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Physical Review Letters

Strongly Interacting Photons in a Nonlinear Cavity

Ataç İmamoğlu, Holger Schmidt, Gary L. Woods, Miriam Deutsch

Published Aug 25, 1997• 1,090 citations
Publisher

Abstract

We consider the dynamics of single photons in a nonlinear optical cavity. When the Kerr nonlinearities of atomic dark resonances are utilized, the cavity mode is well described by a spin- $1/2$ Hamiltonian. We show that it is possible to achieve coherent control of the cavity-mode wave function using $\ensuremath{\pi}$ pulses for single photons that switch the state of the cavity with very high accuracy. The underlying physics is best understood as the nonlinearity induced anticorrelation between single-photon injection/emission events, which we refer to as photon blockade. We also propose a method which uses these strong dispersive interactions to realize a single-photon turnstile device.

DOI
10.1103/physrevlett.79.1467

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We consider the dynamics of single photons in a nonlinear optical cavity. When the Kerr nonlinearities of atomic dark resonances are utilized, the cavity mode is well described by a spin- 1/21/21/2 Hamiltonian. We show that it is possible to achieve coherent control of the cavity-mode wave function using \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses for single photons that switch the state of the cavity with very high accuracy. The underlying physics is best understood as the nonlinearity induced anticorrelation between single-photon injection/emission events, which we refer to as photon blockade. We also propose a method which uses these strong dispersive interactions to realize a single-photon turnstile device.
In this paper, we show that photon blockade can be observed in a system with weak Kerr nonlinearities. The system consists of two spatially overlapping single-mode semiconductor cavities with tunable one- and two-photon tunneling. We find that both conventional and unconventional single-photon blockades are controllable by manipulating the phase in the hopping regardless of the weakness of nonlinearity. We refer to the photon blockade with weak nonlinearities as an unconventional photon blockade. The unconventional photon blockade effect originates from the destructive interference between different paths from the ground state to two-photon states. We analytically derive the exact optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. The optimal parameters for photon blockade are derived. Based on these parameters, the semiconductor cavity systems can be used as a single-photon source in regimes of both weak and strong nonlinearities.
We present an experimental proposal to achieve a strong photon blockade by employing electromagnetically induced transparency (EIT) with a single alkaline-earth-metal atom trapped in an optical cavity. In the presence of optical Stark shift, both the second-order correlation function and cavity transmission exhibit asymmetric structures between the red and blue sidebands of the cavity. For a weak control field, the photon quantum statistics for the coherent transparency window (i.e., atomic quasi-dark-state resonance) are insensitive to the Stark shift, which should also be immune to the spontaneous emission of the excited state by taking advantage of the intrinsic dark-state polariton of EIT. Interestingly, by exploiting the interplay between the Stark shift and control field, the strong photon blockade at atomic quasi-dark-state resonance has an optimal second-order correlation function g ( 2 ) ( 0 ) ∼ 10 − 4 and a high cavity transmission simultaneously. The underlying physical mechanism is ascribed to the Stark shift enhanced spectrum anharmonicity and the EIT hosted strong nonlinearity with loss-insensitive atomic quasi-dark-state resonance, which is essentially different from the conventional proposal with emerging Kerr nonlinearity in cavity-EIT. Our results reveal a new strategy to realize high-quality single photon sources, which could open up a new avenue for engineering nonclassical quantum states in cavity quantum electrodynamics.
Universal photon blockade in a two-mode Jaynes-Cummings model incorporating third-order Kerr nonlinearity is demonstrated with a single two-level atom coupled to a waveguide microcavity. Realization of this universal photon blockade is attributed to the cooperative effects of field-atom coupling and Kerr nonlinearity. More importantly, this antibunching is found to be robust against the atomic spontaneous emission, driving field strength, and defect-induced cavity mode coupling. The strong antibunching effect in this resonance-driven scheme is essentially different from those without Kerr nonlinearity. Moreover, this work expands the platform for achieving universal photon blockade and reveals the cooperative advantages of nonlinearities in enhancing the purity and brightness of single-photon sources, representing a novel strategy toward high-performance single-photon sources in integrated quantum optical devices.
Photon blockade, in analogy to Coulomb's or phonon blockades, is a phenomenon when a single photon in a nonlinear cavity blocks the transmission of a second photon. This effect can occur in Kerr-type systems driven by a laser due to strong nonlinear photon-photon interactions. We predict the occurrence of higher-order photon blockades where the transmission of more than two photons is effectively blocked by single- and two-photon states. This photon blockade can be achieved by tuning the frequency of the laser driving field to be equal to the sum of the Kerr nonlinearity and the cavity resonance frequency. We refer to this phenomenon as two-photon blockade or two-photon state truncation via nonlinear scissors, and can also be interpreted as photon-induced tunneling. We also show that, for a driving-field frequency fulfilling another resonance condition and for higher strengths of the driving field, even a three-photon blockade can occur but less clearly than in the case of single- and two-photon blockades. We demonstrate how various photon blockades can be identified by analyzing photon-number correlations, coherence and entropic properties, Wigner functions, and spectra of squeezing. We show that two- and three-photon blockades can, in principle, be observed in various cavity and circuit quantum electrodynamical systems for which the standard single-photon blockade was observed without the need of using higher-order driving interactions or Kerr media exhibiting higher-order nonlinear susceptibility.
Quantum limit of dissipation-free photon-photon interactions at the few photon level is studied in the context of giant Kerr nonlinearities in cavity electromagneti cally induced transparency (EIT). It is shown that photon-photon interaction is largest when the cavity contains a sing le atom. In contrast to conventional nonlinearities, increasing the number of atoms cannot in crease the interaction strength but will in general degrade the performance by enhancing di spersion. In the non-perturbative regime, the single-atom photon-photon interaction can be limited by lossy states excited from long-lived EIT states. Asymptotically, in the strong coupling limit, photon-photon interaction is determined by the single photon-atom coupling strength. Photon blockade occurs for single atoms but only partial blockade can occur for low dispersion and not at all in the high-dispersion limit of the multi-atom case.
Beyond traditional nonlinear optics with large numbers of atoms and photons, qualitatively new phenomena arise in a quantum regime of strong interactions between single atoms and photons. By using a microscopic optical resonator, we achieved such interactions and demonstrated a robust, efficient mechanism for the regulated transport of photons one by one. With critical coupling of the input light, a single atom within the resonator dynamically controls the cavity output conditioned on the photon number at the input, thereby functioning as a photon turnstile. We verified the transformation from a Poissonian to a sub-Poissonian photon stream by photon counting measurements of the input and output fields. The results have applications in quantum information science, including for controlled interactions of single light quanta and for scalable quantum processing on atom chips.