Open classical and quantum systems with effective parity-time ($\mathcal{PT}$) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocal devices. And yet, how such effective $\mathcal{PT}$-symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. Here, starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED (DQD-circuit QED) set-up, which can be controllably tuned to the $\mathcal{PT}$-symmetric point. This effective Hamiltonian governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them. Our analysis also reveals the effect of quantum fluctuations on the $\mathcal{PT}$ symmetric system. The $\mathcal{PT}$-transition is, then, observed both in the dynamics of cavity observables as well as via an input-output experiment. As a simple application of the $\mathcal{PT}$-transition in this set-up, we show that loss-induced enhancement of amplification and lasing can be observed in the coupled cavities. By comparing our results with two conventional local Lindblad equations, we demonstrate the utility and limitations of the latter. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in quantum regime, as well as its potential applications for quantum technology.
A quantum dot strongly coupled to a single high finesse optical microcavity mode constitutes a new fundamental system for quantum optics. Here, the effect of exciton-phonon interactions on reversible quantum-dot cavity coupling is analysed without making Born-Markov approximation. The analysis is based on techniques that have been used to study the ``spin boson'' Hamiltonian. Observability of vacuum-Rabi splitting depends on the strength and the frequency dependence of the spectral density function characterizing the interactions with phonons, both of which can be influenced by phonon confinem…
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 investigate photon-mediated transport processes in a hybrid circuit-QED structure consisting of two double quantum dots coupled to a common microwave cavity. Under suitable resonance conditions, electron transport in one double quantum dot is facilitated by the transport in the other dot via photon-mediated processes through the cavity. We calculate the average current in the quantum dots, the mean cavity photon occupation, and the current cross-correlations with both a full numerical simulation and a recursive perturbation scheme that allows us to include the influence of the cavity order-…
We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of dynamical evolution one can generate multipartite entangled coherent exciton states or multiqubit $W$ states by initially preparing the cavity field in a superposition of coherent states or the Fock state with one photon, respectively. Finally we study environmental effects on multipartite entanglement generation and find that the decay rate f…
The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant timescales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel control…
The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quan…
A quantum information processing scheme is proposed with semiconductor quantum dots located in a high-Q single mode QED cavity. The spin degrees of freedom of one excess conduction electron of the quantum dots are employed as qubits. Excitonic states, which can be produced ultrafastly with optical operation, are used as auxiliary states in the realization of quantum gates. We show how properly tailored ultrafast laser pulses and Pauli-blocking effects, can be used to achieve a universal encoded quantum computing.
Bell's inequality in three coupled quantum dots (QDs) within cavity QED, including Forster and exciton-phonon interactions, is investigated theoretically. For an initially entangled state, Bell's inequality is valid for certain times and violated for some other times. It is shown that the system moves from a product state to a entangled state and back again during it's time evolution.
Emergent cavity-QED dynamics along the edge of a photonic lattice
Università degli Studi di Palermo（巴勒莫大学）；Zhoukou Normal University（周口师范学院）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Istituto Nanoscienze-CNR（意大利国家研究委员会纳米科学研究所）
We present evidence of cavity quantum electrodynamics from a sparse density of strongly quantum-confined Pb-chalcogenide nanocrystals (between 1 and 10) approaching single-dot levels on moderately high-Q mesoscopic silicon optical cavities. Operating at important near-infrared (1500-nm) wavelengths, large enhancements are observed from devices and strong modifications of the QD emission are achieved. Saturation spectroscopy of coupled QDs is observed at 77K, highlighting the modified nanocrystal dynamics for quantum information processing.
A quantum dot can be used as a source of one- and two-photon states and of polarisation entangled photon pairs. The emission of such states is investigated from the point of view of frequency-resolved two-photon correlations. These follow from a spectral filtering of the dot emission, which can be achieved either by using a cavity or by placing a number of interference filters before the detectors. The combination of these various options is used to iteratively refine the emission in a "distillation" process and arrive at highly correlated states with a high purity. So-called "leapfrog process…
We investigate the photon induced tunneling phenomena in a photonic crystal cavity containing a strongly coupled quantum dot and describe how this tunneling can be used to generate photon states consisting mainly of a particular Fock state. Additionally, we study experimentally the photon-induced tunneling as a function of excitation laser power and frequency and show the signature of second rung of the Jaynes-Cummings Hamiltonian in the observed photon-statistics.
We present a method to enact a deterministic, measurement-free, optically generated controlled-phase gate on two qubits defined by single electrons trapped in large-area quantum dots in a planar microcavity. This method is robust to optical quantum dot inhomogeneity, requires only a modest-$Q$ planar cavity, employs only a single laser pulse, and allows the integration of many entangled qubits on one semiconductor chip. We present the gate in the contexts of both adiabatic evolution and geometric phases, and calculate the degradation of performance in the presence of both spontaneous emission …
We investigate the influence of the electron-phonon interaction on the decay dynamics of a quantum dot coupled to an optical microcavity. We show that the electron-phonon interaction has important consequences on the dynamics, especially when the quantum dot and cavity are tuned out of resonance, in which case the phonons may add or remove energy leading to an effective non-resonant coupling between quantum dot and cavity. The system is investigated using two different theoretical approaches: (i) a second-order expansion in the bare phonon coupling constant, and (ii) an expansion in a polaron-…
We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is observed. We find a minimum second-order correlation $g^{(2)}(0)\approx0.37$ which corresponds to $g^{(2)}(0)\approx0.005$ when corrected for detector jitter, and observe the expected polarization dependenc…
We propose a method to achieve photon pair propagation in an array of three-level superconducting circuits. Assuming experimentally accessible three-level artificial atoms with strong anharmonicity coupled via microwave transmission lines in both one and two dimensions we analyze the circuit Quantum Electrodynamics(QED) of the system. We explicitly show that for a suitable choice of the coupling ratio between different levels, the single photon propagation is suppressed and the propagation of photon pairs emerges. This propagation of photon pairs leads to the pair superfluid of polaritons asso…
The dynamics of the entanglement for coherent excitonic states in the system of two coupled large semiconductor quantum dots ($R/a_{B}\gg 1$) mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is detected in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of…
Motivated by recent experiments on the generation of coherent light in engineered hybrid quantum systems, we investigate gain in a microwave photonic cavity coupled to quantum dot structures, and develop concrete directions for achieving a giant amplification in photon transmission. We propose two architectures for scaling up the electronic gain medium: (i) $N$ double quantum dot systems (N-DQD), (ii) $M$ quantum dots arranged in series akin to a quantum cascade laser setup. In both setups, the fermionic reservoirs are voltage biased, and the quantum dots are coupled to a single-mode cavity. O…
This paper discusses an attempt to develop a mathematically rigorous theory of Quantum Electrodynamics (QED). It deviates from the standard version of QED mainly in two aspects: it is assumed that the Coulomb forces are carried by transversely polarized photons, and a reducible representation of the canonical commutation and anti-commutation relations is used. Both interventions together should suffice to eliminate the mathematical inconsistencies of standard QED.
Condensed matter systems provide alternative `vacua' exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine-structure constant $α$, which parametrizes how strongly matter couples to light: $α_{\mathrm{QSI}}$ is more than an order of magnitude greater than $α_{\mathrm{QED}} \approx 1/13…
We present a semiconductor master equation technique to study the input/output characteristics of coherent photon transport in a semiconductor waveguide-cavity system containing a single quantum dot. We use this approach to investigate the effects of photon propagation and anharmonic cavity-QED for various dot-cavity interaction strengths, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down, even in the weak coupling regime.…
In this work we discuss the emergence of approximate causality in a general setup from waveguide QED -i.e. a one-dimensional propagating field interacting with a scatterer. We prove that this emergent causality translates into a structure for the N-photon scattering matrix. Our work builds on the derivation of a Lieb-Robinson-type bound for continuous models and for all coupling strengths, as well as on several intermediate results, of which we highlight (i) the asymptotic independence of space-like separated wave packets, (ii) the proper definition of input and output scattering states, and (…
In an oxide apertured quantum dot (QD) micropillar cavity-QED system, we found strong QD hysteresis effects and lineshape modifications even at very low intensities corresponding to less than 0.001 intracavity photons. We attribute this to the excitation of charges by the intracavity field; charges that get trapped at the oxide aperture, where they screen the internal electric field and blueshift the QD transition. This in turn strongly modulates light absorption by cavity QED effects, eventually leading to the observed hysteresis and lineshape modifications. The cavity also enables us to obse…
Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al, Phys.Rev. B {\bf 78}, 085307(2008) and ibid {\bf 80}, 205326(2009)]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [S.M. Tan, J. Opt. B {\bf 1}, 424 (1999)]…
We propose a special cavity design that is constructed by terminating a one-dimensional waveguide with a perfect mirror at one end and doping a two-level atom at the other. We show that this atom plays the intrinsic role of a semi-transparent mirror for single photon transports such that quasi-normal modes (QNM's) emerge spontaneously in the cavity system. This atomic mirror has its reflection coefficient tunable through its level spacing and its coupling to the cavity field, for which the cavity system can be regarded as a two-end resonator with a continuously tunable leakage. The overall inv…
We propose that condensed matter phenomena involving the spontaneous emergence and dynamics of crystal lattices can be realized in the setting of ultracold Bose-condensed atoms coupled to multimode cavities. Previously, it was shown that in the case of a transversely pumped single-mode cavity, the atoms self-organize at either the even or the odd antinodes of the cavity mode, given sufficient pump intensity, and hence spontaneously break a discrete translational symmetry. Here, we demonstrate that in multimode cavities the self-organization brings the additional feature of continuous translati…
We theoretically propose a scheme for a spin quantum bit based on a double quantum dot contacted to ferromagnetic elements. Interface exchange effects enable an all electric manipulation of the spin and a switchable strong coupling to a superconducting coplanar waveguide cavity. Our setup does not rely on any specific band structure and can in principle be realized with many different types of nanoconductors. This allows to envision on-chip single spin manipulation and read-out using cavity QED techniques.
Cavity-QED analysis of InAs quantum-dot single photon production
Center for Integrated Nanotechnologies, Sandia National Laboratories（桑迪亚国家实验室集成纳米技术中心）；Sandia National Laboratories（桑迪亚国家实验室）；Department of Electrical and Computer Engineering, University of California, Santa Barbara（加州大学圣塔芭芭拉分校电气与计算机工程系）；Institute for Theoretical Physics, University of Bremen（不来梅大学理论物理研究所）
Structured Non-Locality and Emergent Locality in Cavity-QED Many-Body Dynamics
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；ICREA-Institució Catalana de Recerca i Estudis Avançats（ICREA-加泰罗尼亚高级研究学院）
The cluster state quantum computation is a versatile approach to build a scalable quantum computer. In this thesis we theoretically demonstrate that a one dimensional array of double quantum dots with long spin relaxation time can evolve to a cluster state via capacitive coupling to a transmission line resonator. By applying an oscillating voltage to gates of the double quantum dots, we prove that the evolution operator for such interaction is an Ising-like operator. Subsequently, the interacting qubits will become highly entangled that we realize a cluster state. Furthermore, we propose an ex…
We present a simple extension of the semi-classical model for a two-level system in a cavity, in order to incorporate multiple polarized transitions, such as those appearing in neutral and charged quantum dots (QDs), and two nondegenerate linearly polarized cavity modes. We verify the model by exact quantum master equation calculations, and experimentally using a neutral QD in a polarization non-degenerate micro-cavity, in both cases we observe excellent agreement. Finally, the usefulness of this approach is demonstrated by optimizing a single-photon source based on polarization postselection,…
The bichromatic driving of a solid state cavity quantum electrodynamics system is used to probe cavity dressed state transitions and observe coherent interaction between the system and the light field. We theoretically demonstrate the higher order cavity-dressed states, supersplitting, and AC stark shift in a solid state system comprised of a quantum dot strongly coupled to a photonic crystal cavity for on- and far off-resonant cases. For the off-resonant case, phonons mediate off-resonant coupling between the quantum dot and the photonic resonator, a phenomenon unique to solid state cavity qu…
A polarization degenerate microcavity containing charge-controlled quantum dots (QDs) enables equal coupling of all polarization degrees of freedom of light to the cavity QED system, which we explore through resonant laser spectroscopy. We first measure interference of the two fine-split neutral QD transitions and find very good agreement of this V-type three-level system with a coherent polarization dependent cavity QED model. We also study a charged QD that suffers from decoherence, and find also in this case that availability of the full polarization degrees of freedom is crucial to reveal …
By exploiting a system of three distant cavities, we propose a scheme for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entan-gled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negli-gible the destruction of entanglement due to decoherence arises from photon losses, is effective…
Polarized cross-correlation spectroscopy on a quantum dot charged with a single hole shows the sequential emission of photons with common circular polarization. This effect is visible without magnetic field, but becomes more pronounced as the field along the quantization axis is increased. We interpret the data in terms of electron dephasing in the X+ state caused by the Overhauser field of nuclei in the dot. We predict the correlation timescale can be increased by accelerating the emission rate with cavity-QED.
A scheme for probabilistic entanglement generation between two distant single electron doped quantum dots, each placed in a high-Q microcavity, by detecting strong coherent light which has interacted dispersively with both subsystems and experienced Faraday rotation due to the spin selective trion transitions is discussed. In order to assess the applicability of the scheme for distant entanglement generation between atomic qubits proposed by T.D. Ladd et al. [New J. Phys. 8, 184 (2006)] to two distant quantum dots, one needs to understand the limitations imposed by hyperfine interactions of th…
Emergent Bell Phase in an Electro-Nanomechanical Quantum Simulator
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；ICFO - Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；ICREA（加泰罗尼亚高级研究院）
Optical cavities can induce photon-mediated interactions among intracavity-trapped atoms. Multimode cavities provide the ability to tune the form of these interactions, e.g., by inducing a nonlocal, sign-changing term to the interaction. By accounting for the Gouy phase shifts of the modes in a nearly degenerate, confocal, Fabry-Perot cavity, we provide a theoretical description of this interaction, along with additional experimental confirmation to complement that presented in the companion paper, Ref. [1]. Furthermore, we show that this interaction should be written in terms of a complex ord…
We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave induced consecutive passages under a double resonance condition, we observe novel Landau-Zener-Stückelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system, and are consistent with the simulations based on our theoretical model. This study provides an excellent platform f…
Differences in the confinement of electrons and holes in quantum dots are shown to profoundly impact the magnitude of scattering with acoustic phonons in materials where crystal deformation shifts the conduction and valence band in the same direction. Using an extensive model that includes the non-Markovian nature of the phonon reservoir, we show how the effect may be addressed by photoluminescence excitation spectroscopy of a single quantum dot. We also investigate the implications for cavity QED, i.e. a coupled quantum dot-cavity system, and demonstrate that the phonon scattering may be stro…
The strong-coupling regime of cavity-quantum-electrodynamics (cQED) represents light-matter interaction at the fully quantum level. Adding a single photon shifts the resonance frequencies, a profound nonlinearity. cQED is a test-bed of quantum optics and the basis of photon-photon and atom-atom entangling gates. At microwave frequencies, success in cQED has had a transformative effect. At optical frequencies, the gates are potentially much faster and the photons can propagate over long distances and be easily detected, ideal features for quantum networks. Following pioneering work on single at…
We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to other qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then…
Toida et al. claim in their recent article [Phys. Rev. Lett. 110, 066802 (2013)] that they `report a direct observation of vacuum Rabi splitting in a GaAs/AlGaAs double quantum dot (DQD) based charge qubit coupled with a superconducting coplanar waveguide (CPW) resonator'. In this comment, we challenge the main claims made in their paper and show that their results: a) do not provide any evidence of vacuum Rabi oscillations and b) do not provide any direct evidence of vacuum Rabi splitting.
Quantum coherence in solid-state systems has been demonstrated in superconducting circuits and in semiconductor quantum dots. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons. Coherent coupling of superconducting circuits to microwave photons, circuit quantum electrodynamics (QED), has opened up new research directions and enabled long distance coupling of qubits. Here we demonstrate how the electromagnetic field of a superconducting microwave resonat…
Cavity-QED enhancement of quantum entanglement and battery performance in double quantum dots
P. J. Šafárik University（帕·约·沙法里克大学）；Abbottabad University of Science and Technology（阿伯塔巴德科学与技术大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
We measure the detuning-dependent dynamics of a quasi-resonantly excited single quantum dot coupled to a micropillar cavity. The system is modeled with the dissipative Jaynes-Cummings model where all experimental parameters are determined by explicit measurements. We observe non-Markovian dynamics when the quantum dot is tuned into resonance with the cavity leading to a non-exponential decay in time. Excellent agreement between experiment and theory is observed with no free parameters providing the first quantitative description of an all-solid-state cavity QED system based on quantum dot emit…
Quantum photonic integrated circuit (QPIC) is a promising tool for constructing integrated devices for quantum technology applications. In the optical regime, silicon photonics empowered by complementary-metal-oxide-semiconductor (CMOS) technology provides optical components useful for realizing large-scale QPICs. Optical nonlinearity at the single-photon level is required for QPIC to facilitate photon-photon interaction. However, to date, realization of optical elements with deterministic( i.e., not probabilistic) single-photon nonlinearity by using silicon-based components is challenging, de…
We propose an interface between the spin of a photon and the spin of an electron confined in a quantum dot embedded in a microcavity operating in the weak coupling regime. This interface, based on spin selective photon reflection from the cavity, can be used to construct a CNOT gate, a multi-photon entangler and a photonic Bell-state analyzer. Finally, we analyze experimental feasibility, concluding that the schemes can be implemented with current technology.
