Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity

Abstract

We present a formal theory of single quantum-dot coupling to a planar photonic crystal that supports quasi-degenerate cavity modes, and use this theory to describe, and optimize, entangledphoton-pair generation via the biexciton-exciton cascade. In the generated photon pairs, either both photons are spontaneously emitted from the dot, or one photon is emitted from the biexciton spontaneously and the other is emitted via the leaky-cavity mode. In the strong-coupling regime, the generated photon pairs can be maximally entangled, in qualitative agreement with the simple dressed-state predictions of Johne et al. [Phys. Rev. Lett. vol. 100, 240404 (2008)]. We derive useful and physically-intuitive analytical formulas for the spectrum of the emitted photon pairs in the presence of exciton and biexciton broadening, which is necessary to connect to experiments, and demonstrate the clear failure of using a dressed-state approach. We also present a method for calculating and optimizing the entanglement between the emitted photons, which can account for post-sample spectral filtering. Pronounced entanglement values of greater than 80% are demonstrated using experimentally achievable parameters, even without spectral filtering.

On‐chip single photon sources using planar photonic crystals and single quantum dots

“…A connection to the various experimental and theoretical works appearing in the recent literature has been made. This framework forms the basis for understanding the rich and complex light-matter interactions that can occur in planar PC chips, and can be extended to account for many of the things that we have chosen to leave out, such as coupled QDs, coupled cavities, electron-phonon interactions, input coupling, and entangled photon pair generation [103,104], to name but a few. The on-demand single photon source is an extremely important source for quantum information science and technology.…”

Highly entangled photon pairs generated from the biexciton cascade transition in a quantum-dot–metal-nanoparticle hybrid system

“…In references [27,29,32,33], a four-level QD embedded within an anisotropic photonic crystal is studied as the source of polarized entangled photons by making the intermediate exciton states of the QD degenerate in strong coupling regime. It is widely accepted that achieving a strong coupling regime is often more difficult than achieving a weak coupling regime.…”

“…Several methods have been employed to tune this FSS, including the use of external magnetic fields [34], external electric fields [36], external uniaxial stress [40], and electro-elastic fields [24]. Other approaches include spectral filtering [27], selection of QDs with low FSSs [42], and using a single QD strongly coupled to a planar photonic crystal [29,32,33].…”

“…The radiative biexciton cascade transition in a single semiconductor QD provides a source of entangled photons [24,[30][31][32][33][35][36][37]. A biexciton cascade can be described as a four-level system composed of a biexciton state (|u ), two bright intermediate exciton levels (|x , |y ), and a ground state (|g ) [20].…”

Coupling to a microdisk cavity containing a three-level quantum-dot with two orthogonal modes

“…But an atom or a QD always has more than two energy levels, and it should be necessary for us to consider the more complicated system such as three-or four-level system. Furthermore, entangled photon pairs can be produced through a multi-level quantum state, such as the biexciton decay of a QD strongly coupled to the modes of a photonic crystal [23][24][25]. However, even though QDs are often thought of as artificial atoms, they deviate from the ideal scheme because of the coupling between the exciton states with total angular momentum +1 and −1.…”