This paper deals with non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in high Q cavities or photonic band gap materials. In cases such as the former, we show that the pseudo mode theory for single quantum reservoir excitations can be obtained by applying the Fano diagonalisation method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two and many discrete quasimodes are made. For a simple photonic band gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.
We develop an exact framework to describe the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir. Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion …
The models we use, habitually, to describe quantum nonlinear optical processes have been remarkably successful yet, with few exceptions, they each contain a mathematical flaw. We present this flaw, show how it can be fixed and, in the process, suggest why we can continue to use our favoured Hamiltonians.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, i.e. classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verif…
We report an observation of a delayed all-optical routing/switching phenomenon based on ultraslow group velocity of light via nondegenerate four-wave mixing processes in a defected solid medium. Unlike previous demonstrations of enhanced four-wave mixing processes using the slow light effects, the present observation demonstrates a direct retrieval of the resonant Raman-pulse excited spin coherence into photon coherence through coherence conversion processes.
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of non-resonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally-feasible set of coherent states and its related energy-cut-off approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a f…
Single photon sources to be used in quantum cryptography must show higher order antibunching (HOA). HOA is reported by us in several many wave mixing processes. In the present work we have investigated the possibility of observing HOA in multiwave mixing processes in general. The generalized Hamiltonian is solved for several particular cases in Heisenberg picture and possibility of observing HOA is investigated with the help of criterion of Pathak and Garcia. Several particular cases of the generalized Hamiltonian are solved with the help of short time approximation technique and HOA is report…
We study the effects of time ordering in photon generation processes such as spontaneous parametric down-conversion (SPDC) and four wave mixing (SFWM). The results presented here are used to construct an intuitive picture that allows us to predict when time ordering effects significantly modify the joint spectral amplitude (JSA) of the photons generated in SPDC and SFWM. These effects become important only when the photons being generated lie with the pump beam that travels through the non-linear material for a significant amount of time. Thus sources of spectrally separable photons are ideal …
Using coherent states in optical quantum process tomography is a practically-relevant approach. Here, we develop a framework for complete characterization of quantum-optical processes in terms of normally-ordered moments by using coherent states as probes. We derive the associated superoperator tensors for several optical processes. We also show that our technique can be used to determine nonclassicality features of quantum-optical states and processes. Furthermore, we investigate identification of multi-mode Gaussian processes and show that the number of necessary probe coherent states scales…
In a recent paper [I.I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was shown that one can completely identify the nonclassicality of single- and two-mode Gaussian states by means of certain nonclassicality witnesses which are based on intensity moments up to the third order of optical fields, provided that an appropriate coherent displacement is applied to a given Gaussian state. Here, we utilize a mathematical equivalence between the description of the coherent displaced Gaussian states generated in the spontaneous parametric processes and the Gaussian states generated in the corresponding…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This simulatability result places powerful constraints on the capability to realize exponential quantum speedups as well as on inducing an optical nonlinear transformation via linear optics, photodetection-based measurement and classical feedforward of measurement results, optimal cloning, and a wide range of other processes.
Two strongly-pumped parametric interactions are simultaneously realized in a single nonlinear crystal in order to generate three strongly correlated optical fields. By combining together the outputs of two of the three detectors measuring intensities of the generated fields, we obtain the joint photocount statistics between the single field and the sum of the other two. Moreover, we develop a microscopic quantum theory to determine the joint photon-number distribution and the joint quasi-distributions of integrated intensities and prove nonclassical nature of the three-mode state. Finally, by …
The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement …
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.
Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satified, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different non-linear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. …
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary transformations as input, coherently permutes their ordering, and outputs a new composite operator which can be applied to a quantum state. Here we propose an optical device which implements this type of coherent operator permutation. This device requires only one physical implementation of each operator to be permuted.
Since a general Gaussian process is phase-sensitive, a stable phase reference is required to take advantage of this feature. When the reference is missing, either due to the volatile nature of the measured sample or the measurement's technical limitations, the resulting process appears as random in phase. Under this condition, we consider two single-mode Gaussian processes, displacement and squeezing. We show that these two can be efficiently estimated using photon number states and photon number resolving detectors. For separate estimation of displacement and squeezing, the practical estimati…
A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit and of flipping it into the orthogonal qubit is reported. The adopted experimental apparatus, a Quantum-Injected Optical Parametric Amplifier (QIOPA) is transformed simultaneously into a Universal Optimal Quantum Cloning Machine (UOQCM) and into a Universal NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, will be found to be universal and optimal, i.e. the measured fidelity of both processes F<1 will be found close to the…
Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill-defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique featur…
Nonlinear optical processes are governed by the relative-phase relationships among the relevant electromagnetic fields in these processes. In this Letter, we describe the physics of arbitrary manipulation of nonlinear optical processes (AMNOP) by artificial control of relative phases. As a typical example, we show freely designable optical-frequency conversions to extreme spectral regions, mid-infrared and vacuum-ultraviolet, with near-unity quantum efficiencies. Furthermore, we show that such optical-frequency conversions can be realized by using a surprisingly simple technology where transpa…
We propose a scheme for the dissipative preparation of W-type entangled steady-states of three atoms trapped in an optical cavity. The scheme is based on the competition between the decay processes into and out of the target state. By suitable choice of system parameters, we resolve the whole evolution process and employ the effective operator formalism to engineer four independent decay processes, so that the target state becomes the stationary state of the quantum system. The scheme requires neither the preparation of definite initial states nor the precise control of system parameters and p…
The standard S-matrix formulation cannot generally be used in the treatment of atomic scattering processes, involving bound-state QED effects, due to the special type of singularity that can here appear. This type of singularity can be handled by means of methods designed for structure calculations. It is essentially a consequence of the optical theorem that similar techniques can be applied also in scattering processes. The optical theorem for free particles gives a relation between the effective Hamiltonian and the cross section, a relation that is valid also when bound states are present. W…
We propose a scheme for the deterministic coherent manipulation of two atomic qutrits, trapped in separate cavities coupled through a short optical fibre or optical resonator. We study such a system in the regime of dispersive atom-field interactions, where the dynamics of atoms, cavities and fibre operates through virtual population of both the atomic excited states and photonic states in the cavities and fibre. We show that the resulting effective dynamics allows for the creation of robust qutrit entanglement, and thoroughly investigate the influence of imperfections and dissipation, due to …
We study a highly efficient, matter-wave amplification mechanism in a longitudinally-excited, Bose-Einstein condensate and reveal a very large enhancement due to nonlinear gain from a sixmatter- optical, wave-mixing process involving four photons. Under suitable conditions this opticallydegenerate, four-photon process can be stronger than the usual two-photon inelastic light scattering mechanism, leading to nonlinear growth of the observed matter-wave scattering independent of any enhancement from bosonic stimulation. Our theoretical framework can be extended to encompass even higher-order, no…
It has now been possible to prepare chain of ions in an entangled state and thus question arises --- how the optical properties of a chain of entangled ions differ from say a chain of independent particles. We investigate nonlinear optical processes in such chains. We explicitly demonstrate the possibility of entanglement produced super Raman scattering. Our results in contrast to Dicke's work on superradiance are applicable to stimulated processes and are thus free from the standard complications of multimode quantum electrodynamics. Our results suggest the possibility of similar enhancement …
We propose various schemes for the dissipative preparation of a maximally entangled steady state of two atoms in an optical cavity. Harnessing the natural decay processes of cavity photon loss and spontaneous emission, we use an effective operator formalism to identify and engineer effective decay processes, which reach an entangled steady state of two atoms as the unique fixed point of the dissipative time evolution. We investigate various aspects that are crucial for the experimental implementation of our schemes in present-day and future cavity quantum electrodynamics systems and analytical…
We study the processes of spontaneous four wave mixing and of third-order spontaneous parametric downconversion in optical fibers, as the basis for the implementation of photon-pair and photon-triplet sources. We present a comparative analysis of the two processes including expressions for the respective quantum states and plots of the joint spectral intensity, a discussion of phasematching characteristics, and expressions for the conversion efficiency. We have also included a comparative study based on numerical results for the conversion efficiency for the two sources, as a function of sever…
We have unveiled coherent multiphoton interferences originating from different quantum paths taken by the Auger electron induced by a high-intensity x-ray/XUV pulse under the presence of a strong optical field. These interferences give rise to a clear signature in the angle-resolved Auger electron spectrum: an asymmetry with respect to the energy of the Auger decay channel. In order to illustrate this effect we have considered the resonant Auger decay of the transition $2p^{5} \!\leftrightarrow\! 1s^{-1}2p^{6}$ in Ne$^{+}$. The simulations show that these interferences are very sensitive to th…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities is significantly higher than for the exponential distribution, which is most commonly observed in statistical and quantum optics. The current manuscript gives a practical overview of the generic statistics toolkit concerning heavy-tailed distributions and proposes methods to deal with issues specific to non-linear optics. We take a closer look at superconti…
We investigate multi-"photon" interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low…
We show that off-site processes and multi-orbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions induce competing density-induced hopping processes, the so-called bond-charge interactions. Furthermore, higher bands strongly influence tunneling and on-site interactions. We apply a multi-orbital interaction-induced dressing of the lowest band which leads to renormalized hopping processes. These corrections give rise to an extended Hubbard model with intrin…
Generation and control of quantum states of light on an integrated platform has become an essential tool for scalable quantum technologies. Chip scale sources such as nonlinear optical microcavities have been demonstrated to efficiently generate entangled bi-photon states. However these systems have little control over the continuous variable time-energy entanglement of the photons. We demonstrate such control by preparing bi-photon states with asymmetric temporal wavefunctions by selectively modifying the density of states of the cavity modes taking part in the interaction using Rayleigh scat…
Enabled by x-ray free-electron lasers, nonlinear optical phenomena can be explored in the x-ray domain nowadays. Among the multitude of newly accessible processes, this theoretical study focuses parametric x-ray optical wavemixing for closer investigation. Specifically, we develop a framework based on non-relativistic QED to describe x-ray optical sum- and difference-frequency generation as well as x-ray parametric down-conversion on equal footing. All of these processes promise imaging capabilities similar to regular x-ray diffraction with additional spectroscopic selectivity that is tunable …
Many nonlinear optical technologies require the two-mode spectral amplitude function that describes them---the \emph{joint spectral amplitude} (JSA)---to be separable. We prove that the JSA factorizes \emph{only} when the incident pump field and phase-matching function are Gaussian functions. We show this by mapping our problem to a known result, in continuous variable quantum information, that only squeezed states remain unentangled when combined on a beam splitter. We then conjecture that only a squeezed state minimizes entanglement when sent through a beam splitter with another pre-specifie…
The quantum processes involved in the interaction of matter with, separately, an electron vortex(EV) and an optical vortex (OV) are described, with matter modelled in terms of a neutral two particle atomic system, allowing for both the internal (electronic-type) motion and the gross (center of mass-type) motion of matter to be taken into account. The coupling of the atomic system to the EV is dominated by Coulomb forces, while that of the OV is taken in the $\mathbf{p}\cdot\mathbf{A}$ canonical form which couples $\mathbf{A}$, the transverse vector potential of the optical vortex, to the linea…
Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- ($χ^{(2)}$) or third- $χ^{(3)}$) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this letter, we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric ($χ^{(2)})$ coupling to a lossy ancillary mode shortens the lifetime of the target photonic mod…
Nonlinear optical processes associated with even-order nonlinear susceptibilities are critical for both classical and quantum technologies. Inversion symmetry, however, prevents nonlinear optical responses mediated by even-order susceptibilities in several material systems pertinent for applications in nanophotonics. Here, we demonstrate induced nonlinear optical processes, namely second- and fourth-harmonic generation that are naturally forbidden in an inversion symmetric system, by strongly coupling to a photon mode of a high-Q optical cavity. As an illustrative system with an inversion symm…
Recent experiments have demonstrated that for a quantum dot in an optical resonator off-resonant cavity mode emission can occur even for detunings of the order of 10 meV. We show that Coulomb mediated Auger processes based on additional carriers in delocalized states can facilitate this far off-resonant emission. Using a novel theoretical approach for a non-perturbative treatment of the Auger-assisted quantum-dot carrier recombination, we present numerical calculations of the far off-resonant cavity feeding rate and cavity mean photon number confirming efficient coupling at higher densities of…
The integration of cold atomic systems with optical nanofibres is an increasingly important experimental platform. Here, we report on the spectra observed during a strongly driven, single-frequency, two-photon excitation of cold rubidium atoms near an optical nanofibre. At resonance, two competitive processes, namely a higher excitation rate and stronger pushing of atoms from the nanofibre due to resonance scattering, need to be considered. We discuss the processes that lead to the observed two-peak profile in the fluorescence spectrum as the excitation laser is scanned across the resonance, n…
Many important physical processes have dynamics that are too complex to completely model analytically. Optimisation of such processes often relies on intuition, trial-and-error, or the construction of empirical models. Machine learning based on artificial neural networks has emerged as an efficient means to develop empirical models of complex systems. We implement a deep artificial neural network to optimise the magneto-optic cooling and trapping of neutral atomic ensembles. Cold atomic ensembles have become commonplace in laboratories around the world, however, many-body interactions give ris…
Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that i…
Considering two-level media in the array of weakly coupled nano-cavities, we reveal a variety of dynamical regimes, such as diffusion, self-trapping, soliton, and breathers for the wave-packets in the presence of photon tunneling processes between the next-nearest cavities. We focus our attention on the low branch (LB) bright polariton soliton formation, due to the two-body polariton-polariton scattering processes. When detuning frequency is manipulated adiabatically, the low-branch lattice polariton localized states, i.e., that are solitons and breathers evolving between photon-like and matte…
We report the experimental demonstration of converting coherent optical fields between two different optical wavelengths by coupling two optical modes to a mechanical breathing mode in a silica resonator. The experiment is based on an itinerant approach, in which state-mapping from optical to mechanical and from mechanical to another optical state takes place simultaneously. In contrast to conventional nonlinear optical processes, optomechanical impedance matching as well as efficient optical input-output coupling, instead of phase-matching, plays a crucial role in optomechanics-based waveleng…
We report on experiments that demonstrate dynamical instability in a Bose-Einstein condensate at the band-edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and perform numerical modeling of the experiments using both a mean-field and beyond mean-field approach. We compare our numerical results to the experimental data, and find that the Gross-Pitaevskii equation is not able to describe this experiment. Our beyond mean-field approach, …
Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation laws, such as momentum conservation that requires phase matching conditions for efficient conversion. However, conservation laws alone could not fully capture the features of nonlinear frequency conversion. Here it is shown that topology can provide additional constraints in nonlinear multi-frequency conversion processes. Unlike conservation laws, a topologica…
We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steady-state of this system, which emerge due to the competition between coherent and dissipative processes. Specifically, for strongly anisotropic spin-spin interactions, we find ferromagnetic, antiferromagnetic, spin-density-wave, and staggered-XY steady states, which are separated by nonequilibrium phase transitions meeting at a Lifshitz point. These transitions are accompanied by quantum correlation…
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 study a model of a photon mode dipole-coupled to a medium of two-level oscillators in a microcavity in the presence of dephasing processes introduced by coupling to external baths. Decoherence processes can be classified as pair-breaking or non-pair-breaking in analogy with magnetic or non-magnetic impurities in superconductors. In the absence of dephasing, the ground state of the model is a polariton condensate with a gap in the excitation spectrum. Increase of the pair-breaking parameter $γ$ reduces the gap, which becomes zero at a critical value $γ_{C1}$; for large $γ$, the conventional …
The response functions of a material characterize its behavior under external stimuli, such as electromagnetic radiation. Such responses may grow linearly with the amplitude of the incident radiation, as is the case of absorption, or may be nonlinear. The latter category includes a diverse set of phenomena such as second harmonic generation (SHG), shift current, sum frequency generation, and excited state absorption, among others. Despite decades of research into nonlinear response theory, and the occasional discovery of materials with large nonlinear responses, there has been no systematic in…
