Origin of strong photon antibunching in weakly nonlinear photonic molecules

Abstract

In a recent work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. 104, 183601 (2010)] it was numerically shown that in a photonic 'molecule' consisting of two coupled cavities, near-resonant coherent excitation could give rise to strong photon antibunching with a surprisingly weak nonlinearity. Here, we show that a subtle quantum interference effect is responsible for the predicted efficient photon blockade effect. We analytically determine the optimal on-site nonlinearity and frequency detuning between the pump field and the cavity mode. We also highlight the limitations of the proposal and its potential applications in demonstration of strongly correlated photonic systems in arrays of weakly nonlinear cavities. The photon blockade is a quantum optical effect preventing the resonant injection of more than one photon into a nonlinear cavity mode [1], leading to antibunched (sub-Poissonian) single-photon statistics. Signatures of photon blockade have been observed by resonant laser excitation of an optical cavity containing either a single atom [2] or a single quantum dot [3] in the strong coupling regime. Arguably, the most convincing realization was based on a single atom coupled to a micro-toroidal cavity in the Purcell regime [4], suggesting that the strong coupling regime of cavity-QED need not be a requirement. Concurrently, on the theory side there has been a number of proposals investigating strongly correlated photons in coupled cavity arrays [5][6][7] or one-dimensional optical waveguides [8]. The specific proposals based on the photon blockade effect include the fermionization of photons in one-dimensional cavity of arrays [9], the crystallization of polaritons in coupled array of cavities [10], and the quantum-optical Josephson interferometer in a coupled photonic mode system [11].It is commonly believed that photon blockade necessarily requires a strong on-site nonlinearity U for a photonic mode, whose magnitude should well exceed the mode broadening γ. However, in a recent work [12] Liew and Savona numerically showed that a strong antibunching can be obtained with a surprisingly weak nonlinearity (U ≪ γ) in a system consisting of two coupled zerodimensional (0D) photonic cavities (boxes), as shown in Fig. 1(a) [12]. Such a configuration can be obtained, e.g., by considering two modes in two photonic boxes coupled with a finite mode overlap due to leaky mirrors: the corresponding tunnel strength will be designated with J. In Ref.[12] numerical evidence indicated that a nearly perfect antibunching can be achieved for an optimal value of the on-site repulsion energy U and for an optimal value of the detuning between the pump and mode frequency. However, a physical understanding of the mechanism leading to strong photon antibunching is needed to identify the limitations of the scheme in the context of proposed experiments on strongly correlated photons, as well as to determine the dependence of the optimal coupling and detuning on the relevant physical parameters J and γ.In this letter, we show analytical...

Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule

“…Two bare cavity modes are separated by ∆ o /2π = 118 GHz; a QD is resonant and strongly coupled to one of the modes (a) with interaction strength g/2π = 27.6 GHz (as discussed earlier, g = g 2 1 + g 2 2 , where g 1 and g 2 are the two values of QD-cavity interaction strengths obtained by fitting the PL spectra); mode b is the empty cavity. The mode b is driven and the second order autocorrelation g 2 (0) = b † b † bb b † b 2 of the transmitted light through cavity b is calculated [15]. We also assume the two cavities to have the same cavity decay rate, which is an average of the cavity decay rates measured from the two super-modes.…”

“…Unfortunately, in practice it is very difficult to drive only one cavity mode without affecting the other mode due to the spatial proximity of two cavities. This individual addressability is critical for good performance of the system [15] and to retain such a capability in a photonic molecule the cavities should be coupled via a waveguide [26].…”

“…Most of these proposals, for example observing the quantum phase transition of light, require a nonlinearity in each cavity, which is a formidable task with current technology. However, several proposals involving a single QD coupled to multiple cavities predict novel quantum phenomena, for example, generation of bound photon-atom states [13], or sub-Poissonian light generation in a pair of coupled cavities or in a photonic molecule containing a single QD [14,15]. This photonic molecule, coupled to a single QD, forms the first step towards building an integrated cavity network with coupled QDs.…”

Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity

“…On the other hand, given the small values of typical nonlinear coefficients of most semiconducting and insulating materials [14], an unconventional photon blockade (UPB) process could facilitate achieving antibunched light emission from suitably engineered coupled modes [15]. Such mechanism is based on destructive quantum interference between distinct driven-dissipative pathways [16,17], and requires a significantly smaller optical nonlinearity than its conventional counterpart. It has been recently proposed that UPB might allow to achieve antibunched light * Electronic address: dario.gerace@unipv.it emission either in passive devices made of materials with a large χ (3) susceptibility, such as silicon [18], or in coupled optomechanical systems [19,20].…”

“…15, 17, UPB can be expected to occur in such doubly resonant system even with g nl κ, thus relaxing the stringent conditions on the fundamental mode quality factor, Q 1,2 = ω 1,2 /κ. In particular, an analytic solution can be given for the optimal system parameters giving rise to strong antibunching [17]: laser frequency detuning, ∆ opt 1 = ∆ opt 2 = −κ/2 √ 3, and tunnel-coupling rate,…”