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arXiv:1010.3318

Auto- and Cross-Correlation-Functions as entanglement quantifiers in semiconductor microcavities

Rubén Darío Guerrero

Published Oct 16, 2010• 0 citations
arXivHTMLPDF

Abstract

The dynamics of the exciton-photon entanglement, in a semiconductor microcavity is analyzed. Finding a closed analytical expression for the time evolution of the concurrence. Using as model two coupled, quantum oscillators with detuning between them. Supposing that the system is at a temperature closer to zero. And that the quantum state of the system, remains in the one excitation sector of the total Hilbert space. The former theoretical setup, describes the excitons coupled to the photons in the microcavity accurately, for a system with ultra low density of excitons. We remark in first place, that our closed expression for the concurrence dynamics. Enable us to establish a good analytical criterion, to determine the coupling dynamical regime, in which the system is. Even more, we show that our criterion, is in good agreement with typically accepted, experimental signatures for strong, and wake coupling regimes. Finally we present theoretical evidence, suggesting that the entanglement between the exciton and the photon. Can be measured in experiments, vía the cross correlation contribution, to the time resolved spectra of the system.

DOI
10.48550/arxiv.1010.3318

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The dynamics of the exciton-photon entanglement, in a semiconductor microcavity is analyzed. Finding a closed analytical expression for the time evolution of the concurrence. Using as model two coupled, quantum oscillators with detuning between them. Supposing that the system is at a temperature closer to zero. And that the quantum state of the system, remains in the one excitation sector of the total Hilbert space. The former theoretical setup, describes the excitons coupled to the photons in the microcavity accurately, for a system with ultra low density of excitons. We remark in first place, that our closed expression for the concurrence dynamics. Enable us to establish a good analytical criterion, to determine the coupling dynamical regime, in which the system is. Even more, we show that our criterion, is in good agreement with typically accepted, experimental signatures for strong, and wake coupling regimes. Finally we present theoretical evidence, suggesting that the entanglement between the exciton and the photon. Can be measured in experiments, vía the cross correlation contribution, to the time resolved spectra of the system.
Semiconductor microcavities have great potential for quantum information science, quantum optics, and quantum sensing. Researchers designing devices based on these microcavities could benefit from having accurate figures of merit to guide their design and enhance the entanglement latency and strength of their devices. This article presents a closed formula for computing the exciton-photon concurrence in semiconductor microcavities. The formula is tailored for the ultralow density limit of both excitons and photons, allowing a better understanding of the entanglement properties in this regime. The closed formula allows for accurate and easy quantification of the exciton-photon coupling strength in terms of the parameters of the system like the couplings, frequencies, and linewidths, which has applications in quantum optics and quantum information science. The presented formulas can be used in rational microcavity design for various applications, such as single-photon sources, quantum light sources, and optoelectronic devices. This contributes to the systematic design and control of entanglement properties of quantum devices tailored for specific tasks in quantum information science, quantum optics, and quantum sensing. In summary, this work represents a valuable contribution to both practical applications and fundamental research in the fields of nanostructures, quantum optics, and quantum information science.
While, theoretically, the degree of entanglement of a two-qubit state can be quantified by the concurrence, the experimental determination of a two-qubit state, such as via quantum state tomography of the two-photon state generated by the biexciton cascade in a quantum dot, typically involves the summation of many data points corresponding to a time integration. In the prevalent literature on the biexciton cascade in quantum dots, it is therefore common to define the concurrence in terms of single- or double-time-integrated two-time correlation functions. Here, we compare the behavior of the concurrence according to the different definitions found in the literature and study the relation between the time-integrated concurrences and the actual degree of entanglement of the two-photon states generated by the biexciton cascade in a quantum dot embedded in a microcavity. We focus mainly on the often-discussed situation of a dot with finite biexciton binding energy in a cavity tuned to the two-photon resonance. Analytic and numerical calculations reveal that in this case the single-time-integrated concurrence indeed agrees well with the typical value of the concurrence according to its original definition, even when the interaction between the quantum dot and longitudinal acoustic phonons is taken into account. However, the double-time-integrated concurrence shows completely different trends with respect to changes in the exciton fine structure splitting or the cavity loss rate and should not be interpreted as a measure for the degree of entanglement.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.
The quantum features of the temporal photon statistics of an exciton–cavity coupled system in a quantum-well semiconductor microcavity are investigated analytically. Under the secular approximation, if the nonlinear interactions, i.e. the exciton–exciton coupling and the phase-space filling, are much weaker than the exciton–photon interaction, the evolution of the Fano factor shows that the distribution of the photon numbers exhibits the feature of collapses–revivals (CRs), and the relevant revival time may be adjusted by several factors such as the total particle number, the detuning, and the nonlinear coupling strengths, etc. Especially, the ideal maximum antibunching with the minimum value 0 of the Fano factor occurs periodically for such a situation, with the dissipation of exciton–polariton being ignored.
The quantum entanglement between two excitons in two-dimensional materials, embedded in an optical microcavity, was investigated. The energy eigenstates of a Jaynes-Cummings like Hamiltonian for two qubits coupled to a single cavity mode have been calculated. The quantum entanglement between such states was estimated by calculating the concurrence between two qubits in each of these eigenstates. According to the results of our calculations, if the system is allowed to decay only through the emission of cavity photons at low temperatures, then there is a maximally entangled eigenstate, protected from decay. We demonstrated that the existence of such a state results in the counterintuitive conclusion that, for some initial states of the system, the fact that the cavity is leaky can actually lead to an increase in the average concurrence on the timescales of the average photonic lifetime. By briefly analyzing the three-qubit model, we have demonstrated that the probability for the entanglement to be preserved is enhanced when the number of qubits is increased. In addition, we calculated the time evolution of the concurrence between a pair of excitons in a strained graphene monolayer.
Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.