I. Friedler, G. Kurizki, D. Petrosyan
Giantly enhanced cross-phase modulation with suppressed spectral broadening is predicted between optically-induced dark-state polaritons whose propagation is strongly affected by photonic bandgaps of spatially periodic media with multilevel dopants. This mechanism is shown to be capable of fully entangling two single-photon pulses with high fidelity.
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The fluorescence intensity and quadrature spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The non-Markovian nature of the problem caused by the non-uniform distribution of the photonic density of states is handled by linearizing the generalized optical Bloch equations with the Liouville operator expansion. Unlike the case in free space, we find that the bandgap effects will not only modify the fluorescence spectral shape but also cause squeezing in the in-phase quadrature spectra.
We have experimentally observed superluminal and infinite group velocities in bulk hexagonal two-dimensional photonic bandgap crystals with bandgaps in the microwave region. The group velocities depend on the polarization of the incident radiation and the air-filling fraction of the crystal.
We propose an atom-cavity chip that combines laser cooling and trapping of neutral atoms with magnetic microtraps and waveguides to deliver a cold atom to the mode of a fiber taper coupled photonic bandgap (PBG) cavity. The feasibility of this device for detecting single atoms is analyzed using both a semi-classical treatment and an unconditional master equation approach. Single-atom detection seems achievable in an initial experiment involving the non-deterministic delivery of weakly trapped atoms into the mode of the PBG cavity.
We demonstrate lasing oscillation in a three-dimensional photonic crystal nanocavity. The laser is realized by coupling a cavity mode, which is localized in a complete photonic bandgap and exhibits the highest quality factor of ~38,500, with high-quality semiconductor quantum dots. We show a systematic change in the laser characteristics, including the threshold and the spontaneous emission coupling factor by controlling the crystal size, which consequently changes the strength of photon confinement in the third dimension. This opens up many interesting possibilities for realizing future ultim…
When a resonance associated with electromagnetically induced transparency (EIT) in an atomic ensemble is modulated by an off-resonant standing light wave, a band of frequencies can appear for which light propagation is forbidden. We show that dynamic control of such a bandgap can be used to coherently convert a propagating light pulse into a stationary excitation with non-vanishing photonic component. This can be accomplished with high efficiency and negligble noise even at a level of few-photon quantum fields thereby facilitating possible applications in quantum nonlinear optics and quantum i…
Using a two-photon interference technique, we measure the delay for single-photon wavepackets to be transmitted through a multilayer dielectric mirror, which functions as a ``photonic bandgap'' medium. By varying the angle of incidence, we are able to confirm the behavior predicted by the group delay (stationary phase approximation), including a variation of the delay time from superluminal to subluminal as the band edge is tuned towards to the wavelength of our photons. The agreement with theory is better than 0.5 femtoseconds (less than one quarter of an optical period) except at large angle…
Photonic bandgap cavities are prime solid-state systems to investigate light-matter interactions in the strong coupling regime. However, as the cavity is defined by the geometry of the periodic dielectric pattern, cavity control in a monolithic structure can be problematic. Thus, either the state coherence is limited by the read-out channel, or in a high Q cavity, it is nearly decoupled from the external world, making measurement of the state extremely challenging. We present here a method for ameliorating these difficulties by using a coupled cavity arrangement, where one cavity acts as a swi…
Steady-state fluorescence spectra of a two-level atom embedded in a three-dimensional photonic bandgap crystal and driven by a monochromatic classical electrical field is calculated theoretically for the first time as we know. The non-Markovian noises caused by the non-uniform distribution of photon density of states near the photonic bandgap are handled by a new approach in which the Liouville operator expansion is utilized to linearize the generalized optical Bloch equations. The fluorescence spectra are then directly solved by the linearized Bloch equations in the frequency domain. We find …
We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involve…
We study the propagation of electromagnetic pulses through photonic bandgap materials and relate time-domain pulse reshaping to observable transit times. For layered dielectric mirrors we demonstrate how pulse reshaping of slowly varying classical fields results in transit-time delays that are equivalent to the group delay. The time-domain analysis emphasizes the causal origin of negative group delays. We also study an analogous fully-quantized model and show how the same time-domain analysis may be used to interpret observed delays of single-photon fields.
This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate …
Synthesis of many-body quantum systems in the laboratory can help provide further insight into the emergent behavior of quantum materials, whose properties may provide improved methods for energy conversion, signal transport, or information processing. While the majority of engineerable many-body systems, or quantum simulators, consist of particles on a lattice with local interactions, quantum systems featuring long-range interactions are particularly challenging to model and interesting to study due to the rapid spatio-temporal growth of quantum entanglement and correlations. Here, we present…
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation: (a) Self-induced transparency (SIT) solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b) Cross-coupling between pulses exhibiting electromagnetically induced transparency (EIT) and SIT gap solitons. We show that extremely strong correlatio…
Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a two-level quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of two level system with that of light propagation in a classical one-dimensional photonic crystal, commonly known as distributed-Bragg-reflector (DBR).This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabatic passage (R…
Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a `two-level' quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of two level atomic system with that of light propagation in a classical `one-dimensional' photonic crystal, commonly known as distributed-Bragg-reflector (DBR). This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabati…
The cross-Kerr nonlinearity (XKNL) effect can induce efficient photon interactions in principle with which photonic multiqubit gates can be performed using far fewer physical resources than linear optical schemes. Unfortunately, it is extremely challenging to generate giant cross-Kerr nonlinearities. In recent years, much effort has been made to perform multiqubit gates via weak XKNLs. However, the required nonlinearity strengths are still difficult to achieve in the experiment. We here propose an XKNL-based scheme for realizing a two-photon polarization-parity gate, a universal two-qubit gate…
Tunneling of optical pulses at 1.5 micron wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of the structure, the transit time is paradoxically short, implying Superluminal propagation, and almost independent of the distance between the barriers. These results are in agreement with theoretical predictions based on phase time analysis and also provide an experimental evidence, in the optical context, of the analogous phenomenon expected in Quantum Mechan…
We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in Photonic Crystal Waveguides (PCWs). In particular, we derive the equations for two modes propagating in PCWs and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analy…
Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $π$) to boost photonic quantum computing and …
In this paper we propose a novel approach to enhance the efficiency of the two-photon spontaneous emission process that is driven by the multifractal optical mode density of photonic structures based on the aperiodic distributions of Eisenstein and Gaussian primes. In particular, using the accurate Mie-Lorenz multipolar theory in combination with multifractal detrended fluctuation analysis, we compute the local density of states of periodic and aperiodic systems and demonstrate the formation of complete bandgaps with distinctive fractal scaling behavior for scattering arrays of dielectric nano…
The construction of photon-photon quantum phase gate based on photonic nonlinearity has long been a fundamental issue, which is vital for deterministic and scalable photonic quantum information processing. It requires not only strong nonlinear interaction at the single-photon level, but also suppressed phase noise and spectral entanglement for high gate fidelity. In this paper, we propose that high-quality factor microcavity with strong $χ^{(2)}$ nonlinearity can be quantized to anharmonic energy levels and be effectively treated as an artificial atom. Such artificial atom has a size much larg…
Photon statistics in a weakly driven optomechanical photonic crystal cavity, with Kerr-type nonlinearity, is analyzed both analytically and numerically. Single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function $g^{(2)}(0)$. The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. The experimental feasibility with state-of-the-art device parameters is discussed. It is observed that photon blockade could be gener…
Kerr nonlinearity in nanophotonic cavities provides a versatile platform to explore fundamental physical sciences and develop novel photonic technologies. This is driven by the precise dispersion control and significant field enhancement with nanoscale structures. Beyond dispersion and pump engineering, the direct control of Kerr nonlinearity can release the ultimate performance and functionality of photonic systems. Here, we report the in situ control of integrated Kerr nonlinearity through its interplay with the cascaded Pockels nonlinear process. Kerr nonlinearity is tuned over 10~dB dynami…
It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \texti…
We characterize photonic transport in a boundary driven array of nonlinear optical cavities. We find that the output field suddenly drops when the chain length is increased beyond a threshold. After this threshold a highly chaotic and unstable regime emerges, which marks the onset of a super-diffusive photonic transport. We show the scaling of the threshold with pump intensity and nonlinearity. Finally, we address the competition of disorder and nonlinearity presenting a diffusive-insulator phase transition.
We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhances localization in one type, and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of $δ$-like wavepackets in the presence of disorder. A transition from ballistic wavepacket expansion to exponential (Anderson) localization is observed. We find an intermediate…
Local control of the generation and interaction of indistinguishable single photons is a key requirement for photonic quantum networks. Waveguide-based architectures, in which embedded quantum emitters act as both highly coherent single photon sources and as nonlinear elements to mediate photon-photon interactions, offer a scalable route to such networks. However, local electrical control of a quantum optical nonlinearity has yet to be demonstrated in a waveguide geometry. Here, we demonstrate local electrical tuning and switching of single photon generation and nonlinear interaction by embedd…
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