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arXiv:cond-mat/0109223 · Physical review. B, Condensed matter

Biexcitons in coupled quantum dots as a source of entangled photons

Oliver Gywat, Guido Burkard, Daniel Loss

Published May 22, 2002• 83 citations
arXivHTMLPDF

Abstract

We study biexcitonic states in two tunnel-coupled semiconductor quantum dots and show that such systems provide the possibility to produce polarization-entangled photons or spin-entangled electrons that are spatially separated at production. We distinguish between the various spin configurations and calculate the low-energy biexciton spectrum using the Heitler-London approximation as a function of magnetic and electric fields. The oscillator strengths for the biexciton recombination involving the sequential emission of two photons are calculated. The entanglement of the photon polarizations resulting from the spin configuration in the biexciton states is quantified as a function of the photon emission angles.

DOI
10.1103/physrevb.65.205329

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We study biexcitonic states in two tunnel-coupled semiconductor quantum dots and show that such systems provide the possibility to produce polarization-entangled photons or spin-entangled electrons that are spatially separated at production. We distinguish between the various spin configurations and calculate the low-energy biexciton spectrum using the Heitler-London approximation as a function of magnetic and electric fields. The oscillator strengths for the biexciton recombination involving the sequential emission of two photons are calculated. The entanglement of the photon polarizations resulting from the spin configuration in the biexciton states is quantified as a function of the photon emission angles.
Semiconductor quantum dots are promising sources for polarization-entangled photons. As an alternative to the usual cascaded biexciton-exciton emission, direct two-photon emission from the biexciton can be used. With a high-quality optical resonator tuned to half the biexciton energy, a large proportion of the photons can be steered into the two-photon emission channel. In this case the degree of polarization entanglement is inherently insensitive to the exciton fine-structure splitting. In the present work we analyze the biexciton emission with particular emphasis on the influence of coupling of the quantum-dot cavity system to its environment. Especially for a high-quality cavity, the coupling to the surrounding semiconductor material can open up additional phonon-assisted decay channels. Our analysis demonstrates that with the cavity tuned to half the biexciton energy, the potentially detrimental influence of the phonons on the polarization entanglement is strongly suppressed---high degrees of entanglement can still be achieved. We further discuss spectral properties and statistics of the emitted twin photons.
Emitters based on semiconductor quantum dots are promising sources for both single photons and pairs of polarization-entangled photons. Typically, single photons are generated through a photon emission event bringing the electronic system from a single-exciton state back to the ground state. In the case of entangled photons two photons are generated through a cascaded emission from the biexciton to either one of the single-exciton states and then back to the ground state. Alternatively, emission of two photons can also be achieved through a higher-order two-photon process bringing the quantum dot directly from the biexciton state (through a virtual intermediate state) back to the ground state. Here we discuss in particular how this two-photon process can lead to certain conceptual advantages in both the generation of polarization-entangled photon pairs and generation of single photons.
We theoretically model the electronic dynamics of a coupled quantum dot pair in a static electric field. We then investigate the possibility of polarization-entangled photon emission from the radiative cascade of the molecular biexciton state. Through numerical simulations, we analyze the dependence of entanglement fidelity on temperature and electric field, as well as tunnel coupling. We establish a regime of direct-indirect exciton detunings for which coupled quantum dots are superior to single dots for entangled photon generation, yielding near-unit fidelity over a larger range of exchange splittings.
Semiconductor Quantum dots are potentially an attractive source of non-classical light. They can confine bound electron-hole pairs, excitons, in all three spatial dimensions giving them discrete optical emission energies, much like the electronic states in atomic systems. The semiconductor nature of the system allows quantum dots to be integrated into complicated device structures including optical cavities [1] and electrical injection [2]. The radiative exciton emission from a semiconductor quantum dot can provide the simplest form of quantum light, a single photon source [2]. The finite re-excitation time following the radiative decay of an exciton in a quantum dot prevents the dot from emitting more than one photon if excited with a short optical or electronic pulse. In a similar fashion excitation of the biexciton state, consisting of two electrons and holes, in the quantum dot results in the emission of a pair of photons at the energy of the biexciton and exciton transitions. The biexciton state was, in fact, proposed as a possible source of polarisation-entangled photons in 2000 by Benson et al. [3] as it consists of two polarisation-correlated decay paths which could potentially be indistinguishable. The condition of indistinguishability is fundamental to the generation of entangled photons and is, in general, not true of the two decay paths from the biexciton state in a quantum dot; physical anisotropy causes the intermediate exciton states to hybridise and separate in energy providing ‘which-path’ information about the route taken through the biexciton decay. We demonstrate how the splitting between the intermediate exciton states in a single InAs quantum dot can be controlled by growth [4], rapid thermal annealing [5] and the application of an external magnetic field [6]. Each of these three techniques can be used to make the intermediate exciton states degenerate allowing the biexciton decay to produce singe pairs of entangled photons triggered by short laser pulses [7,8]. Entangled photon pair sources are essential for applications such as entanglement based quantum key distribution, and optical quantum computing. For these applications it is important that no more than one entangled photon pair is generated in a cycle, a requirement met by our quantum dot source which is not possible with traditional methods for generating entangled pairs of photons. Entanglement also enables quantum interferometry and metrology, the basis of image resolution beyond that possible with equivalent classical light. Biphoton interferometry using entangled emission from the biexciton decay reveals fringes with half the period of classical light [9], and less that that of the laser. In addition, interferometry suggests that this type of entangled light source is not limited by decoherence, we fine the biphoton is surprising robust against dephasing, in stark contrast to the devastating effect of decoherence upon single photons emitted by similar structures.
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.
We develop a theoretical model to study the intensity–intensity correlation of polarization-entangled photons emitted in a biexciton–exciton cascade. We calculate the degree of correlation and show how polarization correlations are affected by the presence of dephasing and energy-level splitting of the excitonic states. Our theoretical calculations are in agreement with the recent observation of polarization-dependent intensity–intensity correlations from a single semiconductor quantum dot (Stevenson et al 2006 Nature 439 179). Our model can be extended to study polarization-entangled photon emission in coupled quantum dot systems.