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arXiv:1112.3211 · Physical Review B

Entangled photons from the polariton vacuum in a switchable optical cavity

Adrian Auer, Guido Burkard

Published Jun 21, 2012• 45 citations
arXivHTMLPDF

Abstract

We study theoretically the entanglement of two-photon states in the ground state of the intersubband cavity system, i.e., the so-called polariton vacuum. The system consists of a sequence of doped quantum wells located inside a microcavity and the photons can interact with intersubband excitations inside the quantum wells. Using an explicit solution for the ground state of the system, operated in the ultrastrong-coupling regime, a postselection is introduced, where only certain two-photon states are considered and analyzed for mode entanglement. We find that a fast quench of the coupling creates entangled photons and that the degree of entanglement depends on the absolute values of the in-plane wave vectors of the photons. Maximally entangled states can be generated by choosing the appropriate modes in the postselection.

DOI
10.1103/physrevb.85.235140

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We study theoretically the entanglement of two-photon states in the ground state of the intersubband cavity system, i.e., the so-called polariton vacuum. The system consists of a sequence of doped quantum wells located inside a microcavity and the photons can interact with intersubband excitations inside the quantum wells. Using an explicit solution for the ground state of the system, operated in the ultrastrong-coupling regime, a postselection is introduced, where only certain two-photon states are considered and analyzed for mode entanglement. We find that a fast quench of the coupling creates entangled photons and that the degree of entanglement depends on the absolute values of the in-plane wave vectors of the photons. Maximally entangled states can be generated by choosing the appropriate modes in the postselection.
The ultrastrong coupling between the elementary excitations of matter and microcavity modes is studied in a fully analytical quantum-mechanical theoretical framework. The elementary excitation could be phonons, excitons, plasmons, etc. From the diagonalization of the Hamiltonian, we obtain the ground state of the polariton Hamiltonian. The ground state belongs to the Gaussian class. Using the Gaussian property, we calculate the quantum entanglement in the ground state. We use two different measures for quantum entanglement---entanglement entropy and the logarithmic negativity parameter---and obtain rather simple analytical expressions for the entanglement measures. Our findings show that the amount of quantum entanglement in the ground state is quite significant in the ultrastrong-coupling regime. It can be obtained from the measurement of the polariton frequencies.
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.
We study theoretically a photon-coincidence counting technique aimed at measuring the entanglement between two optical cavities connected by an optical waveguide. Delocalized doubly excited polariton states can be selectively probed by two-photon absorption of an entangled photon pair generated by spontaneous parametric down-conversion with a narrowband pump. Deviations from unity of the second-order correlation function g (2) (τ) of photons emitted from remote cavities reveal intercavity correlations. The coincidence counting signal in the frequency domain reveals the transition frequencies between single-polariton states and between single polaritons and tripolaritons. High-frequency spectral features arise from the counter-rotating terms in the cavity–molecule coupling, rendering them a direct signature for the ultrastrong coupling regime in cavity quantum electrodynamics.
The ground state of an atom interacting with the electromagnetic field in the ultrastrong coupling regime is composed of virtual photons entangled with the atom. We propose a method to promote to real the entire photonic state, while preserving the entanglement with the atom. The process can be reversed, and the entangled state can be restored in the vacuum. We consider a four-level atom, with two of these levels ultrastrongly coupled to a cavity mode. The process is obtained by making use of either an ideal ultrafast pulse or a more realistic multitone $\ensuremath{\pi}$ pulse that drives only the atom. An experimental realization of this proposal will not only enable the investigation of the exotic phenomena of emission of particles from the vacuum, but will also prove that quantum superposition states can be extracted from the vacuum. Moreover, it will allow one to inspect the ground state in the ultrastrong coupling regime, and to generate on-demand entangled states for quantum information processing.
We consider two spin-1/2 fermions inside an optical cavity which supports a single-mode quantized light field. We demonstrate that the atom-light coupling (ALC) gives rise to the two-atom polariton states, where the two atoms are highly entangled with cavity photons. We focus on the case where the cavity light is on resonant with the bare atomic transition. We show that in the absence of interatomic interaction, the polariton is unbound, has finite center-of-mass momentum, and contains no atomic spin-singlet fraction in its ground state. When strong attractive interatomic contact interaction is present, a stable bound polariton state exists when the ALC strength is below a critical value. When the ALC strength exceeds the critical value, a first-order transition is observed and the bound polariton becomes unbound. The first-order transition is characterized by abrupt changes of various quantities associated with the polariton and should be readily detectable.
Theoretical study on entangled photon generation from a quantum dot (QD) embedded in microcavity is briefly reviewed within a strong coupling regime. In this system, entangled photon pairs can be generated through the cascade photon emission via dressed states in the cavity quantum electrodynamics (CQED). Excitation levels of a QD are modeled by a V-type three-level system and four-level system including a biexciton. In contrast to the entangled-photon generation until now, all four Bell states can be generated from an identical cavity system by simply selecting applied-field polarizations and frequencies as characteristic features of the CQED. The CQED effects play a crucial role in providing a high degree of entanglement: (i) spectral fi ltering can be used to extract entangled photons due to the vacuum Rabi splitting and (ii) non-entangled co-polarized photons are strongly suppressed due to the photon blockade effect.