Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a coupled cavity waveguide, which are of current experimental interest. For the case of optical cavities, we directly compare and contrast the spectra from three distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning and cavity dot coupling. We show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general reservoir approach and explain its differences from the above approaches in the low Q limit of a Lorentzian cavity. We subsequently use this general reservoir to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects. Our quantum theory can be applied to a wide range of photonic structures including photonic molecules and coupled-cavity waveguide systems.
We study the time-dependent properties of double quantum dots coupled to two reservoirs using the nonequilibrium Green function method. For an arbitrary time-dependent bias, we derive an expression for the time-dependent electron density of a dot and several currents, including the current between the dots in the wide-band-limit approximation. For the special case of a constant bias, we calculate the electron density and the currents numerically. As a result, we find that these quantities oscillate and that the number of crests in a single period of the current from a dot changes with the bias…
The spontaneous emission rate of a quantum dot coupled to a structured photonic reservoir is determined by the frequency dependence of its local density of photon states. Through phonon-dressing, a breakdown of Fermi's golden rule can occur for certain photonic structures whose photon decay time become comparable to the longitudinal acoustic phonon decay times. We present a polaron master equation model to calculate the photoluminescence intensity from a coherently excited quantum dot coupled to a structured photonic reservoir. We consider examples of a semiconductor microcavity and a coupled …
We propose a method to generate a two-dimensional cluster state of polarization encoded photonic qubits from two coupled quantum dot emitters. We combine the recent proposal [N. H. Lindner and T. Rudolph, Phys. Rev. Lett. 103, 113602 (2009)] for generating 1-dimensional cluster state strings from a single dot, with a new proposal for an optically induced conditional phase (CZ) gate between the two quantum dots. The entanglement between the two quantum dots translates to entanglement between the two photonic cluster state strings. Further inter-pair coupling of the quantum dots using cavities a…
We present a theoretical study of an electronic quantum refrigerator based on four quantum dots arranged in a square configuration, in contact with as many thermal reservoirs. We show that the system implements the basic minimal mechanism for acting as a self-contained quantum refrigerator, by demonstrating heat extraction from the coldest reservoir and the cooling of the nearby quantum-dot.
A theoretical investigation on slow light propagation based on eletromagnetically induced transparency in a three-level quantum-dot system is performed including non-Markovian effects and correlated dephasing reservoirs. It is demonstraonated that the non-Markovian nature of the process is quite essential even for conventional dephasing typical of quantum dots leading to significant enhancement or inhibition of the group velocity slow-down factor as well as to the shifting and distortion of the transmission window. Furthermore, the correlation between dephasing reservoirs may also either enhan…
We demonstrate the ability to control the spontaneous emission dynamics of self-assembled quantum dots via the local density of optical modes in 2D-photonic crystals. We show that an incomplete 2D photonic bandgap is sufficient to significantly lengthen the spontaneous emission lifetime ($>2\times$) over a wide bandwidth ($Δλ\geq40$ nm). For dots that are both \textit{spectrally} and \textit{spatially} coupled to strongly localized ($V_{mode}\sim1.5(λ/n)^{3}$), high $Q\sim2700$ optical modes, we have directly measured a strong Purcell enhanced shortening of the emission lifetime $\geq5.6\times…
Systems of photonic crystal cavities coupled to quantum dots are a promising architecture for quantum networking and quantum simulators. The ability to independently tune the frequencies of laterally separated quantum dots is a crucial component of such a scheme. Here, we demonstrate independent tuning of laterally separated quantum dots in photonic crystal cavities coupled by in-plane waveguides by implanting lines of protons which serve to electrically isolate different sections of a diode structure.
Using a polaron master equation approach we investigate the resonance fluorescence spectra from coherently driven quantum dots (QDs) coupled to an acoustic phonon bath and a photonic crystal waveguide with a rich local density of photon states (LDOS). Resonance fluorescence spectra from QDs in semiconductor crystals are known to show strong signatures of electron-phonon interactions, but when coupled to a structured photonic reservoir, the QD emission properties are also determined by the frequency dependence of the LDOS of the photon reservoir. Here, we investigate the simultaneous role of co…
This chapter will primarily focus on the studies of quantum optics with semiconductor, epitaxially grown quantum dots embedded in photonic crystal cavities. We will start by giving brief introductions into photonic crystals and quantum dots, then proceed with the introduction to cavity quantum electrodynamics (QED) effects, with a particular emphasis on the demonstration of these effects on the quantum dot-photonic crystal platform. Finally, we will focus on the applications of such cavity QED effects.
We show unusual cooperative two-photon resonance between two-modes of field inside a photonic crystal cavity. The two-photon resonance occurs when two off resonant quantum dots emit one photon in each cavity mode and de-excite simultaneously. In the presence of phonon coupling the conditions for two-photon resonance change significantly. Using such two-photon two-mode interaction we propose to generate entangled state of two qutrits. The basis of a qutrit are formed by the state of the cavity mode containing $0$, $1$ and $2$ photons. We also discuss effect of phonon coupling on negativity of t…
Quantum dots are both excellent single-photon sources and hosts for single spins. This combination enables the deterministic generation of Raman-photons -- bandwidth-matched to an atomic quantum-memory -- and the generation of photon cluster states, a resource in quantum communication and measurement-based quantum computing. GaAs quantum dots in AlGaAs can be matched in frequency to a rubidium-based photon memory, and have potentially improved electron spin coherence compared to the widely used InGaAs quantum dots. However, their charge stability and optical linewidths are typically much worse…
A structured electromagnetic reservoir can result in novel dynamics of quantum emitters. In particular, the reservoir can be tailored to have a memory of past interactions with emitters, in contrast to memory-less Markovian dynamics of typical open systems. In this Article, we investigate the non-Markovian dynamics of a superconducting qubit strongly coupled to a superconducting slow-light waveguide reservoir. Tuning the qubit into the spectral vicinity of the passband of this waveguide, we find non-exponential energy relaxation as well as substantial changes to the qubit emission rate. Furthe…
We study the mutual interaction between two identical quantum dots coupled to the normal modes of two-site photonic crystal molecules in a planar waveguide geometry, i.e. photonic crystal dimers. We find that the radiative coupling between the two quantum emitters is maximized when they are in resonance with either the bonding or the antibonding modes of the coupled cavity system. Moreover, we find that such effective interdot coupling is sizable, in the meV range, and almost independent from the cavities distance, as long as a normal mode splitting exceeding the radiative linewidth can be est…
We present measurements of the beta-factor, describing the coupling efficiency of light emitted by single InAs/GaAs semiconductor quantum dots into a photonic crystal waveguide mode. The beta-factor is evaluated by means of time-resolved frequency-dependent photoluminescence spectroscopy. The emission wavelength of single quantum dots is temperature tuned across the band edge of a photonic crystal waveguide and the spontaneous emission rate is recorded. Decay rates up to 5.7 ns^(-1), corresponding to a Purcell factor of 5.2, are measured and beta-factors up to 85% are extracted. These results …
Implementations for quantum computing require fast single- and multi-qubit quantum gate operations. In the case of optically controlled quantum dot qubits theoretical designs for long-range two- or multi-qubit operations satisfying all the requirements in quantum computing are not yet available. We have developed a design for a fast, long-range two-qubit gate mediated by a photonic microcavity mode using excited states of the quantum dot-cavity system that addresses these needs. This design does not require identical qubits, it is compatible with available optically induced single qubit operat…
We propose a quantum absorption refrigerator using the quantum physics of resonant tunneling through quantum dots. The cold and hot reservoirs are fermionic leads, tunnel coupled via quantum dots to a central fermionic cavity, and we propose configurations in which the heat absorbed from the (very hot) central cavity is used as a resource to selectively transfer heat from the cold reservoir on the left, to the hot reservoir on the right. The heat transport in the device is particle---hole symmetric; we find two regimes of cooling as a function of the energy of the dots---symmetric with respect…
Interfacing single emitters and photonic nanostructures enables modifying their emission properties, such as enhancing individual decay rates or controlling the emission direction. To achieve full control, the single emitter must be positioned in the nanostructures deterministically. Here, we use spectroscopy to gain spectral and spatial information about individual quantum dots in order to position each emitter in a pre-determined location in a unit cell of a photonic-crystal waveguide. Depending on the spatial and spectral positioning within the structured nanophotonic mode, we observe that …
We show that fractional decay may be observable in experiments using quantum dots and photonic crystals with parameters that are currently achievable. We focus on the case of inverse opal photonic crystals and locate the position in the crystal where the effect is most pronounced. Furthermore, we quantify the influence of absorptive loss and show that it is a limiting but not prohibitive effect.
Indistinguishable single photons are necessary for quantum information processing applications. Resonant or quasiresonant excitation of single quantum dots provides greater single photon indistinguishability than incoherent pumping, but is also more challenging experimentally. Here, we demonstrate high signal to noise quasiresonant excitation of InP/InGaP quantum dots. The excitation is provided via second harmonic generated from a telecommunications wavelength laser resonant with the fundamental mode of a photonic crystal cavity, fabricated at twice the quantum dot transition wavelength. The …
We propose a new scheme for solid-state photonic quantum computation in which trapped photons in optical cavities are taken as a quantum bit. Quantum gates can be realized by coupling the cavities with quantum dots through waveguides. The proposed scheme allows programmable and deterministic gate operations and the system can be scaled up to many quantum bits.
We present time-resolved spontaneous emission measurements of single quantum dots embedded in photonic crystal waveguides. Quantum dots that couple to the photonic crystal waveguide are found to decay up to 27 times faster than uncoupled quantum dots. From these measurements $β$-factors of up to 0.89 are derived, and an unprecedented large bandwidth of 20 nm is demonstrated. This shows the promising potential of photonic crystal waveguides for efficient single-photon sources. The scaled frequency where the enhancement is observed is in excellent agreement with theory taking into account that t…
We have measured the variation of the spontaneous emission rate with polarization for self-assembled single quantum dots in two-dimensional photonic crystal membranes. We observe a maximum anisotropy factor of 6 between the decay rates of the two bright exciton states. This large anisotropy is attributed to the substantially different projected local density of optical states for differently oriented dipoles in the photonic crystal.
We propose a scheme for realizing two-qubit quantum phase gates with two nonidentical quantum dots trapped in two coupled photonic crystal cavities and driven by classical laser fields. During the gate operation, neither the cavity modes nor the quantum dots are excited, so the decoherence can be suppressed. The system can acquire a phase conditional upon the states of the quantum dots, which can be used to realize the controlled phase gate.
Highly entangled graph states of photons have applications in universal quantum computing and in quantum communications. In the latter context, they have been proposed as the key ingredient in the establishment of long-distance entanglement across quantum repeater networks. Recently, a general deterministic approach to generate repeater graph states from quantum emitters was given. However, a detailed protocol for the generation of such states from realistic systems is still needed in order to guide experiments. Here, we provide such explicit protocols for the generation of repeater graph stat…
We describe how a structured photonic medium controls the spontaneous emission rate from an excited quantum dot in the presence of electron-phonon coupling. We analyze this problem using a polaron transformed master equation and we consider specific examples of a photonic crystal cavity and a coupled cavity waveguide. We find that when the relaxation times of the photon and phonon baths are comparable, phonons influence spontaneous emission in a non-trivial way. We demonstrate why and how the broadband frequency dependence of the local photon density of states determines the photon emission ra…
We use single self-assembled InGaAs quantum dots as internal probes to map the local density of optical states of photonic crystal membranes. The employed technique separates contributions from non-radiative recombination and spin-flip processes by properly accounting for the role of the exciton fine structure. We observe inhibition factors as high as 55 and compare our results to local density of optical states calculations available from the literature, thereby establishing a quantitative understanding of photon emission in photonic crystal membranes.
We propose a scheme for realizing a two-qubit controlled phase gate via an unconventional geometric phase with two nonresonant quantum dots trapped in a photonic crystal cavity. In this system, the quantum dots simultaneously interact with a large detuned cavity mode and strong driving classical light fields. During the gate operation, the quantum dots undergo no transitions, while the cavity mode is displaced along a closed path in the phase space. In this way, the system can acquire geometric phases conditional upon the states of the quantum dots. After implementing single-qubit operations, …
We show that the two-photon transition rates of quantum dots coupled to nanocavities are enhanced by up to 8 orders of magnitude relative to quantum dots in bulk host. We then propose how to take advantage of this enhancement to implement coherent quantum dot excitation by two-photon absorption, entangled photon pair generation by two-photon spontaneous emission, and single-photon generation at telecommunication wavelengths by two-photon stimulated and spontaneous emission.
We develop a general microscopic theory describing the phonon decoherence of quantum dots and indistinguishability of the emitted photons in photonic structures. The coherence is found to depend fundamentally on the dimensionality of the structure resulting in vastly different performance for quantum dots embedded in a nano-cavity (0D), waveguide (1D), slab (2D), or bulk medium (3D). In bulk, we find a striking temperature dependence of the dephasing rate scaling as $T^{11}$ implying that phonons are effectively 'frozen out' for $T \lesssim 4 \mathrm{K}$. The phonon density of states is strong…
We investigate whether and how the quantum Zeno effect, i.e., the inhibition of quantum evolution by frequent measurements, can be employed to isolate a quantum dot from its surrounding electron reservoir. In contrast to the often studied case of tunneling between discrete levels, we consider the tunnelling of an electron from a continuum reservoir to a discrete level in the dot. Realizing the quantum Zeno effect in this scenario can be much harder because the measurements should be repeated before the wave packet of the hole left behind in the reservoir moves away from the vicinity of the dot…
We propose a method to generate path-entangled $N00N$-state photons from quantum dots (QDs) and coupled nanocavities. In the systems we considered, cavity mode frequencies are tuned close to the biexciton two-photon resonance. Under appropriate conditions, the system can have the target $N00N$ state in the energy eigenstate, as a consequence of destructive quantum interference. The $N00N$ state can be generated by the resonant laser excitation. This method, first introduced for two-photon $N00N$ state ($N=2$), can be extended toward higher $N00N$ state ($N>2$) based on our recipe, which is app…
Photonic nanostructures provide means of tailoring the interaction between light and matter and the past decade has witnessed a tremendous experimental and theoretical progress in this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics experiments on, e.g., spontaneous-emission control, …
The electro-optic, acousto-optic and nonlinear properties of lithium niobate make it a highly versatile material platform for integrated quantum photonic circuits. A prerequisite for quantum technology applications is the ability to efficiently integrate single photon sources, and to guide the generated photons through ad-hoc circuits. Here we report the integration of quantum dots in monolayer WSe2 into a Ti in-diffused lithium niobate directional coupler. We investigate the coupling of individual quantum dots to the waveguide mode, their spatial overlap, and the overall efficiency of the hyb…
We demonstrate scattering of laser light from two InAs quantum dots coupled to a photonic crystal waveguide, which is achieved by strain-tuning the optical transitions of the dots into mutual resonance. By performing measurements of the intensity and photon statistics of transmitted laser light before and after tuning the dots into resonance, we show that the nonlinearity is enhanced by collective scattering. In addition to providing a means of manipulating few-photon optical nonlinearities, our approach establishes new opportunities for multi-emitter quantum optics in a solid-state platform.
We proposed the general concept of quantum antenna in the strong coupling regime. It is based on the theory of open quantum systems. The antenna emission to the space is considered as an interaction with the thermal photonic reservoir. For modeling of the antenna dynamics is formulated a master equation with the correspondent Lindblad super-operators as the radiation terms. It is shown that strong coupling dramatically changes the radiation pattern of antenna. The total power pattern splits to three partial components; each corresponds to the spectral line of Mollow triplet. We analyzed the de…
We observe large spontaneous emission rate modification of individual InAs Quantum Dots (QDs) in 2D a photonic crystal with a modified, high-Q single defect cavity. Compared to QDs in bulk semiconductor, QDs that are resonant with the cavity show an emission rate increase by up to a factor of 8. In contrast, off-resonant QDs indicate up to five-fold rate quenching as the local density of optical states (LDOS) is diminished in the photonic crystal. In both cases we demonstrate photon antibunching, showing that the structure represents an on-demand single photon source with pulse duration from 2…
The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In…
Semiconductor quantum dots embedded in photonic-crystal nanostructures have been the subject of intense study. In this context, quantum dots are often considered to be simple two-level emitters, i.e., the complexities arising from the internal finestructure are neglected. We show that due to the intricate spatial variations of the electric field polarization found in photonic crystal, the two orthogonal finestructure states of quantum dots in general both couple significantly to a cavity mode, implying that the two-level description is not sufficient. As a consequence the emission dynamics and…
We demonstrate room temperature visible wavelength photoluminescence from In0.5Ga0.5As quantum dots embedded in a GaP membrane. Time-resolved above band photoluminescence measurements of quantum dot emission show a biexpontential decay with lifetimes of ~200 ps. We fabricate photonic crystal cavities which provide enhanced outcoupling of quantum dot emission, allowing the observation of narrow lines indicative of single quantum dot emission. This materials system is compatible with monolithic integration on Si, and is promising for high efficiency detection of single quantum dot emission as we…
Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5K into non-guided and guided modes is determined by direct hyperspectral imaging. This enables measurement of the absolute coupling efficiency into the guided modes, the beta-factor, directly, without assumptions on decay rates used previously. Notably, we found beta-factors above 90% over a wide spectral range of 40meV in the fast light regime, reaching a maximum of (99 $\pm$ 1)%. We measure the directional emission of the circularly polarized transitions in a magnetic field i…
We report on a series of experiments on the dynamics of spontaneous emission controlled nanolasers. The laser cavity is a photonic crystal slab cavity, embedding self-assembled quantum dots as gain material. The implementation of cavity electrodynamics effects increases significantly the large signal modulation bandwidth, with measured modulation speeds of the order of 10 GHz while keeping an extinction ratio of 19 dB. A linear transient wavelength shift is reported, corresponding to a chirp of less than 100 pm for a 35-ps laser pulse. We observe that the chirp characteristics are independent …
We demonstrate the coupling of PbS quantum dot emission to photonic crystal cavities at room temperature. The cavities are defined in 33% Al, AlGaAs membranes on top of oxidized AlAs. Quantum dots were dissolved in Poly-methyl-methacrylate (PMMA) and spun on top of the cavities. Quantum dot emission is shown to map out the structure resonances, and may prove to be viable sources for room temperature cavity coupled single photon generation for quantum information processing applications. These results also indicate that such commercially available quantum dots can be used for passive structure …
We provide a microscopic theory for semiconductor quantum dots that explains the pronounced deviations from the prevalent point-dipole description that were recently observed in spectroscopic experiments on quantum dots in photonic nanostructures. At the microscopic level the deviations originate from structural inhomogeneities generating a large circular quantum current density that flows inside the quantum dot over mesoscopic length scales. The model is supported by the experimental data, where a strong variation of the multipolar moments across the emission spectrum of quantum dots is obser…
Future scalable photonic quantum information processing relies on the ability of integrating multiple interacting quantum emitters into a single chip. Quantum dots provide ideal on-chip quantum light sources. However, achieving quantum interaction between multiple quantum dots on-a-chip is a challenging task due to the randomness in their frequency and position, requiring local tuning technique and long-range quantum interaction. Here, we demonstrate quantum interactions between distant two quantum dots on a nanophotonic waveguide. We achieve a photon-mediated long-range interaction by integra…
We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady-state, thanks to their radiative coupling by mutual interaction through the normal modes of a photonic crystal dimer. We employ a quantum master equation formalism to quantify the steady-state entanglement by calculating the system {\it negativity}. Calculations are specified to consider realistic semiconductor nanostructure parameters for the photonic crystal dimer-quantum dots coupled system, determined by a guided mode expansion solution of Ma…
A method for generating entangled cat states of two modes of a microwave cavity field is proposed. Entanglement results from the interaction of the field with a beam of atoms crossing the microwave resonator, giving rise to non-unitary dynamics of which the target entangled state is a fixed point. We analyse the robustness of the generated two-mode photonic "cat state" against dephasing and losses by means of numerical simulation. This proposal is an instance of quantum reservoir engineering of photonic systems.
The coupling between single photon emitters and integrated photonic circuits is an emerging topic relevant for quantum information science and other nanophotonic applications. We investigate the coupling between a hybrid system of colloidal quantum dots and propagating gap modes of a silicon nitride waveguide system. We furthermore explore the density of optical states of the system by using a scanning probe technique and find that the quantum dots couple significantly to the photonic circuit. Our results indicate that a scalable slot-waveguide might serve as a promising platform in future dev…
