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arXiv:1209.3935 · Physical Review A

Photon blockade induced by atoms with Rydberg coupling

Jin‐Feng Huang, Jie‐Qiao Liao, C. P. Sun

Published Feb 19, 2013• 66 citations
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Abstract

We study the photon blockade of two-photon scattering in a one-dimensional waveguide, which contains two atoms coupled via the Rydberg interaction. We obtain the analytic scattering solution of photonic wave packets with the Laplace transform method. We examine the photon correlation by addressing the two-photon relative wave function and the second-order correlation function in the single- and two-photon resonance cases. It is found that, under the single-photon resonance condition, photon bunching and antibunching can be observed in the two-photon transmission and reflection, respectively. In particular, the bunching and antibunching effects become stronger with the increasing of the Rydberg coupling strength. In addition, we find a phenomenon of bunching-antibunching transition caused by the two-photon resonance.

DOI
10.1103/physreva.87.023822

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We study the photon blockade of two-photon scattering in a one-dimensional waveguide, which contains two atoms coupled via the Rydberg interaction. We obtain the analytic scattering solution of photonic wave packets with the Laplace transform method. We examine the photon correlation by addressing the two-photon relative wave function and the second-order correlation function in the single- and two-photon resonance cases. It is found that, under the single-photon resonance condition, photon bunching and antibunching can be observed in the two-photon transmission and reflection, respectively. In particular, the bunching and antibunching effects become stronger with the increasing of the Rydberg coupling strength. In addition, we find a phenomenon of bunching-antibunching transition caused by the two-photon resonance.
Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.
We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency, where they form strongly interacting massive particles, termed Rydberg polaritons. Depending on the strength of the van der Waals-type interactions of the atoms either bunching or antibunching of photons can be observed when driving the atoms off-resonantly. The bunching is associated with the formation of bound states. We employ a Green's function approach and numerical wave-function simulations to analyze the conditions for the creation and the dynamics of these photonic molecules and their interplay with the scattering continuum which can also show photon bunching. Analytic solutions of the pair-propagation problem obtained from a pseudopotential approximation and verified numerically provide a detailed understanding of bound and scattering states. We find that the scattering contributions acquire asymptotically a robust relative phase which can be employed to separate bound state and scattering contributions by a homodyne detection scheme.
We investigate one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.
We study multiphoton blockade effects in a single-mode cavity interacting with two three-level atoms in $\mathrm{\ensuremath{\Lambda}}$ configuration having position-dependent atom-field coupling. We consider the effects of dipole-dipole interaction (DDI) between the three-level atoms and show how the presence of DDI strongly influences the multiphoton blockade. For symmetric coupling of the atoms with the field, the DDI induces an asymmetry in the emission spectra as a function of pump field detuning. At positive detuning, the single-photon blockade gets stronger as a function of DDI strength, leading to photon antibunching. However, it becomes weaker at negative detuning and can also completely vanish. We show that this vanishing single-photon blockade is associated with a strong two-photon blockade, leading to two-photon bunching. Therefore, by just tuning the frequency of the pump field, we can achieve two very distinct features. We also study the effects of DDI when the atoms are asymmetrically coupled with the field and show that the proposed system exhibits two-photon bunching. We believe our results are important for the experimental realization of such systems where DDI may be present.
We investigate the two-photon transport properties inside one-dimensional waveguide side coupled to a cavity. The cavity is doped with a four-level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field, the transmission and reflection of the correlated photons can be controlled.
We investigate the two-photon transport through a waveguide side coupling to a whispering-gallery-atom system. Using the Lehmann-Symanzik-Zimmermann reduction approach, we present the general formula for the two-photon processes including the two-photon scattering matrices, the wave functions, and the second order correlation functions of the outgoing photons. Based on the exact results of the second order correlation functions, we analyze the quantum statistics behaviors of the outgoing photons for two different cases: (a) the ideal case without the intermodal coupling in the whispering-gallery resonator; and (b) the case in the presence of the intermodal coupling which leads to more complex nonlinear behavior. In the ideal case, we show that the system consists of two independent scattering pathways, a free pathway by a cavity mode without atomic excitation, and a ``Jaynes-Cummings'' pathway described by the Jaynes-Cummings Hamiltonian of a single-mode cavity coupling to an atom. The presence of the free pathway leads to two-photon correlation properties that are distinctively different from the standard Jaynes-Cummings model, in both the strong and weak-coupling regime. In the presence of intermodal mixing, the system no longer exhibits a free resonant pathway. Instead, both the single-photon and the two-photon transport properties depend on the position of the atom. Thus, in the presence of intermodal mixing, one can in fact tune the photon correlation properties by changing the position of the atom. Our formalism can be used to treat resonator and cavity dissipation as well.