high-Q Cavity Mode Research Articles

Giant Second Harmonic Generation Enhancement in a High-Q Doubly Resonant Hybrid Plasmon-Fiber Cavity System.

A high-quality plasmon-fiber cavity in a doubly resonant configuration can exhibit second-harmonic generation (SHG) with over 5 orders of magnitude enhancement compared to gold nanoparticles on a fused silica substrate. Through coupling to a fiber cavity with the proper diameter, a high-quality (Q ≈ 160) resonance can be achieved in combination with a single gold nanoparticle. In a classical picture, where the incident electric field travels coherently Q times around the fiber during the nonlinear process, the high Q of the coupled mode aids in highly efficient SHG. We accomplish two feats: First, we analyze the Q factor dependence of the SHG efficiency, proving the expected Q4 dependence and thus confirming coherent E-field amplification in the fiber cavity. Second, we carefully adjust the fiber size further and tune the plasmon response of a gold nanoparticle to a high-Q cavity mode. We make sure that the second harmonic wavelength is simultaneously in resonance with a higher order fiber cavity mode, fulfilling the doubly resonant condition. As a result, a giant SH response with conversion efficiency up to 1.6 × 10-5 is detected upon a pump intensity of 5 × 108 W/cm2 for 100 fs pump pulses around 840 nm incident wavelength. Additionally, the importance of the doubly resonant condition is proven by detuning the size of the fiber, which leads to a drastic drop in SHG efficiency. This disparity of the SHG efficiency can be observed even by eye, when monitoring the intensity changes of the visible SH light during detuning.

Lamb Shift and the Vacuum Rabi Splitting in a Strongly Dissipative Environment.

We study the vacuum Rabi splitting of a qubit ultrastrongly coupled to a high-Q cavity mode and a radiation reservoir. Three methods are employed: a numerically exact variational approach with a multiple Davydov ansatz, the rotating-wave approximation (RWA), and the transformed RWA. Agreement between the variational results and the transformed RWA results is found in the regime of validity of the latter, where the RWA breaks down completely. We illustrate that the Lamb shift plays an essential role in modifying the vacuum Rabi splitting in the ultrastrong coupling regime, leading to off-resonant qubit-cavity coupling even though the cavity frequency equals the bare transition frequency of the qubit. Specifically, the emission spectrum exhibits one broad low-frequency peak and one narrow high-frequency peak in the presence of relatively weak cavity-qubit coupling. As the cavity-qubit coupling increases, the low-frequency peak narrows while the high-frequency peak broadens until they have similar widths.

Lithium niobate photonic-crystal electro-optic modulator

Modern advanced photonic integrated circuits require dense integration of high-speed electro-optic functional elements on a compact chip that consumes only moderate power. Energy efficiency, operation speed, and device dimension are thus crucial metrics underlying almost all current developments of photonic signal processing units. Recently, thin-film lithium niobate (LN) emerges as a promising platform for photonic integrated circuits. Here, we make an important step towards miniaturizing functional components on this platform, reporting high-speed LN electro-optic modulators, based upon photonic crystal nanobeam resonators. The devices exhibit a significant tuning efficiency up to 1.98 GHz V−1, a broad modulation bandwidth of 17.5 GHz, while with a tiny electro-optic modal volume of only 0.58 μm3. The modulators enable efficient electro-optic driving of high-Q photonic cavity modes in both adiabatic and non-adiabatic regimes, and allow us to achieve electro-optic switching at 11 Gb s−1 with a bit-switching energy as low as 22 fJ. The demonstration of energy efficient and high-speed electro-optic modulation at the wavelength scale paves a crucial foundation for realizing large-scale LN photonic integrated circuits that are of immense importance for broad applications in data communication, microwave photonics, and quantum photonics.

Wave-scattering method for waveguide–microcavity coupling

The coupling between a waveguide and a dielectric cavity is an important issue in many studies. Time differential coupling-mode theory is commonly used but invalid when the coupling is too strong due to the restriction of perturbation method. Although the finite-element method (FEM) is an accurate numerical method, in any case, it often requires extensive computing resources and costs too much time. In our work, a universal method is introduced to solve the coupling question in the two-dimensional waveguide–microcavity system. Through considering the field as a waveform which scatters between cavity and waveguide back and forth, the practical field can be obtained by summing these scattering waves. As a result, transmission spectrum, resonance frequency shift of a high-Q cavity mode, and mode weight inside the cavity are acquired. Furthermore, we have also analyzed the case under the strong coupling condition, in which the spectrum manifests a non-Lorentzian shape. Meanwhile, the field distribution and mode weight analysis show that multiple cavity modes are excited simultaneously. In terms of computational efficiency, our method is two orders of magnitude faster than FEM.

Hyperuniform disordered phononic structures

We demonstrate the existence of large phononic band gaps in designed hyperuniform (isotropic) disordered two-dimensional (2D) phononic structures of Pb cylinders in epoxy matrix. The phononic band gaps in hyperuniform disordered phononic structures are comparable to band gaps of similar periodic structures, for both out-of-plane and in-plane polarizations. A large number of localized modes is identified near the band edges, as well as, diffusive transmission throughout the rest of the frequency spectrum. Very high-Q cavity modes for both out-of-plane and in-plane polarizations are formed by selectively removing a single cylinder out of the structure. Efficient waveguiding with almost 100% transmission trough waveguide structures with arbitrary bends is also presented. We expand our results to thin three-dimensional layers of such structures and demonstrate effective band gaps related to the respective 2D band gaps. Moreover, the drop in the Q factor for the three-dimensional structures is not more than three orders of magnitude compared to the 2D ones.

Design of quasi-one-dimensional phononic crystal cavity for efficient photoelastic modulation

We propose and design a phononic crystal (PnC) cavity for efficient photoelastic modulation. A strongly confined acoustic field in the cavity enhances light-sound interaction, which results in efficient phase modulation of light. As one of the possible configurations, an acoustic cavity formed in a quasi-one-dimensional (quasi-1D) PnC was investigated. By carefully tuning geometrical parameters, we successfully designed a high-Q cavity mode for a longitudinal wave within a complete phononic band gap. The acoustic Q was calculated to be as high as 9.5 × 104. This enables efficient optical modulation by a factor of 2.5 compared with a bar-type structure without PnCs.

Subwavelength metallic cavities with high-Q resonance modes

Metallic cavities have been extensively studied to realize small-volume nanocavities and nanolasers. However cavity-resonance quality (Q) factors of nanolasers observed up to now remain low (up to ∼500) due to metal optical absorption. In this paper, we report the observation of highest Q factors of 9000 at low temperature and ∼6000 near room temperature in a metallic cavity with a probe of sub-bandgap emission of Si-doped GaAs. We analyze the temperature dependence of cavity-mode resonance wavelengths and show that the refractive-index term dominates the measured temperature dependence. We also show that this refractive-index term is cavity-mode dependent and the fitting procedure offers a new method to identify cavity modes. We simulate the metallic cavity with finite-element method and attribute the high-Q cavity mode to a whispering gallery optical mode. This mode is shown to have isotropic polarization dependence of the output emission, which is preferable for quantum information applications.

Correlations of a single atom and a resonance mode and their manifestation in some physical phenomena

A kinetic equation governing relaxation of a single two-level atom and a high-Q cavity mode in an entangled thermostat exhibiting quantum correlations is presented. Based on two kinds of collective operators, we demonstrate the possibility of the existence of dual squeezed states in this system. One kind of generator of collective operators corresponds to algebra obtained by polynomial deformation of the angular-momentum algebra, while the other kind corresponds to the Heisenberg-Weyl algebra. Squeezed states of the collective system are defined in terms of commutative relations for operators of the corresponding generator algebras. It is shown that quantum correlations in the system manifest themselves in two physical phenomena. The first one is the known entanglement-swapping protocol and is based on the projection measurement. In the other case, quantum correlations reveal themselves in the coherent scattering dynamics of an atom in the field of a standing light wave.

Strong Optical-Mechanical Coupling in a Vertical GaAs/AlAs Microcavity for Subterahertz Phonons and Near-Infrared Light

We show that distributed Bragg reflector GaAs/AlAs vertical cavities designed to confine photons are automatically optimal to confine phonons of the same wavelength, strongly enhancing their interaction. We study the impulsive generation of intense coherent and monochromatic acoustic phonons by following the time evolution of the elastic strain in picosecond-laser experiments. Efficient optical detection is assured by the strong phonon backaction on the high-Q optical cavity mode. Large optomechanical factors are reported (~THz/nm range). Pillar cavities based in these structures are predicted to display picogram effective masses, almost perfect sound extraction, and threshold powers for the stimulated emission of phonons in the range μW-mW, opening the way for the demonstration of phonon "lasing" by parametric instability in these devices.

Dual squeezed states in an atom-photon cluster and their manifestations

The general kinetic equation for an isolated two-level atom and a high-Q cavity mode in a heat bath exhibiting quantum correlations (entangled bath) is applied to the analysis of the squeezed states of the collective system. Two types of collective operators are introduced for the analysis: one is based on bosonic commutation relations, and the other, on the commutation relations of the algebra obtained by a polynomial deformation of the angular momentum algebra. On the basis of these relations, formulas for observables are constructed that identify squeezed states in the system. It is shown that, under certain conditions, the collective system exhibits dual squeezing within the relations for boson operators, as well as for the operators constructed from the angular momentum algebra. Such squeezing is demonstrated under a projective measurement of an atom and for an entanglement swapping protocol. In the latter case, when measuring two initially independent atomic systems, depending on the type of measurement, two cavity modes collapse into a nonseparable state, which is described either by a nonseparability relation based on boson operators or by a relation based on the operators of the algebra of the quasimomentum of the collective system consisting of these two modes.

Quantum theory of open systems in the representation of effective Hamiltonian and stochastic differential equations

An original general approach to the description of open quantum systems in the Markovian approximation was formulated for the example of the dynamics of high-Q cavity mode photons in the presence of nonresonant cavity atoms bound with an external vacuum electromagnetic field.

Quasieigenstate Coalescence in an Atom-Cavity Quantum Composite

We report the first direct observation of an exceptional point (EP) in an open quantum composite of a single atom and a high-Q cavity mode. The atom-cavity coupling constant was made a continuous variable by utilizing the multisublevel nature of a single rubidium atom when it is optimally coupled to the cavity mode. The spectroscopic properties of quasieigenstates of the atom-cavity composite were experimentally investigated near the EP. Branch-point singularity of quasieigenenergies was observed and its 4pi symmetry was demonstrated. Consequently, the cavity transmission at the quasieigenstate was observed to exhibit a critical behavior at the EP.

Ultrafast and low-power photonic crystal all-optical switching with resonant cavities

We theoretically investigate and discuss the response time, switching contrast, and pump power of all-optical switching in a nonlinear photonic crystal structure with high quality factor (high-Q) cavity. For the response time of all-optical switching, the drop and rise time are considered, respectively. Moreover, we find that when the duration of pump pulse is shorter than the lifetime, the response curve of all-optical switching is asymmetric, and the drop time is determined by both the lifetime of high-Q cavity and duration of pump pulse, and the rise time is mainly determined by lifetime of high-Q cavity. In contrast, when the duration of pump pulse is much longer than the lifetime, the dynamic response curve is symmetric, and both the drop and rise time are determined by the duration of pump pulse. On the other hand, the pump power can be significantly reduced by using a setup where the probe beam is located at the high-Q cavity mode with very narrow linewidth. Furthermore, if the central wavelength of pump pulse is also set to match with this or another high-Q cavity mode, the pump power will be reduced further due to the large field enhancement within the photonic crystal, and more importantly there is no extra prolonged response time of all-optical switching. By this method, the pump power as low as 210 KW/cm2 is observed in our model structure with the quality factor of only 32 096 for the ordinary polystyrene material.

Electrical control of spontaneous emission and strong coupling for a single quantum dot

We report the design, fabrication and optical investigation of electrically tunable single quantum dots—photonic crystal defect nanocavities operating in both the weak and strong coupling regimes of the light–matter interaction. Unlike previous studies where the dot–cavity spectral detuning was varied by changing the lattice temperature, or by the adsorption of inert gases at low temperatures, we demonstrate that the quantum-confined Stark effect can be employed to quickly and reversibly switch the dot–cavity coupling simply by varying a gate voltage. Our results show that exciton transitions from individual dots can be tuned by ∼4 meV relative to the nanocavity mode before the emission quenches due to carrier tunneling escape. This range is much larger than the typical linewidth of the high-Q cavity modes (∼100 μeV) allowing us to explore and contrast regimes where the dots couple to the cavity or decay by spontaneous emission into the two-dimensional photonic bandgap. In the weak-coupling regime, we show that the dot spontaneous emission rate can be tuned using a gate voltage, with Purcell factors ⩾7. New information is obtained on the nature of the dot–cavity coupling in the weak coupling regime, and electrical control of zero-dimensional polaritons is demonstrated for the highest-Q cavities (Q⩾12 000). Vacuum Rabi splittings up to ∼120 μeV are observed, larger than the linewidths of either the decoupled exciton (γ⩽40 μeV) or cavity mode. These observations represent a voltage switchable optical nonlinearity at the single photon level, paving the way towards on-chip dot-based nano-photonic devices that can be integrated with passive optical components.

Relaxation of an atom and a cavity mode in an entangled environment

The master equation is derived for an atom and a single high-Q cavity mode interacting with the bath modes produced by a two-mode broadband source based on two degenerate optical parametric oscillators. The relaxation superoperator, found in the resonant and dispersive limits, contains new terms describing correlations between the atom and the cavity mode. Collective coherent states are introduced to show that squeezed states of the atom-cavity subsystem are generated via interaction with an entangled environment. It is shown that a correlated initial state of the atom and the cavity mode manifests itself in two cavity QED phenomena: spontaneous atomic emission in the strong-coupling regime and population inversion in the Jaynes-Cummings model.

Ultracold atoms in optical lattices generated by quantized light fields

We study an ultracold gas of neutral atoms subject to the periodic optical potential generated by a high-Q cavity mode. In the limit of very low temperatures, cavity field and atomic dynamics require a quantum description. Starting from a cavity QED single atom Hamiltonian we use different routes to derive approximative multiparticle Hamiltonians in Bose-Hubbard form with rescaled or even dynamical parameters. In the limit of large enough cavity damping the different models agree. Compared to free space optical lattices, quantum uncertainties of the potential and the possibility of atom-field entanglement lead to modified phase transition characteristics, the appearance of new phases or even quantum superpositions of different phases. Using a corresponding effective master equation, which can be numerically solved for few particles, we can study time evolution including dissipation. As an example we exhibit the microscopic processes behind the transition dynamics from a Mott insulator like state to a self-ordered superradiant state of the atoms, which appears as steady state for transverse atomic pumping.

Collective entangled dark states

We describe a type of collective entangled dark state which exists when a group of many-level atoms interact simultaneously with both high-Q cavity modes and free space modes of the electromagnetic field. As an example we describe a collection of atoms with a level structure of the form of and show that there are states of this system in which the atoms remain trapped in a collective coherent superposition of ground state levels in spite of the presence of photons in resonant field modes. Efficient methods of generalization of these results to other atomic level structures and cavity fields are described.

Cavity QED with Semiconductor Nanocrystals

We report on a strongly coupled cavity quantum electrodynamic (CQED) system consisting of a CdSe nanocrystal coupled to a single photon mode of a polymer microsphere. The strong exciton-photon coupling is manifested by the observation of a cavity mode splitting variant Planck's over 2piOmega(exp) between 30 und 45 microeV and photon lifetime measurements of the coupled exciton-photon state. The single photon mode is isolated by lifting the mode degeneracy in a slightly deformed microsphere cavity and addressing it by high-resolution imaging spectroscopy. This cavity mode is coupled to a localized exciton of an anisotropically shaped CdSe nanocrystal that emits highly polarized light in resonance to the cavity mode and that was placed in the maximum electromagnetic field close to the microsphere surface. The exciton confined in the CdSe nanorod exhibits an optical transition dipole moment much larger than that of atoms, the standard system for CQED experiments, and a low-temperature homogeneous line width much narrower than the high-Q cavity mode width. The observation of strong coupling in a colloidal semiconductor nanocrystal-cavity system opens the way to study fundamental quantum-optics phenomena and to implement quantum information processing concepts that work in the visible spectral range and are based on solid-state nanomaterials.

Optically triggered Q-switched photonic crystal laser

An optically triggered liquid crystal infiltrated Q-switched photonic crystal laser is demonstrated. A photonic crystal laser cavity was designed and fabricated to support two orthogonally polarized high-Q cavity modes after liquid crystal infiltration. By controlling the liquid crystal orientation via a layer of photoaddressable polymer and a writing laser, the photonic crystal lasing mode can be reversibly switched between the two modes which also switches the laser's emission polarization and wavelength. The creation of the Q-switched laser demonstrates the benefits of customizing photonic crystal cavities to maximally synergize with an infiltrated material and illustrates the potential of integrating semiconductor nanophotonics with optical materials.

Quantum motion of laser-driven atoms in a cavity field

We investigate the quantum motion of coherently driven ultracold atoms in the field of a damped high-Q optical cavity mode. The laser field is chosen far detuned from the atomic transition but close to a cavity resonance, so that spontaneous emission is strongly suppressed but a coherent field builds up in the resonator by stimulated scattering. On one hand the shape of the atomic wave function determines the field dynamics via the magnitude of the scattering and the effective refractive index the atoms create for the mode. The mode intensity on the other hand determines the optical dipole force on the atoms. The system shows rich coupled atom-field dynamics including self-organisation, self trapping, cooling or heating. In the limit of deep trapping we are able to derive a system of closed, coupled equations for a finite set of atomic expectations values and the field. This allows to determine the self consistent ground state of the system as well as the eigenfrequencies and damping rates for excitations.