Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots

Location Qubits in a Multiple-Quantum-Dot System

A physical platform for nodes of the envisioned quantum Internet is long-sought. Here we propose such a platform, along with a conceptually simple and experimentally uncomplicated quantum information processing scheme, realized in a system of multiple crystal-phase quantum dots. We introduce novel location qubits, describe a method to construct a universal set of all-optical quantum gates, and simulate their performance in realistic structures, including decoherence sources. Our results show that location qubits are robust against the main decoherence mechanisms, and realistic single-qubit gate fidelities exceed 99.9%. Our scheme paves a clear way toward constructing multiqubit solid-state quantum registers with a built-in photonic interface─a key building block of the forthcoming quantum Internet.

Optimizing Performance of Quantum Operations with Non-Markovian Decoherence: The Tortoise or the Hare?

The interaction between a quantum system and its environment limits our ability to control it and perform quantum operations on it. We present an efficient method to find optimal controls for quantum systems coupled to non-Markovian environments, by using the process tensor to compute the gradient of an objective function. We consider state transfer for a driven two-level system coupled to a bosonic environment, and characterize performance in terms of speed and fidelity. This allows us to determine the best achievable fidelity as a function of process duration. We show there can be a trade-off between speed and fidelity, and that slower processes can have higher fidelity by exploiting non-Markovian effects.

Signatures of Dynamically Dressed States

The interaction of a resonant light field with a quantum two-level system is of key interest both for fundamental quantum optics and quantum technological applications employing resonant excitation. While emission under resonant continuous-wave excitation has been well studied, the more complex emission spectrum of dynamically dressed states-a quantum two-level system driven by resonant pulsed excitation-has so far been investigated in detail only theoretically. Here, we present the first experimental observation of the complete resonance fluorescence emission spectrum of a single quantum two-level system, in the form of an excitonic transition in a semiconductor quantum dot, driven by finite Gaussian pulses. We observe multiple emerging sidebands as predicted by theory, with an increase of their number and spectral detuning with excitation pulse intensity and a dependence of their spectral shape and intensity on the pulse length. Detuning-dependent measurements provide additional insights into the emission features. The experimental results are in excellent agreement with theoretical calculations of the emission spectra, corroborating our findings.

Coherence in cooperative photon emission from indistinguishable quantum emitters

Photon-mediated interactions between atoms can arise via coupling to a common electromagnetic mode or by quantum interference. Here, we probe the role of coherence in cooperative emission arising from two distant but indistinguishable solid-state emitters because of path erasure. The primary signature of cooperative emission, the emergence of "bunching" at zero delay in an intensity correlation experiment, is used to characterize the indistinguishability of the emitters, their dephasing, and the degree of correlation in the joint system that can be coherently controlled. In a stark departure from a pair of uncorrelated emitters, in Hong-Ou-Mandel-type interference measurements, we observe photon statistics from a pair of indistinguishable emitters resembling that of a weak coherent state from an attenuated laser. Our experiments establish techniques to control and characterize cooperative behavior between matter qubits using the full quantum optics toolbox, a key step toward realizing large-scale quantum photonic networks.

Stimulated Generation of Indistinguishable Single Photons from a Quantum Ladder System

We propose a scheme for the generation of highly indistinguishable single photons using semiconductor quantum dots and demonstrate its performance and potential. The scheme is based on the resonant two-photon excitation of the biexciton followed by stimulation of the biexciton to selectively prepare an exciton. Quantum-optical simulations and experiments are in good agreement and show that the scheme provides significant advantages over previously demonstrated excitation methods. The two-photon excitation of the biexciton suppresses re-excitation and enables ultralow multiphoton errors, while the precisely timed stimulation pulse results in very low timing jitter of the photons, and consequently, high indistinguishability. In addition, the polarization of the stimulation pulse allows us to deterministically program the polarization of the emitted photon (H or V). This ensures that all emission of interest occurs in the polarization of the detection channel, resulting in higher brightness than cross-polarized resonant excitation.

Double-Pulse Generation of Indistinguishable Single Photons with Optically Controlled Polarization

Single-photon sources play a key role in photonic quantum technologies. Semiconductor quantum dots can emit indistinguishable single photons under resonant excitation. However, the resonance fluorescence technique typically requires cross-polarization filtering, which causes a loss of the unpolarized quantum dot emission by 50%. To solve this problem, we demonstrate a method for generating indistinguishable single photons with optically controlled polarization by two laser pulses off-resonant with neutral exciton states. This scheme is realized by exciting the quantum dot to the biexciton state and subsequently driving the quantum dot to an exciton eigenstate. By combining with a magnetic field, we demonstrated the generation of photons with optically controlled polarization (the degree of polarization is 101(2)%), laser-neutral exciton detuning up to 0.81 meV, high single-photon purity (99.6(1)%), and indistinguishability (85(4)%). Laser pulses can be blocked using polarization and spectral filtering. Our work makes an important step toward indistinguishable single-photon sources with near-unity collection efficiency.

Optically driving the radiative Auger transition

In a radiative Auger process, optical decay leaves other carriers in excited states, resulting in weak red-shifted satellite peaks in the emission spectrum. The appearance of radiative Auger in the emission directly leads to the question if the process can be inverted: simultaneous photon absorption and electronic demotion. However, excitation of the radiative Auger transition has not been shown, neither on atoms nor on solid-state quantum emitters. Here, we demonstrate the optical driving of the radiative Auger transition, linking few-body Coulomb interactions and quantum optics. We perform our experiments on a trion in a semiconductor quantum dot, where the radiative Auger and the fundamental transition form a Λ-system. On driving both transitions simultaneously, we observe a reduction of the fluorescence signal by up to 70%. Our results suggest the possibility of turning resonance fluorescence on and off using radiative Auger as well as THz spectroscopy with optics close to the visible regime.

Radiative Auger is a process that leads to a red-shift of the optical emission of an atom or a charged solid-state quantum emitter. Here, the authors realize the inverse process by optically driving the radiative Auger transition of a short-lived electronic state in a semiconductor quantum dot.

Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems

We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of control procedures for quantum systems with strong coupling to structured environments-where time-local descriptions fail-is a computationally challenging task. We modify the numerically exact time evolving matrix product operator (TEMPO) method, such that it allows the repeated computation of the time evolution of the reduced system density matrix for various sets of control parameters at very low computational cost. This method is potentially useful for studying numerous optimal control problems, in particular in solid state quantum devices where the coupling to vibrational modes is typically strong.

Coherent Dynamics in Quantum Emitters under Dichromatic Excitation

We characterize the coherent dynamics of a two-level quantum emitter driven by a pair of symmetrically detuned phase-locked pulses. The promise of dichromatic excitation is to spectrally isolate the excitation laser from the quantum emission, enabling background-free photon extraction from the emitter. While excitation is not possible without spectral overlap between the exciting pulse and the quantum emitter transition for ideal two-level systems due to cancellation of the accumulated pulse area, we find that any additional interactions that interfere with cancellation of the accumulated pulse area may lead to a finite stationary population inversion. Our spectroscopic results of a solid-state two-level system show that, while coupling to lattice vibrations helps to improve the inversion efficiency up to 50% under symmetric driving, coherent population control and a larger amount of inversion are possible using asymmetric dichromatic excitation, which we achieve by adjusting the ratio of the intensities between the red- and blue-detuned pulses. Our measured results, supported by simulations using a real-time path-integral method, offer a new perspective toward realizing efficient, background-free photon generation and extraction.

Suppression of decoherence tied to electron-phonon coupling in telecom-compatible quantum dots: low-threshold reappearance regime for quantum state inversion

We demonstrate suppression of dephasing tied to deformation potential coupling of confined electrons to longitudinal acoustic (LA) phonons in optical control experiments on large semiconductor quantum dots (QDs) with emission compatible with the low-dispersion telecommunications band at 1.3 µm. By exploiting the sensitivity of the electron-phonon spectral density to the size and shape of the QD, we demonstrate a fourfold reduction in the threshold pulse area required to enter the decoupled regime for exciton inversion using adiabatic rapid passage (ARP). Our calculations of the quantum state dynamics indicate that the symmetry of the QD wave function provides an additional means to engineer the electron-phonon interaction. Our findings will support the development of solid-state quantum emitters in future distributed quantum networks using semiconductor QDs.

Photon Statistics of Filtered Resonance Fluorescence

Spectral filtering of resonance fluorescence is widely employed to improve single photon purity and indistinguishability by removing unwanted backgrounds. For filter bandwidths approaching the emitter linewidth, complex behavior is predicted due to preferential transmission of components with differing photon statistics. We probe this regime using a Purcell-enhanced quantum dot in both weak and strong excitation limits, finding excellent agreement with an extended sensor theory model. By changing only the filter width, the photon statistics can be transformed between antibunched, bunched, or Poissonian. Our results verify that strong antibunching and a subnatural linewidth cannot simultaneously be observed, providing new insight into the nature of coherent scattering.

Entropy Dynamics of Phonon Quantum States Generated by Optical Excitation of a Two-Level System

In quantum physics, two prototypical model systems stand out due to their wide range of applications. These are the two-level system (TLS) and the harmonic oscillator. The former is often an ideal model for confined charge or spin systems and the latter for lattice vibrations, i.e., phonons. Here, we couple these two systems, which leads to numerous fascinating physical phenomena. Practically, we consider different optical excitations and decay scenarios of a TLS, focusing on the generated dynamics of a single phonon mode that couples to the TLS. Special emphasis is placed on the entropy of the different parts of the system, predominantly the phonons. While, without any decay, the entire system is always in a pure state, resulting in a vanishing entropy, the complex interplay between the single parts results in non-vanishing respective entanglement entropies and non-trivial dynamics of them. Taking a decay of the TLS into account leads to a non-vanishing entropy of the full system and additional aspects in its dynamics. We demonstrate that all aspects of the entropy’s behavior can be traced back to the purity of the states and are illustrated by phonon Wigner functions in phase space.

Vibrational enhancement of quadrature squeezing and phase sensitivity in resonance fluorescence

Vibrational environments are commonly considered to be detrimental to the optical emission properties of solid-state and molecular systems, limiting their performance within quantum information protocols. Given that such environments arise naturally it is important to ask whether they can instead be turned to our advantage. Here we show that vibrational interactions can be harnessed within resonance fluorescence to generate optical states with a higher degree of quadrature squeezing than in isolated atomic systems. Considering the example of a driven quantum dot coupled to phonons, we demonstrate that it is feasible to surpass the maximum level of squeezing theoretically obtainable in an isolated atomic system and indeed come close to saturating the fundamental upper bound on squeezing from a two-level emitter. We analyse the performance of these vibrationally-enhanced squeezed states in a phase estimation protocol, finding that for the same photon flux, they can outperform the single mode squeezed vacuum state.

Vibrational interactions are usually considered an obstacle to the creation and manipulation of quantum states; looking at the paradigmatic example of a driven quantum dot, the authors show how they could actually help to engineer optical states that are impossible to reach in the perfectly isolated case.

Fundamental Limits to Coherent Photon Generation with Solid-State Atomlike Transitions

Coherent generation of indistinguishable single photons is crucial for many quantum communication and processing protocols. Solid-state realizations of two-level atomic transitions or three-level spin-Λ systems offer significant advantages over their atomic counterparts for this purpose, albeit decoherence can arise due to environmental couplings. One popular approach to mitigate dephasing is to operate in the weak-excitation limit, where the excited-state population is minimal and coherently scattered photons dominate over incoherent emission. Here we probe the coherence of photons produced using two-level and spin-Λ solid-state systems. We observe that the coupling of the atomiclike transitions to the vibronic transitions of the crystal lattice is independent of the driving strength, even for detuned excitation using the spin-Λ configuration. We apply a polaron master equation to capture the non-Markovian dynamics of the vibrational manifolds. These results provide insight into the fundamental limitations to photon coherence from solid-state quantum emitters.

Phonon-Induced Enhancement of Photon Entanglement in Quantum Dot-Cavity Systems

We report on simulations of the degree of polarization entanglement of photon pairs simultaneously emitted from a quantum dot-cavity system that demand revisiting the role of phonons. Since coherence is a fundamental precondition for entanglement and phonons are known to be a major source of decoherence, it seems unavoidable that phonons can only degrade entanglement. In contrast, we demonstrate that phonons can cause a degree of entanglement that even surpasses the corresponding value for the phonon-free case. In particular, we consider the situation of comparatively small biexciton binding energies and either finite exciton or cavity mode splitting. In both cases, combinations of the splitting and the dot-cavity coupling strength are found where the entanglement exhibits a nonmonotonic temperature dependence which enables entanglement above the phonon-free level in a finite parameter range. This unusual behavior can be explained by phonon-induced renormalizations of the dot-cavity coupling g in combination with a nonmonotonic dependence of the entanglement on g that is present already without phonons.

Coupling between Rydberg States and Landau Levels of Electrons Trapped on Liquid Helium

We investigate the coupling between Rydberg states of electrons trapped on a liquid helium surface and Landau levels induced by a perpendicular magnetic field. We show that this realizes a prototype quantum system equivalent to an atom in a cavity, where their coupling strength can be tuned by a parallel magnetic field. We determine experimentally the renormalization of the atomic transition energies induced by the coupling to the cavity, which can be seen as an analog of the Lamb shift. When the coupling is sufficiently strong, the transition between the ground and first excited Rydberg states splits into two resonances corresponding to dressed states with vacuum and one photon in the cavity. Our results are in quantitative agreement with the energy shifts predicted by the effective atom in a cavity model where all parameters are known with high accuracy.

High Purcell factor generation of indistinguishable on-chip single photons

On-chip single-photon sources are key components for integrated photonic quantum technologies. Semiconductor quantum dots can exhibit near-ideal single-photon emission, but this can be significantly degraded in on-chip geometries owing to nearby etched surfaces. A long-proposed solution to improve the indistinguishablility is to use the Purcell effect to reduce the radiative lifetime. However, until now only modest Purcell enhancements have been observed. Here we use pulsed resonant excitation to eliminate slow relaxation paths, revealing a highly Purcell-shortened radiative lifetime (22.7 ps) in a waveguide-coupled quantum dot-photonic crystal cavity system. This leads to near-lifetime-limited single-photon emission that retains high indistinguishablility (93.9%) on a timescale in which 20 photons may be emitted. Nearly background-free pulsed resonance fluorescence is achieved under π-pulse excitation, enabling demonstration of an on-chip, on-demand single-photon source with very high potential repetition rates.

Environment-assisted quantum transport through single-molecule junctions

Single-molecule electronics has been envisioned as the ultimate goal in the miniaturisation of electronic circuits. While the aim of incorporating single-molecule junctions into modern technology still proves elusive, recent developments in this field have begun to enable experimental investigation of fundamental concepts within the area of chemical physics. One such phenomenon is the concept of environment-assisted quantum transport which has emerged from the investigation of exciton transport in photosynthetic complexes. Here, we study charge transport through a two-site molecular junction coupled to a vibrational environment. We demonstrate that vibrational interactions can significantly enhance the current through specific molecular orbitals. Our study offers a clear pathway towards finding and identifying environment-assisted transport phenomena in charge transport settings.

Real-time path-integral approach for dissipative quantum dot-cavity quantum electrodynamics: impure dephasing-induced effects

A dissipative quantum dot (QD)-cavity system, where the QD is initially prepared in the excited state with no photon in the cavity, coupled to a longitudinal acoustic (LA) phonon reservoir is studied using a numerically exact real-time path-integral approach. Three distinct dynamical regimes of weak (WC), strong (SC), and coherent coupling (CC) are discussed and more accurate conditions identifying them are presented. Our results show that to have the CC regime, which is characterized by clear vacuum Rabi oscillation (VRO), vacuum Rabi splitting (VRS) should be larger than the sum of the widths of the corresponding peaks. In order to distinguish between contributions of population decay and impure dephasing, induced by LA phonon bath and the dissipations, we propose a two-part phenomenological expression, corresponding to the population decay and impure dephasing, which fits the QD-cavity decay curves perfectly and is used to calculate the corresponding spectra. We demonstrate that the effective population decay rate (the emission rate) increases from the carrier recombination rate to a maximum value, which is the mean of the QD and cavity dissipation rates, with QD-cavity coupling strength. To study the role of the effective impure dephasing rate on the width of the central peak of the spectra we introduce a quantity that can also be applied in determining the distinct coupling regimes. This quantity enables us to identify the onset of the SC regime as the point where the impure dephasing term begins to contribute to the central band of the spectrum significantly, as a result of the existence of VRO with a very small frequency (unclear VRO) at the corresponding decay curve. Its contribution to the width of the central peak increases with the coupling strength up to the onset of the CC regime, then reduces as a result of the appearance of sidebands in the spectra, which originates from clear VRO. The effective population decay and impure dephasing rate contribute solely to the width-of the central and sideband peaks of the triplet spectra respectively-only beyond a very large coupling strength which is the same across the considered temperature range. For higher temperatures, the maximum achievable emission rate can be obtained at larger coupling strengths.

When do perturbative approaches accurately capture the dynamics of complex quantum systems?

Understanding the dynamics of higher-dimensional quantum systems embedded in a complex environment remains a significant theoretical challenge. While several approaches yielding numerically converged solutions exist, these are computationally expensive and often provide only limited physical insight. Here we address the question: when do more intuitive and simpler-to-compute second-order perturbative approaches provide adequate accuracy? We develop a simple analytical criterion and verify its validity for the case of the much-studied FMO dynamics as well as the canonical spin-boson model.

Near-Transform-Limited Single Photons from an Efficient Solid-State Quantum Emitter

By pulsed s-shell resonant excitation of a single quantum dot-micropillar system, we generate long streams of 1000 near-transform-limited single photons with high mutual indistinguishability. The Hong-Ou-Mandel interference of two photons is measured as a function of their emission time separation varying from 13 ns to 14.7  μs, where the visibility slightly drops from 95.9(2)% to a plateau of 92.1(5)% through a slow dephasing process occurring at a time scale of 0.7  μs. A temporal and spectral analysis reveals the pulsed resonance fluorescence single photons are close to the transform limit, which are readily useful for multiphoton entanglement and interferometry experiments.

Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity

Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms.

Harvesting, Coupling, and Control of Single-Exciton Coherences in Photonic Waveguide Antennas

We perform coherent nonlinear spectroscopy of individual excitons strongly confined in single InAs quantum dots (QDs). The retrieval of their intrinsically weak four-wave mixing (FWM) response is enabled by a one-dimensional dielectric waveguide antenna. Compared to a similar QD embedded in bulk media, the FWM detection sensitivity is enhanced by up to 4 orders of magnitude, over a broad operation bandwidth. Three-beam FWM is employed to investigate coherence and population dynamics within individual QD transitions. We retrieve their homogenous dephasing in a presence of low-frequency spectral wandering. Two-dimensional FWM reveals off-resonant Förster coupling between a pair of distinct QDs embedded in the antenna. We also detect a higher order QD nonlinearity (six-wave mixing) and use it to coherently control the FWM transient. Waveguide antennas enable us to conceive multicolor coherent manipulation schemes of individual emitters.

Modelling exciton-phonon interactions in optically driven quantum dots

We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We additionally consider the role of phonons in altering the optical emission characteristics of quantum dot devices, outlining how we must modify standard quantum optics treatments to account for the presence of the solid-state environment.

Deterministic generation of bright single resonance fluorescence photons from a Purcell-enhanced quantum dot-micropillar system

We report on the observation of bright emission of single photons under pulsed resonance fluorescence conditions from a single quantum dot (QD) in a micropillar cavity. The brightness of the QD fluorescence is greatly enhanced via the coupling to the fundamental mode of a micropillar, allowing us to determine a single photon extraction efficiency of (20.7 ± 0.8) % per linear polarization basis. This yields an overall extraction efficiency of (41.4 ± 1.5) % in our device. We observe the first Rabi-oscillation in a weakly coupled quantum dot-micropillar system under coherent pulsed optical excitation, which enables us to deterministically populate the excited QD state. In this configuration, we probe the single photon statistics of the device yielding g(2)(0) = 0.072 ± 0.011 at a QD-cavity detuning of 75 μeV.

Transform-limited single photons from a single quantum dot

Developing a quantum photonics network requires a source of very-high-fidelity single photons. An outstanding challenge is to produce a transform-limited single-photon emitter to guarantee that single photons emitted far apart in the time domain are truly indistinguishable. This is particularly difficult in the solid-state as the complex environment is the source of noise over a wide bandwidth. A quantum dot is a robust, fast, bright and narrow-linewidth emitter of single photons; layer-by-layer growth and subsequent nano-fabrication allow the electronic and photonic states to be engineered. This represents a set of features not shared by any other emitter but transform-limited linewidths have been elusive. Here, we report transform-limited linewidths measured on second timescales, primarily on the neutral exciton but also on the charged exciton close to saturation. The key feature is control of the nuclear spins, which dominate the exciton dephasing via the Overhauser field.

Photons emitted from a quantum dot typically have slightly different frequencies owing to various sources of noise. Here, the authors suppress the noise, notably the noise arising from the nuclear spins, and demonstrate single-photon emission with a transform-limited optical linewidth.

Theory of phonon-modified quantum dot photoluminescence intensity in structured photonic reservoirs

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 becomes 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 cavity waveguide, and show clear photoluminescence intensity spectral features that contain unique signatures of the interplay between phonon and photon bath coupling.

Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation

We demonstrate a new method to realize the population inversion of a single InGaAs/GaAs quantum dot excited by a laser pulse tuned within the neutral exciton phonon sideband. In contrast to the conventional method of inverting a two-level system by performing coherent Rabi oscillation, the inversion is achieved by rapid thermalization of the optically dressed states via incoherent phonon-assisted relaxation. A maximum exciton population of 0.67±0.06 is measured for a laser tuned 0.83 meV to higher energy. Furthermore, the phonon sideband is mapped using a two-color pump-probe technique, with its spectral form and magnitude in very good agreement with the result of path-integral calculations.

Deterministic and robust generation of single photons from a single quantum dot with 99.5% indistinguishability using adiabatic rapid passage

Single photons are attractive candidates of quantum bits (qubits) for quantum computation and are the best messengers in quantum networks. Future scalable, fault-tolerant photonic quantum technologies demand both stringently high levels of photon indistinguishability and generation efficiency. Here, we demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single semiconductor quantum dot using adiabatic rapid passage, a method robust against fluctuation of driving pulse area and dipole moments of solid-state emitters. The emitted photons are background-free, have a vanishing two-photon emission probability of 0.3% and a raw (corrected) two-photon Hong-Ou-Mandel interference visibility of 97.9% (99.5%), reaching a precision that places single photons at the threshold for fault-tolerant surface-code quantum computing. This single-photon source can be readily scaled up to multiphoton entanglement and used for quantum metrology, boson sampling, and linear optical quantum computing.

The role of phonons for exciton and biexciton generation in an optically driven quantum dot

For many applications of semiconductor quantum dots in quantum technology, well-controlled state preparation of the quantum dot states is mandatory. Since quantum dots are embedded in the semiconductor matrix, their interaction with phonons often plays a major role in the preparation process. In this review, we discuss the influence of phonons on three basically different optical excitation schemes that can be used for the preparation of exciton, biexciton and superposition states: a resonant excitation leading to Rabi rotations in the excitonic system, an excitation with chirped pulses exploiting the effect of adiabatic rapid passage and an off-resonant excitation giving rise to a phonon-assisted state preparation. We give an overview of experimental and theoretical results, showing the role of phonons and compare the performance of the schemes for state preparation.

Energy transport and coherence properties of acoustic phonons generated by optical excitation of a quantum dot

The energy transport of acoustic phonons generated by the optical excitation of a quantum dot as well as the coherence properties of these phonons are studied theoretically both for the case of a pulsed excitation and for a continuous wave (CW) excitation switched on instantaneously. For a pulsed excitation, depending on pulse area and pulse duration, a finite number of phonon wave packets is emitted, while for the case of a CW excitation a sequence of wave packets with decreasing amplitude is generated after the excitation has been switched on. We show that the energy flow associated with the generated phonons is partly related to coherent phonon oscillations and partly to incoherent phonon emission. The efficiency of the energy transfer to the phonons and the details of the energy flow depend strongly and in a non-monotonic way on the Rabi frequency exhibiting a resonance behavior. However, in the case of CW excitation it turns out that the total energy transferred to the phonons is directly linked in a monotonic way to the Rabi frequency.

Temperature-dependent Mollow triplet spectra from a single quantum dot: Rabi frequency renormalization and sideband linewidth insensitivity

We investigate temperature-dependent resonance fluorescence spectra obtained from a single self-assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalization of the driven dot Rabi frequency. We also present first evidence for a nonperturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is canceled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum dots may be less sensitive to changes in temperature than expected from a standard weak-coupling analysis of phonon effects.

Lamb-shift enhancement and detection in strongly driven superconducting circuits

It is shown that strong driving of a quantum system substantially enhances the Lamb shift induced by broadband reservoirs, which are typical for solid-state devices. By varying drive parameters the impact of environmental vacuum fluctuations with continuous spectral distribution onto system observables can be tuned in a distinctive way. This provides experimentally feasible measurement schemes for the Lamb shift in superconducting circuits based on Cooper pair boxes, where it can be detected either in shifted dressed transition frequencies or in pumped charge currents.

Continuous measurement of a non-Markovian open quantum system

Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural or engineered complex systems. The system is monitored via a probe resonator coupled to a broadband (Markovian) reservoir. Based on this model, we derive a formalism of stochastic hierarchy equations of motion describing the decoherence dynamics of the system conditioned on the measurement record. Furthermore, we demonstrate a spectroscopy method based on weak quantum measurement to reveal the non-Markovian nature of the environment, which we term weak spectroscopy.

Measurement of an exciton Rabi rotation in a single GaN/Al(x)Ga(1-x)N nanowire-quantum dot using photoluminescence spectroscopy: evidence for coherent control

Experimental observation of excited state exciton Rabi rotation in a single GaN quantum dot is presented. The dot is embedded in a site-controlled GaN/AlGaN nanowire. Damped oscillation is observed in the power-dependent spectra of the quantum-dot ground state upon resonant pumping of an excited state that had been identified by photoluminescence excitation spectroscopy. A discussion on the origins of the damping is given.

Excitation-induced dephasing in a resonantly driven InAs/GaAs quantum dot

We report on coherent emission of the neutral exciton state in a single semiconductor self-assembled InAs/GaAs quantum dot embedded in a one-dimensional waveguide, under resonant picosecond pulsed excitation. Direct measurements of the radiative lifetime and coherence time are performed as a function of excitation power and temperature. The characteristic damping of Rabi oscillations observed is attributed to an excitation-induced dephasing due to a resonant coupling between the emitter and the acoustic phonon bath of the matrix. Other sources responsible for the decrease of the coherence time have been evidenced, in particular an enhancement of the radiative recombination rate due to the resonant strong coupling between the dot and the one-dimensional optical mode. As a consequence, the emission couples very efficiently into the waveguide mode, leading to an additional relaxation term of the excited-state population.

Model of the optical emission of a driven semiconductor quantum dot: phonon-enhanced coherent scattering and off-resonant sideband narrowing

We study the crucial role played by the solid-state environment in determining the photon emission characteristics of a driven quantum dot. For resonant driving, we predict a phonon enhancement of the coherently emitted radiation field with increasing driving strength, in stark contrast to the conventional expectation of a rapidly decreasing fraction of coherent emission with stronger driving. This surprising behavior results from thermalization of the dot with respect to the phonon bath and leads to a nonstandard regime of resonance fluorescence in which significant coherent scattering and the Mollow triplet coexist. Off resonance, we show that despite the phonon influence, narrowing of dot spectral sideband widths can occur in certain regimes, consistent with an experimental trend.

Collective suppression of linewidths in circuit QED

We report the experimental observation and a theoretical explanation of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.

Thermal effects on photon-induced quantum transport in a single quantum dot

We theoretically investigate laser induced quantum transport in a single quantum dot attached to electrical contacts. Our approach, based on a nonequilibrium Green function technique, allows us to include thermal effects on the photon-induced quantum transport and excitonic dynamics, enabling the study of non-Markovian effects. By solving a set of coupled integrodifferential equations, involving correlation and propagator functions, we obtain the photocurrent and the dot occupation as a function of time. Two distinct sources of decoherence, namely, incoherent tunneling and thermal fluctuations, are observed in the Rabi oscillations. As temperature increases, a thermally activated Pauli blockade results in a suppression of these oscillations. Additionally, the interplay between photon and thermally induced electron populations results in a switch of the current sign as time evolves and its stationary value can be maximized by tuning the laser intensity.

On-demand semiconductor single-photon source with near-unity indistinguishability

Single-photon sources based on semiconductor quantum dots offer distinct advantages for quantum information, including a scalable solid-state platform, ultrabrightness and interconnectivity with matter qubits. A key prerequisite for their use in optical quantum computing and solid-state networks is a high level of efficiency and indistinguishability. Pulsed resonance fluorescence has been anticipated as the optimum condition for the deterministic generation of high-quality photons with vanishing effects of dephasing. Here, we generate pulsed single photons on demand from a single, microcavity-embedded quantum dot under s-shell excitation with 3 ps laser pulses. The π pulse-excited resonance-fluorescence photons have less than 0.3% background contribution and a vanishing two-photon emission probability. Non-postselective Hong-Ou-Mandel interference between two successively emitted photons is observed with a visibility of 0.97(2), comparable to trapped atoms and ions. Two single photons are further used to implement a high-fidelity quantum controlled-NOT gate.

Noncanonical statistics of a spin-boson model: theory and exact Monte Carlo simulations

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid, and equilibrium quantum statistics of the system may be noncanonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study noncanonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify noncanonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, noncanonical statistics enhances as temperature decreases but vanishes at high temperature.

Coherent optical control of the spin of a single hole in an InAs/GaAs quantum dot

We demonstrate coherent optical control of a single hole spin confined to an InAs/GaAs quantum dot. A superposition of hole-spin states is created by fast (10-100 ps) dissociation of a spin-polarized electron-hole pair. Full control of the hole spin is achieved by combining coherent rotations about two axes: Larmor precession of the hole spin about an external Voigt geometry magnetic field, and rotation about the optical axis due to the geometric phase shift induced by a picosecond laser pulse resonant with the hole-trion transition.

Resonance fluorescence from semiconductor quantum dots: beyond the Mollow triplet

We show that the resonance fluorescence spectrum of a quantum dot excited by a strong optical pulse contains multiple peaks beyond those of the Mollow triplet. We show that as the area of the optical pulse is increased, new side peaks split off the central peak and shift in frequency. A simple analytical theory has been derived, which quantitatively accounts for the appearance and position of the peaks. This theory explains the physics responsible for the multiple peaks. By considering the time-dependent spectrum we demonstrate a time ordering of the side peaks, which is further evidence for the suggested physical explanation.

Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity

Detailed properties of resonance fluorescence from a single quantum dot in a micropillar cavity are investigated, with particular focus on emission coherence in the dependence on optical driving field power and detuning. A power-dependent series over a wide range reveals characteristic Mollow triplet spectra with large Rabi splittings of |Ω|≤15  GHz. In particular, the effect of dephasing in terms of systematic spectral broadening ∝Ω(2) of the Mollow sidebands is observed as a strong fingerprint of excitation-induced dephasing. Our results are in excellent agreement with predictions of a recently presented model on phonon-dressed quantum dot Mollow triplet emission in the cavity-QED regime.

Phonon-dressed Mollow triplet in the regime of cavity quantum electrodynamics: excitation-induced dephasing and nonperturbative cavity feeding effects

We study the resonance fluorescence spectra of a driven quantum dot placed inside a high-Q semiconductor cavity and interacting with an acoustic phonon bath. The dynamics is calculated using a time-convolutionless master equation in the polaron frame. We predict pronounced spectral broadening of the Mollow sidebands through off-resonant cavity emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency in direct agreement with recent experiments using semiconductor micropillars [S. M. Ulrich et al., preceding Letter, Phys. Rev. Lett. 106, 247402 (2011)]. We also demonstrate that, surprisingly, phonon coupling actually helps resolve signatures of the elusive second rungs of the Jaynes-Cummings ladder states via off-resonant cavity feeding. Both multiphonon and multiphoton effects are shown to play a qualitatively important role on the fluorescence spectra.