Spontaneous decay of an excited atom in a waveguide is essentially modified by the spatial structure of vacuum reservoir. This is particularly exciting in view of a range of applications for quantum information science. We found out that spontaneous decay can be incomplete, so the time dependence of the excited state population asymptotically approaches to a nonzero value, under the conditions when the atomic transition frequency is larger than the cutoff frequency of a waveguide and far from the vicinities of the cut-offs. Discovered effect is explained by the emergence of the dark state, which is non-decaying due to polarization selection rules. It was revealed for single-mode waveguide with rectangular cross section both in single-atom case and diatomic case when the long-range dipole-dipole interaction plays a significant role.
An electronically excited atom or molecule located outside but near a planar optical waveguide can decay by spontaneous emission of a photon into a guided mode of the waveguide. We outline a QED theory for calculating the probability for this process and describe general physical insights from that theory. A couple of representative examples are discussed in detail.
Quantum mechanical treatment of light inside dielectric media is important to understand the behavior of an optical system. In this paper, a two-level atom embedded in a rectangular waveguide surrounded by a perfect electric conductor is considered. Spontaneous emission, propagation, and detection of a photon are described by the second quantization formalism. The quantized modes for light are divided into two types: photonic propagating modes and localized modes with exponential decay along the direction of waveguide. Though spontaneous emission depends on all possible modes including the loc…
Periodically-tapered-waveguides technique is an emerging potential route to establish quasi-phase-matching schemes for efficient on-demand parametric interactions in third-order nonlinear materials. In this paper, I investigate this method in enhancing spontaneous photon-pairs emission in fibres and planar waveguides with sinusoidally-varying cross sections. I have developed a general robust quantum model to study this process under continuous or pulsed-pump excitations. The model shows a great enhancement in photon-pairs generation in waveguides with a small number of tapering periods that ar…
A novel time-domain approach using the momentum operator is used to model spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of self- and cross-phase modulation on the photon-pair production rate and heralded photon purity are investigated. We show that in the special case where only one half of the photon-pair state is filtered that the generation rate and purity of the heralded photons are unmodified by the presence of self- and cross-phase modulation. The significance of this special case arises when we consider heralded single-photon sources, where future schemes a…
We investigate the spontaneous emission of a two-level system, e.g. an atom or atomlike object, coupled to a single-end, i.e., semi-infinite, one-dimensional photonic waveguide such that one end behaves as a perfect mirror while light can pass through the opposite end with no back-reflection. Through a quantum microscopic model we show that such geometry can cause non-exponential and long-lived atomic decay. Under suitable conditions, a bound atom-photon stationary state appears in the atom-mirror interspace so as to trap a considerable amount of initial atomic excitation. Yet, this can be rel…
We study a quantum electrodynamics (QED) system made of an two-level atom and a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one end. The spatial dependence of the atomic spontaneous emission has been included in the coupling strength relevant to the eigenmodes of the waveguide. The role of retardation is studied for the atomic transition frequency far away from the cutoff frequencies. The atom-mirror distance introduces different phases and retardation times into the dynamics of the atom interacting resonantly with the corresponding transverse modes. It is found t…
In this paper we show that by suitably tailoring the dispersion characteristics of a Bragg reflection waveguide (BRW) mode, it is possible to achieve efficient photon pair generation over a large pump bandwidth while maintaining narrow signal bandwidth. The structure proposed consists of a high index core BRW with a periodically poled GaN core and periodically stratified cladding made up of alternate layers of $Al_{0.02}Ga_{0.98}N$ and $Al_{0.45}Ga_{0.55}N$. Such photon-pair generators should find applications in realizing compact and stable sources for quantum information processing.
We report on the demonstration of correlated photon pair generation in quasi-phase-matched superlattice AlGaAs waveguides with a high coincidence-to-accidental ratio (CAR); with a continuous (CW) pump, the observed CAR (>100) is more than two order of magnitudes improvement over previously reported spontaneous down conversion (SPDC) schemes in AlGaAs waveguides with a pulsed pump.
We study the spontaneous emission (SE) of an excited two-level nonrelativistic system (TLS) interacting with the vacuum in a waveguide of rectangular cross section. All TLS's transitions and the center-of-mass motion of the TLS are taken into account. The SE rate and the carried frequency of the emitted photon for the TLS initial being at rest is obtained, it is found in the first order of the center of mass (c.m.) that the frequency of the emitted photon could be smaller or larger than the transition frequency of the TLS but the SE rate is smaller than the SE rate $Γ_{f}$ of the TLS fixed in …
We present a new method to measure the guided, radiated and total decay rates in one-dimensional waveguides. It is also theoretically shown that large modifications of the total decay rate can be achieved in realistic EDFAs and EDWAs with effective mode area radii smaller than ~ 1 micrometer.
The spontaneous decay of a V-type three-level atom placed in a negative-refractive-index waveguide is analyzed. We find that in thin waveguides, highly efficient surface guided modes are supported, which do not occur in positive index waveguides. In addition, at low absorption, the mode density and thus spontaneous emission into particular regular guided modes is enhanced by several orders of magnitude as compared to regular dielectric waveguides. The asymmetries between emission into the different modes and the enhancement of particular guided modes allow to induce strong spontaneous-emission…
We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss. Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients. In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator,…
We analyze the process of simultaneous photon pair generation and quantum walks realized by spontaneous parametric down conversion of a pump beam in a quadratic nonlinear waveguide array. We demonstrate that this flexible platform allows for creating quantum states with different spatial correlations. In particular, we predict that the output photon correlations can be switched from photon bunching to antibunching controlled entirely classically by varying the temperature of the array or the spatial profile of the pump beam.
We investigate the entanglement dynamics of two two-level emitters (qubits) mediated by a semiinfinite, one-dimensional (1D) photonic waveguide. The coupling of each qubit to the waveguide is chiral, which depends on the propagation direction of light. The finite end of the waveguide is terminated by a perfect mirror, such that coherent quantum feedback is introduced to the system. We show that the chirally generated entanglement between the qubits can be preserved by controlling the time delay of the feedback. Moreover, when the time delay is negligible, the qubit-qubit reduced system evolves…
We demonstrate a monolithically integrable heralded photon source in a femtosecond laser direct written glass waveguide. The generation of photon pairs with a wide wavelength separation requires a concomitant large birefringence in the normal dispersion regime. Here, by incorporation of side-stress tracks, we produce a waveguide with a birefringence of $1.64\times~10^{-4}$ and propagation loss as low as 0.21 dB/cm near 980~nm. We measure photon pairs with 300~nm wavelength separation at an internal generation rate exceeding $5.05\times10^6$/s. The second order correlations indicate that the ge…
High-efficient and high-purity photon sources are highly desired for quantum information processing. We report the design of a chip-scale hybrid SixNy and thin film periodically-poled lithium niobate waveguide for generating high-purity type-II spontaneous parametric down conversion (SPDC) photons in telecommunication band. The modeled second harmonic generation efficiency of 225% W^(-1)*cm^(-2) is obtained at 1560nm. Joint spectral analysis is performed to estimate the frequency correlation of SPDC photons, yielding intrinsic purity with up to 95.17%. The generation rate of these high-purity …
We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\cal PT$ or $\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first tim…
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single ph…
A new method for generating entangled photons with controllable frequency correlation via spontaneous parametric down-conversion (SPDC) is presented. The method entails initiating counter-propagating SPDC in a single-mode nonlinear waveguide by pumping with a pulsed beam perpendicular to the waveguide. The method offers several advantages over other schemes, including the ability to generate frequency-correlated photon pairs regardless of the dispersion characteristics of the system. Numerical evidence demonstrates the improvement provided by this source in the special case of frequency-correl…
We study the spectral properties of Spontaneous Parametric Down Conversion in a periodically poled waveguided structure of KTP crystal pumped by ultra-short pulses. Our theoretical analysis reveals a strongly multimode and asymmetric structure of the two-photon spectral amplitude for type-II SPDC. Experimental evidence, based on Hong-Ou-Mandel polarization interference with narrowband filtering, confirms this result.
We show that a useful connection exists between spontaneous parametric downconversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result deepens the relationship between quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of their quantum performance in the presence of loss based solely on classical measurements.
Multi-emitter oscillating bound states in Waveguide QED
Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所（INMA），西班牙科学研究中心-萨拉戈萨大学）；Departamento de Fisica de la Materia Condensada, Universidad de Zaragoza（萨拉戈萨大学凝聚态物理系）；Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学学院）
We theoretically investigate the spontaneous emission of a point--like dipolar emitter located near a two--dimensional (2D) plasmonic waveguide of arbitrary form. We invoke an explicite link with the density of modes of the waveguide describing the electromagnetic channels into which the emitter can couple. We obtain a closed form expression for the coupling to propagative plasmon, extending thus the Purcell factor to plasmonic configurations. Radiative and non-radiative contributions to the spontaneous emission are also discussed in details.
We study the presence of nontrivial bound states of two multilevel quantum emitters and the photons propagating in a linear waveguide. We characterize the conditions for the existence of such states and determine their general properties, focusing in particular on the entanglement between the two emitters, that increases with the number of excitations. We discuss the relevance of the results for entanglement preservation and generation by spontaneous relaxation processes.
We consider a quantum-electrodynamic problem of the spontaneous emission from a two-dimensional (2D) emitter, such as a quantum well or a 2D semiconductor, placed in a quasi-2D waveguide or cavity with subwavelength confinement in one direction. We apply the Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. The Langevin noise operators that we introduce do not depend on any particular model of dissipative reservoir and can be applied to any dissipation mechanism. Moreover, our approac…
Josephson circuits provide a realistic physical setup where the light-matter fine structure constant can become of order one, allowing to reach a regime dominated by non-perturbative effects beyond standard quantum optics. Simple processes, such as spontaneous emission, thus acquire a many-body character, that can be tackled using a new description of the time-dependent state vector in terms of quantum-superposed coherent states. We find that spontaneous atomic decay at ultrastrong coupling leads to the emission of spectrally broad Schrödinger cats rather than of monochromatic single photons. …
Linear discrete diffraction of light within a waveguide array allows control over the longitudinal spatial profile of light. We propose a method of using this control to effectively modulate the nonlinearity in a spontaneous four wave mixing system. This allows the removal spurious frequency correlations between the generated signal and idler photon pairs. Weaving our method into a recipe for waveguide design, we demonstrate a spectral purity improvement from P = 0.78 to near saturation at P = 0.97, for a simple silicon-on-insulator geometry.
Light escape from an optical waveguide side-coupled to a waveguide lattice provides a photonic analogue of the spontaneous emission process of an excited two-level atom in a one-dimensional array of cavities. According to the Fermi golden rule the decay process is prevented when the atomic resonance frequency falls in a stop band of the lattice, while time-reversal symmetry ensures that the spontaneously emitted photon has equal probability to propagate in opposite directions of the array. This scenario is drastically modified when the quantum emitter drifts along the lattice at a constant spe…
We investigate the behavior of two quantum emitters (two-level atoms) embedded in a linear waveguide, in a quasi-one-dimensional configuration. Since the atoms can emit, absorb and reflect radiation, the pair can spontaneously relax towards an entangled bound state, under conditions in which a single atom would instead decay. We analyze the properties of these bound states, which occur for resonant values of the interatomic distance, and discuss their relevance with respect to entanglement generation. The stability of such states close to the resonance is studied, as well as the properties of …
In this paper, we analyze spontaneous parametric down conversion in a 2D slant strip type periodically poled planar waveguide and show that such a configuration has efficiencies higher than in the case of bulk crystals with the possibility of ease of collection like in channel waveguides with the additional feature of wavelength tunability. The proposed design should find applications in quantum processing using integrated quantum optics.
We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in $k$-space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the …
Bragg waveguides are promising optical filters for pump suppression in spontaneous Four-Wave Mixing (FWM) photon sources. In this work, we investigate the generation of unwanted photon pairs in the filter itself. We do this by taking advantage of the relation between spontaneous and classical FWM, which allows for the precise characterisation of the nonlinear response of the device. The pair generation rate estimated from the classical measurement is compared with the theoretical value calculated by means of a full quantum model of the filter, which also allows to investigate the spectral prop…
We propose to integrate the electro-optic tuning function into polarization-entangled photon pair generation process in a periodically poled lithium niobate (PPLN). Due to the versatility of PPLN, both the spontaneously parametric down conversion and electro-optic polarization rotation effects could be realized simultaneously. Orthogonally-polarized and parallel-polarized photon pairs thus are instantly switchable by tuning the applied field. The characteristics of the source are investigated showing adjustable bandwidths and high entanglement degrees. Moreover, other kinds of reconfigurable e…
In this paper we show how to generate efficiently entanglement between two artificial giant atoms with photon-mediated interactions in a waveguide. Taking advantage of the adjustable decay processes of giant atoms into the waveguide, and of the interference processes, spontaneous sudden birth of entanglement can be strongly enhanced with giant atoms. Highly entangled states can also be generated in the steady-state regime when the system is driven by a resonant classical field. We show that the statistics of the light emitted by the system can be used as a witness of the presence of entangleme…
Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in t…
We study the generation of spontaneous entanglement between two qubits chirally coupled to a waveguide. The maximum achievable concurrence is demonstrated to increase by a factor of $4/e \sim 1.5$ as compared to the non-chiral coupling situation. The proposed entanglement scheme is shown to be robust against variation of the qubit properties such as detuning and separation, which are critical in the non-chiral case. This result relaxes the restrictive requirements of the non-chiral situation, paving the way towards a realistic implementation. Our results demonstrate the potential of chiral wav…
Robust Superradiance and Spontaneous Spin Ordering in Disordered Waveguide Quantum Electrodynamics
Technical University of Munich（慕尼黑工业大学）；TUM School of Natural Sciences, Physics Department（慕尼黑工业大学自然科学学院物理系）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
Photonic-based qubits and integrated photonic circuits have enabled demonstrations of quantum information processing (QIP) that promises to transform the way in which we compute and communicate. To that end, sources of polarization-entangled photon pair states are an important enabling technology, especially for polarization-based protocols. However, such states are difficult to prepare in an integrated photonic circuit. Scalable semiconductor sources typically rely on nonlinear optical effects where polarization mode dispersion (PMD) degrades entanglement. Here, we directly generate polarizat…
We put forward a new highly efficient source of paired photons entangled in polarization with an ultra-large bandwidth. The photons are generated by means of a conveniently designed spontaneous parametric down-conversion process in a semiconductor type-II Bragg reflection waveguide. The proposed scheme aims at being a key element of an integrated source of polarization-entangled photon pairs highly suitable for its use in a multi-user quantum-key-distribution system.
We report an interference experiment of spontaneous emission of light from two distant solid-state ensembles of atoms that are coherently excited by a short laser pulse. The ensembles are Erbium ions doped into two LiNbO3 crystals with channel waveguides, which are placed in the two arms of a Mach-Zehnder interferometer. The light that is spontaneously emitted after the excitation pulse shows first-order interference. By a strong collective enhancement of the emission, the atoms behave as ideal two-level quantum systems and no which-path information is left in the atomic ensembles after emissi…
Quantum optics with giant emitters has shown a new route for the observation and manipulation of non-Markovian properties in waveguide-QED. In this paper we extend the theory of giant atoms, hitherto restricted to the perturbative light-matter regime, to deal with the ultrastrong coupling regime. Using static and dynamical polaron methods we address the low energy subspace of a giant atom coupled to an Ohmic waveguide beyond the standard rotating wave approximation. We analyze the equilibrium properties of the system by computing the atomic frequency renormalization as a function of the coupli…
Recently, it has been suggested that the collective radiative decay of two point-like quantum emitters coupled to a waveguide, separated by a distance comparable to the coherence length of a spontaneously emitted photon, leads to an apparent $^{\prime}$superradiance paradox$^{\prime}$ by which one cannot decide whether independent or collective emission occurs. The resolution of the paradox stems from the strong non-Markovian dynamics arising from the delayed field-mediated atom interaction. Here we suggest an integrated optics platform to emulate the superradiance paradox, based on photon esc…
In this paper we discuss the use of the transition operator method for the theoretical description of a multi-qubit system in a one-dimensional waveguide. A general calculation has been performed for the N-qubit system, which was then applied to the case of spontaneous decay for one and two qubits. The probabilities of transitions in such systems, as well as the emission spectra, are investigated in detail.
In this work we investigate the nonperturbative decay dynamics of a quantum emitter coupled to a composite right/left handed transmission line (CRLH-TL). Our theory captures the contributions from the different spectral features of the waveguide, providing an accurate prediction beyond the weak coupling regime, and illustrating the multiple possibilities offered by the nontrivial dispersion of metamaterial waveguides. We show that the waveguide is characterized by a band-gap with two asymmetric edges: (i) a mu-near-zero (MNZ) band edge, where spontaneous emission is inhibited and an unstable p…
We demonstrate experimentally that spontaneous parametric down-conversion in an AlGaAs semiconductor Bragg reflection waveguide can make for paired photons highly entangled in the polarization degree of freedom at the telecommunication wavelength of 1550 nm. The pairs of photons show visibility higher than 90% in several polarization bases and violate a Clauser-Horne-Shimony-Holt Bell-like inequality by more than 3 standard deviations. This represents a significant step toward the realization of efficient and versatile self pumped sources of entangled photon pairs on-chip.
