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arXiv:2008.10234 · Advanced Quantum Technologies

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

Tim Seidelmann, M. Cosacchi, Moritz Cygorek, Doris E. Reiter, Alexei Vagov, V. M. Axt

Published Dec 14, 2020• 8 citations
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Abstract

Abstract Bell states are the most prominent maximally entangled photon states. In a typical four‐level emitter, like a semiconductor quantum dot, the photon states exhibit only one type of Bell state entanglement. By adding an external driving to the emitter system, also other types of Bell state entanglement are reachable without changing the polarization basis. In this work, it is shown under which conditions the different types of entanglement occur and analytical equations are given to explain these findings. Furthermore, special points are identified, where the concurrence, being a measure for the degree of entanglement, drops to zero, while the coherences between the two‐photon states stay strong. Results of this work pave the way to achieve a controlled manipulation of the entanglement type in practical devices.

DOI
10.1002/qute.202000108

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Abstract Bell states are the most prominent maximally entangled photon states. In a typical four‐level emitter, like a semiconductor quantum dot, the photon states exhibit only one type of Bell state entanglement. By adding an external driving to the emitter system, also other types of Bell state entanglement are reachable without changing the polarization basis. In this work, it is shown under which conditions the different types of entanglement occur and analytical equations are given to explain these findings. Furthermore, special points are identified, where the concurrence, being a measure for the degree of entanglement, drops to zero, while the coherences between the two‐photon states stay strong. Results of this work pave the way to achieve a controlled manipulation of the entanglement type in practical devices.
The cascaded decay in a four-level quantum emitter is a well-established mechanism to generate polarization-entangled photon pairs, the building blocks of many applications in quantum technologies. The four most prominent maximally entangled photon pair states are the Bell states. In a typical experiment based on an undriven emitter, only one type of Bell state entanglement can be observed in a given polarization basis. Other types of Bell state entanglement in the same basis can be created by continuously driving the system by an external laser. In this work, we propose a protocol for time-dependent entanglement switching in a four-level quantum emitter–cavity system that can be operated by changing the external driving strength. By selecting different two-photon resonances between the laser-dressed states, we can actively switch back and forth between the different types of Bell state entanglement in the same basis as well as between entangled and nonentangled photon pairs. This remarkable feature demonstrates the possibility to achieve a controlled, time-dependent manipulation of the entanglement type that could be used in many innovative applications.
Entangled photon pairs are essential for many applications in quantum technologies. Recent theoretical studies demonstrated that different types of entangled Bell states can be created in a constantly driven four-level quantum emitter-cavity system. Unlike other candidates for the realization of the four-level emitter, semiconductor quantum dots unavoidably interact with their environment, resulting in carrier-phonon interactions. Surprisingly, phonons change the entanglement of emitted photon pairs in a qualitative way, already at low temperatures on the order of 4 K. While one type of Bell state can still be generated using small driving strengths, the other type is suppressed due to phonon interactions in strongly confined quantum dots. The degree of entanglement decreases with rising temperature and driving strength until it vanishes at a certain parameter value. Because it remains zero afterward, we encounter a phonon-induced transition between entangled and nonentangled photon emission that resembles a phase transition. The transition occurs at temperatures below 30 K and, independent of the driving strength, the concurrence as a function of the reduced temperature is found to obey a power law with exponent one near the transition point.
We introduce a new entangled state, which is composed of two photon-added coherent states. We discuss the entanglement of this state by using several sufficient entanglement criteria, such as higher-order entanglement criterion, EPR criterion, SU(1,1) algebra and Cauchy–Schwarz inequality. These criteria reflect some entanglement effects of this new state, but fail to find the degree of entanglement directly. Thus, we use the covariance to measure the entanglement in this state. Our findings show that the degree of entanglement decreases with the increasing of photon-number and the amplitude of the coherent states. One interesting result is that the new entangled state becomes a maximally entangled state when the photon-added number is 1 and the amplitude of the coherent states is zero, which is just one of the four Bell states.
The generation of entanglement between two identical, interacting quantum dots---initially in ground states---by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside the cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.
We theoretically investigate polarization-entangled-photon generation by using a quantum dot embedded in a microcavity. In the absence of a biexciton, two of the four Bell states can be generated by applying cross-circularly polarized laser fields because of a cavity quantum electrodynamics effect [Ajiki et al., New J. Phys. 11, 033033 (2009)]. In the presence of the biexciton state, the generation of these Bell states can be forbidden under specific conditions. Furthermore, another type of Bell state can be generated by applying cross-circularly polarized fields. Our results indicate that one can generate three different types of Bell-state photon pairs just by changing the frequencies of the applied fields.
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of on-demand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic fine-structure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a two-photon resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser pulse itself. Hence, in the setting explored here, the excitation process limits the achievable concurrence for entangled photons generated in an optically excited four-level quantum emitter.