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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Entangled Photon Pairs Generated from Atomic Three-Level Systems and their Cross Correlation Functions

Kwang Jun Ahn

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Photon pairs generated from electronic transitions in atomic three-level systems are now considered as a highly promising quantum state for constructing qubit, because of easy on-demand generation and low photon-photon interaction [1]. While polarization-entangled biphotonic states have been successfully demonstrated by using diamond-shaped four level systems with degenerated intermediates states in atoms and quantum dots and verified through the violation of Bell inequality [2,3], quantifying spectrally entangled photon pairs in experiments is still hardly available even with state-of-art techniques. In this theoretical study, we investigated the possibility of the cross correlation function of two photons as an observable for verifying the entanglement. To calculate the cross photon density-density correlation function and the degree of entanglement, Heisenberg's quantum kinetic equations of motion for single electron interacting with photons and two coherent pump fields are derived within the framework of density matrix formalism. In figure 1 (a), the energy configuration of a three-level light emitter is depicted with specially focused observables such as photon number densities (Ck†Ck) and (Cq†Cq) and their normalized cross correlation function g12(2)(t) = (ck†cq†cqck)/(ck†ck)(cq†cq). We compared (2) the temporal behavior of g(2)12(t) and the entanglement criterion D(t) introduced by Duan et al. [4] and find peculiar similarities between them for coherently generated photon pairs, as presented in figure (b).

DOI
10.1109/cleoe-eqec.2019.8872396

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We theoretically investigate temporal dynamics of the second order cross correlation function at zero delay time ( G 12 ( 2 ) ( t ) ) and spectral entanglement of two photons emitted from an atomic three-level cascade. In Heisenberg’s picture, a closed set of quantum kinetic equations of motion for G 12 ( 2 ) ( t ) is derived within density matrix formalism with cluster expansion rule. G 12 ( 2 ) ( t ) shows qualitatively distinctive features depending on the spectral entanglement of two photons. Although incoherent photon pairs generated from spontaneous radiation of the excited electron are not entangled, their correlation and anti-correlation properties can be found in G 12 ( 2 ) ( t ) depending on the radiative decay rates. In the coherent excitation regime where the light emitter is located in a high Q-cavity, and its atomic polarizations are predominantly initialized, spectral entanglement between two coherent photons is established. We show that G 12 ( 2 ) ( t ) is well fitted by the entanglement criterion by Duan-Giedke-Cirac-Zoller and explain the close relationship between them by means of the optically forbidden transition in the three-level cascade.
Every quantum system subjected to measurements is an open quantum system. The cavity QED system is elegant in that it probes the interaction between two quantum systems, the atom and the field, while its loss mechanisms are well understood and can be externally monitored. The study of cross-correlations in cavity QED is important for understanding how entanglement evolves in open quantum systems. As quantum information science grows we need to learn more about entanglement and how it can be quantified and measured. Correlation functions have been used to compare an electromagnetic field (intensity) of one mode with the electromagnetic field (intensity) of the same mode at a later time or different spatial location. In quantum optics, correlation functions have been calculated and measured to probe the nonclassical field that results from the interaction of a single mode of the electromagnetic field and an ensemble of two-level atoms (the canonical cavity QED system). This field can exhibit antibunching, squeezing, and can violate inequalities required for a classical field. Entanglement in the steady state of a cavity QED system cannot be measured directly with traditional correlation functions (Hanbury-Brown and Twiss type experiments). Cross-correlations, however, interrogate directly both modes of the entangled pair, the transmitted (cavity) and the fluorescent (atom) intensities, and can act as an entanglement witness. This thesis presents the implementation of a cross-correlation measurement in a cavity QED system. The work has required the construction of an apparatus that incorporates laser cooling and trapping with quantum optics to carefully control both the external (center of mass motion) and internal (atomic state) degrees of freedom of a collection of atoms that interact with a single mode of a high finesse Fabry-Perot cavity. We examine theoretically and experimentally a new intensity cross-correlation function which probes the evolution of the cavity field conditioned on the detection of a fluorescent photon from an atom in the cavity. The results open the possibility to generalize the dynamics of entanglement as a physical resource necessary for the nascent quantum information science.
The first two-photon entanglement experiment performed 50 years ago by Kocher and Commins (KC) provided isolated pairs of entangled photons from an atomic three-state fluorescence cascade. In view of questioning of Bell’s theorem, data from these experiments are re-analyzed and shown sufficiently precise to confirm quantum mechanical and dismiss semi-classical theory without need for Bell’s inequalities. Polarization photon correlation anisotropy (A) is useful: A is near unity as predicted quantum mechanically and well above the semi-classic range, 0⩽A⩽1/2. Although yet to be found, one may envisage a three-state molecule emitting entangled photon pairs, in analogy with the KC atomic system. Antibunching in fluorescence from single molecules in matrix and entangled photons from quantum dots promise it be possible. Molecules can have advantages to parametric down-conversion as the latter photon distribution is Poissonian and unsuitable for producing isolated pairs of entangled photons. Analytical molecular applications of entangled light are also envisaged.
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We study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on demand by sending coherent states into the proposed system. We calculate the second-order correlation function of the transmitted field and observe bunching and antibunching caused by the bound states. Furthermore, we demonstrate that the proposed system can produce photon pairs with a high degree of spectral entanglement, which have a large capacity for carrying information and are important for large-alphabet quantum communication.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.