energies calculated here through the configuration interaction method. We demonstrate the possibility of enhancing photon entanglement concurrence via providing an energy coincidence for biexciton-exciton (XXXXXX \ensuremath{\rightarrow} XXX) and exciton-ground (XXX \ensuremath{\rightarrow} 0) emissions within the weak coupling regime.
Entanglement resources are key ingredients of future quantum technologies. If they could be efficiently integrated into a semiconductor platform, a new generation of devices could be envisioned, whose quantum-mechanical functionalities are controlled via the mature semiconductor technology. Epitaxial quantum dots (QDs) embedded in diodes would embody such ideal quantum devices, but a fine-structure splitting (FSS) between the bright exciton states lowers dramatically the degree of entanglement of the sources and hampers severely their real exploitation in the foreseen applications. In this work, we overcome this hurdle using strain-tunable optoelectronic devices, where any QD can be tuned for the emission of photon pairs featuring the highest degree of entanglement ever reported for QDs, with concurrence as high as 0.75 ± 0.02. Furthermore, we study the evolution of Bell's parameters as a function of FSS and demonstrate for the first time that filtering-free violation of Bell's inequalities requires the FSS to be smaller than 1 μeV. This upper limit for the FSS also sets the tuning range of exciton energies (∼1 meV) over which our device operates as an energy-tunable source of highly entangled photons. A moderate temporal filtering further increases the concurrence and the tunability of exciton energies up to 0.82 and 2 meV, respectively, though at the expense of 60% reduction of count rate.
Hereby, we study the generation of pairs of polarization-entangled photons at telecom C-band by biexciton-exciton cascade from non-resonantly excited epitaxial InAs/InP quantum dots (QDs). It is realized without external tuning of the fine structure splitting (FSS), which does not exceed 10 μμμeV in as-grown nanostructures, due to their high in-plane symmetry. Excitonic complexes are identified by means of excitation power-dependent and polarization-resolved magneto)microphotoluminescence. Their origin from different carrier configurations confined in the same QD is confirmed by time correlations of emitted photons. Experimental results are supported by 8-band kp calculations, followed by the configuration interaction method to include excitonic effects. This comparison reveals the structure of higher energy states, allowing for the reconstruction of the QD structural parameters. To verify and quantify the entanglement, we perform quantum state tomography and reconstruct the two-photon density matrix. Its diagonalization allows a detailed analysis of the entangled state and reveals an unfavourable interplay between phase accumulation and decoherence, pointing to a clear route for boosting entanglement by using a XX resonant, pulsed excitation scheme and shortening the radiative lifetimes.
The biexciton-exciton cascade in quantum dots (QDs) yields entangled photon pairs, and recent developments in engineering photonic structures around the dot for efficient light extraction and proper control of the fine-structure splitting, has led to significant breakthroughs in achieving an ideal entangled photon source -- exhibiting properties such as high extraction efficiency, low multi-photon emission and high entanglement fidelity. This thesis presents our development in enhancing the performance of entangled photon generation of QDs towards near-unity efficiency and fidelity. We study InAsP quantum dots in photonic nanowires for efficient light extraction and to reveal the effect of a quantum dot with high nuclear spin on the entanglement fidelity. \n \nRevealing the ultimate limit of entanglement in QDs is still a challenge, and it is generally believed that a sample made of atoms possessing high nuclear spins exhibits limited entanglement due to the dephasing caused by spin-spin interactions. Moreover, it is assumed that the fine-structure splitting of QDs degrades the entanglement fidelity, as it introduces a which-path information in the biexciton-exciton cascade. We have performed two-photon state tomography on InAsP QDs in InP nanowires, comprising of nuclear spin 9/2, and have realized that such a source is capable of generating entangled photon pairs with negligible dephasing during the emission lifetime, with a peak concurrence C = 77% and a count-weighted average concurrence 62%. This result was obtained by comparing the outcome of our measurements with a theoretical model that assumes no dephasing, however, takes into account the details of the detection system, i.e., dark-count rates and timing resolution, as well as, specific features of the QD, e.g., emission lifetime, fine-structure splitting, multi-photon emission probability, etc. Proper engineering of tapered nanowires allows for extraction of the emitted photons with high efficiency, which makes it possible to perform a complete two-photon state tomography and monitoring the evolution of the exciton state, as well as, the entanglement fidelity of the photon-pair, during the emission lifetime. This enabled us to reveal the effect of an imperfect detection system, as well as, multi-photon emission in recording low values for entanglement fidelity. Moreover, our calculations show that proper analysis of the time-energy uncertainty relation provides the necessary means to measure a high entanglement fidelity even in the presence of fine-structure splitting; since, a detection system with high timing resolution can overlook the which-path information, as the uncertainty in measuring the energy of the photons will be larger than the fine-structure splitting. Therefore, realizing near-unity entanglement fidelity using QDs is merely a technical challenge, i.e., resonant excitation of the QD, in order to suppress multi-photon emission, and use of a detection system with low timing jitter and dark-count rates. \n \nAs a next step to achieve this goal, we have performed the resonant two-photon excitation scheme for the first time on a QD in a photonic nanowire, which resulted in an enhancement of the performance of our source. We managed to improve the single-photon purity of the source, g^(2)(0), by two orders of magnitude; moreover, analysis of the emission spectrum reveals that this scheme increases the pair-production efficiency to values above 93% for the biexciton-exciton cascade. Taking the efficiency of our experimental setup into consideration, the results indicate an approximately eight-fold enhancement of the pair-extraction efficiency as compared to the quasi-resonant excitation scheme (12.55% vs. 1.6%). Based on these results, two-photon state tomography on our source, under resonant two-photon excitation and performed by a detection system with high timing resolution and low dark-count rates, yields near-unity entanglement fidelity. By considering the enhancement in pair-extraction efficiency that we obtained, QDs in photonic nanowires can surpass the performance of spontaneous parametric down conversion sources in terms of entanglement fidelity and pair-extraction efficiency. \n \nEven though we have shown a finite fine-structure splitting does not degrade the entanglement fidelity in QDs, for various application in quantum information removing the fine-structure splitting is beneficial. Therefore, we have proposed a universal all-optical approach for removing the fine-structure splitting. In this scheme, the energy of the photons are shifted by using a pair of quarter-wave plates and fast-rotating half-wave plates after they have been emitted; and as a result, the energy difference between the two decay paths in the biexciton-exciton cascade is erased. This method is applicable to any QD source and can be easily implemented using the currently available technology; moreover, no further sample processing will be required in order to achieve zero fine-structure splitting.
A scheme for creating biexcitons without undesirable excitons is demonstrated in GaAs quantum dots (QDs) using an optical pumping method. This scheme utilizes resonant two-photon excitation processes for biexcitons with carefully set excitation conditions. In this scheme, biexcitons are directly created from the ground state while suppressing unnecessary exciton creation. Theoretical analysis confirms that our scheme works in actual QDs. Directly created biexcitons will make ideal entangled photons via cascade photoemission processes in a biexciton–exciton system with the reduction in the number of undesirable single photons from excitons that are not related to the cascade processes.
The entanglement between photon pairs generated from the biexciton cascade transition in a semiconductor quantum dot located in the vicinity of a metal nanoparticle is theoretically investigated. In the model scheme, the biexciton-exciton and exciton--ground-state transitions are assumed to be coupled to two principal plasmon modes of orthogonal polarizations. For a broad spectral window, because the horizontal and vertical spectra overlap, the biexciton and exciton photons are degenerate in energy. This allows us to overcome the natural splitting between the intermediate exciton states. Moreover, the degree of entanglement depends on the geometrical parameters of the system, i.e., the radius of the metal nanoparticle and the distance between the quantum dot and the nanoparticle. The results reveal that such a hybrid system profoundly modifies the photon entanglement even in the absence of strong coupling between the emitter and the metal nanosphere.
We study the quantum properties and statistics of photons emitted by a quantum-dot biexciton inside a cavity. In the biexciton-exciton cascade, fine-structure splitting between exciton levels degrades polarization-entanglement for the emitted pair of photons. However, here we show that the polarization-entanglement can be preserved in such a system through simultaneous emission of two degenerate photons into cavity modes tuned to half the biexciton energy. Based on detailed theoretical calculations for realistic quantum-dot and cavity parameters, we quantify the degree of achievable entanglement.