Nonperturbative Treatment Research Articles

Coulomb-assisted cavity feeding in nonresonant optical emission from a quantum dot

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. A theoretical approach is developed for the nonperturbative treatment of the Auger-assisted quantum-dot carrier recombination. Using this method we present numerical calculations of the far off-resonant cavity feeding rate and cavity mean photon number, confirming efficient coupling at higher densities of carriers in the delocalized states. In comparison to fast Auger-like intraband scattering processes, we find a reduced overall efficiency of Coulomb-mediated interband transitions due the required electron-hole correlations for the recombination processes.

Neutron in a strong magnetic field: Finite volume effects

We investigate the neutron's response to magnetic fields on a torus with the aid of chiral perturbation theory, and expose effects from nonvanishing holonomies. The determination of such effects necessitates nonperturbative treatment of the magnetic field; and, to this end, a strong-field power counting is employed. Using a novel coordinate-space method, we find the neutron propagates in a coordinate-dependent effective potential that we obtain by integrating out charged pions winding around the torus. Knowledge of these finite volume effects will aid in the extraction of neutron properties from lattice QCD computations in external magnetic fields. In particular, we obtain finite volume corrections to the neutron magnetic moment and magnetic polarizability. These quantities have not been computed correctly in the literature. In addition to effects from nonvanishing holonomies, finite volume corrections depend on the magnetic flux quantum through an Aharonov-Bohm effect. We make a number of observations that demonstrate the importance of nonperturbative effects from strong magnetic fields currently employed in lattice QCD calculations. These observations concern neutron physics in both finite and infinite volume.

Magnetic quantum phase diagram of magnetic impurities in two-dimensional disordered electron systems

The quantum phase diagram of disordered electron systems as function of the concentration of magnetic impurities nm and the local exchange coupling J is studied in the dilute limit. We take into account the Anderson localisation of the electrons by a nonperturbative numerical treatment of the disorder potential. The competition between RKKY interaction JRKKY and the Kondo effect, as governed by the temperature scale TK, is known to gives rise to a rich magnetic quantum phase diagram, the Doniach diagram. Our numerical calculations show that in a disordered system both the Kondo temperature TK and JRKKY are widely distributed. Accordingly, also their ratio, JRKKY /TK is widely distributed as shown in Fig. 1 (a). However, we find a sharp cutoff of that distribution, which allows us to define a critical density of magnetic impurities nc below which Kondo screening wins at all sites of the system above a critical coupling Jc, forming the Kondo phase[see Fig. 1 (b)]. As disorder is increased, Jc increases and a spin coupled phase is found to grow at the expense of the Kondo phase. From these distribution functions we derive the magnetic susceptibility which show anomalous power law behavior. In the Kondo phase that power is determined by the wide distribution of the Kondo temperature, while in the spin coupled phase it is governed by the distribution of JRKKY. At low densities and small J < Jc we identify a paramagnetic phase. We also report results on a honeycomb lattice, graphene, where we find that the spin coupled phase is more stable against Kondo screening, but is more easily destroyed by disorder into a PM phase.

Quark-hadron thermodynamics in a magnetic field

Nonperturbative treatment of the quark-hadron transition at nonzero temperature $T$ and chemical potential $\ensuremath{\mu}$ in the framework of the field correlator method is generalized to the case of nonzero magnetic field B. A compact form of the quark pressure for arbitrary $B,\ensuremath{\mu},T$ is derived. As a result, the transition temperature is found as a function of B and $\ensuremath{\mu}$, which depends only on the following parameters: the vacuum gluonic condensate ${G}_{2}$ and the field correlator ${D}_{1}^{E}(x)$, which defines the Polyakov loops and is known both analytically and on the lattice. A moderate (25%) decrease of ${T}_{c}(\ensuremath{\mu}=0)$ for $eB$ changing from zero to $1\text{ }\text{ }{\mathrm{GeV}}^{2}$ is found. A sequence of transition curves in the $(\ensuremath{\mu},T)$ plane is obtained for $B$ in the same interval, monotonically decreasing in scale for growing $B$.

A hybrid model for coupling kinetic corrections of fusion reactivity to hydrodynamic implosion simulations

Inertial confinement fusion requires an imploded target in which a central hot spot is surrounded by a cold and dense pusher. The hot spot/pusher interface can take complicated shape in three dimensions due to hydrodynamic mix. It is also a transition region where the Knudsen and inverse Knudsen layer effect can significantly modify the fusion reactivity in comparison with the commonly used value evaluated with background Maxwellians. Here, we describe a hybrid model that couples the kinetic correction of fusion reactivity to global hydrodynamic implosion simulations. The key ingredient is a non-perturbative treatment of the tail ions in the interface region where the Gamow ion Knudsen number approaches or surpasses order unity. The accuracy of the coupling scheme is controlled by the precise criteria for matching the non-perturbative kinetic model to perturbative solutions in both configuration space and velocity space.

Roles of the vacuum field bath in a cavity QED system beyond the Weisskopf-Wigner approximation: Coupling renormalization, off-resonance assisted feeding, and pure dephasing

We present nonperturbative treatment of the vacuum field bath for two cases, a two-level emitter (TLE) in free space and a lossy TLE coupled to a cavity mode (CM), and the condition that guarantees the validity of the perturbative treatment in both cases is studied. It is shown that the perturbative treatment in the first case is always valid for a real system. In the second case, nevertheless, the perturbative treatment ignores a coupling term, which can bring effects similar to a phonon bath, e.g., coupling renormalization, off-resonance assisted feeding, and pure dephasing inside the resonance region. All of these effects are important for understanding the experimental observations, including the far-off-resonance cavity fluorescence and the additional CM line inside the resonance region in the strong coupling regime.

Advanced Capabilities of the PYXAID Program: Integration Schemes, Decoherence Effects, Multiexcitonic States, and Field-Matter Interaction.

In our previous work [J. Chem. Theory Comput. 2013, 9, 4959], we introduced the PYXAID program, developed for the purpose of performing nonadiabatic molecular dynamics simulations in large-scale condensed matter systems. The methodological aspects and the basic capabilities of the program have been extensively discussed. In the present work, we perform a thorough investigation of advanced capabilities of the program, namely, the advanced integration techniques for the time-dependent Schrodinger equation (TD-SE), the decoherence corrections via decoherence-induced surface hopping, the use of multiexciton basis configurations, and the direct simulation of photoexcitation via explicit light-matter interaction. We demonstrate the importance of the mentioned features by studying the electronic dynamics in a variety of systems. In particular, we demonstrate that the advanced integration techniques for solving TD-SE may lead to a significant speedup of the calculations and provide more stable solutions. We show that decoherence is necessary for accurate description of slow relaxation processes such as electron-hole recombination in solid C60. By using multiexciton configurations and direct, nonperturbative treatment of field-matter interactions, we found nontrivial optimality conditions for the multiple exciton generation in a small silicon cluster.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The ‘dressed’ many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. We employ a Caldeira–Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study non-Markovian and non-perturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current–voltage (I–V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system–bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers. We find two distinct types of current oscillations, with large and small oscillation amplitudes, respectively. These two types of oscillation appear differently in the Wigner space, with one exhibiting tornado-like motion and the other exhibiting a two piston engine-like motion.

Volume renormalization and the Higgs

Traditionally, Quantum Field Theory (QFT) treats particle excitations as point-like objects, which is the source of ubiquitous divergences. We demonstrate that a minimal modification of QFT with finite-volume particles may cure QFT of divergences and illuminate the physics behind the mathematical construct of our theories. The method allows for a non-perturbative treatment of the free field and self-interacting theories (though extensions to all interacting field theories might be possible). In particular, non-perturbatively defined mass is finite. When applied to the standard model Higgs mechanism, the method implies that a finite range of parameters allows for creation of a well-defined Higgs particle, whose Compton wavelength is larger than its physical size, in the broken symmetry phase (as small oscillations around the vacuum). This has profound consequences for Higgs production at the LHC. The parameter range in which the Higgs excitation with the mass of 125 GeV behaves as a proper particle is very restricted.

Gaussian field induced spectral hole burning in a Doppler broadened system and spontaneously generated coherence

The hole burning phenomenon is investigated for a four-level N-type atomic system interacting with three electromagnetic fields. The fields have a typical Gaussian transverse profile, in the presence of a Doppler broadening medium and spontaneously generated coherence due to nearby decaying levels. We present numerical results for the probe susceptibility via non-perturbative treatment of the density matrix elements solution. Some interesting features are enhanced for the spectral hole burning behaviors such as gain spectral hole burning and resonant fluorescence line narrowing. Also, the phenomenon of suppression of spectral curve, the propagation of slow and fast light in the system have been focused.

Non-perturbative treatment of molecules in linear magnetic fields: Calculation of anapole susceptibilities

In the present study a non-perturbative approach to ab initio calculations of molecules in strong, linearly varying, magnetic fields is developed. The use of London atomic orbitals (LAOs) for non-uniform magnetic fields is discussed and the standard rationale of gauge-origin invariance is generalized to invariance under arbitrary constant shifts of the magnetic vector potential. Our approach is applied to study magnetically induced anapole moments (or toroidal moments) and the related anapole susceptibilities for a test set of chiral and nonchiral molecules. For the first time numerical anapole moments are accessible on an ab initio level of theory. Our results show that the use of London atomic orbitals dramatically improves the basis set convergence also for magnetic properties related to non-uniform magnetic fields, at the cost that the Hellmann-Feynman theorem does not apply for a finite LAO basis set. It is shown that the mixed anapole susceptibility can be related to chirality, since its trace vanishes for an achiral molecule.

Quasi-Monte Carlo methods for lattice systems: A first look

We investigate the applicability of quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N−1/2, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to N−1, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling. Program summaryProgram title: qar-0.1Catalogue identifier: AERJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public Licence version 3No. of lines in distributed program, including test data, etc.: 67759No. of bytes in distributed program, including test data, etc.: 2165365Distribution format: tar.gzProgramming language: C and C++.Computer: PC.Operating system: Tested on GNU/Linux, should be portable to other operating systems with minimal efforts.Has the code been vectorized or parallelized?: NoRAM: The memory usage directly scales with the number of samples and dimensions: Bytes used = “number of samples” × “number of dimensions” × 8 Bytes (double precision).Classification: 4.13, 11.5, 23.External routines: FFTW 3 library (http://www.fftw.org)Nature of problem:Certain physical models formulated as a quantum field theory through the Feynman path integral, such as quantum chromodynamics, require a non-perturbative treatment of the path integral. The only known approach that achieves this is the lattice regularization. In this formulation the path integral is discretized to a finite, but very high dimensional integral. So far only Monte Carlo, and especially Markov chain-Monte Carlo methods like the Metropolis or the hybrid Monte Carlo algorithm have been used to calculate approximate solutions of the path integral. These algorithms often lead to the undesired effect of autocorrelation in the samples of observables and suffer in any case from the slow asymptotic error behavior proportional to N−1/2, if N is the number of samples.Solution method:This program applies the quasi-Monte Carlo approach and the reweighting technique (respectively the weighted uniform sampling method) to generate uncorrelated samples of observables of the anharmonic oscillator with an improved asymptotic error behavior.Unusual features:The application of the quasi-Monte Carlo approach is quite revolutionary in the field of lattice field theories.Running time:The running time depends directly on the number of samples N and dimensions d. On modern computers a run with up to N=216=65536 (including 9 replica runs) and d=100 should not take much longer than one minute.

Photoexcited electron and hole dynamics in semiconductor quantum dots: phonon-induced relaxation, multiple exciton generation and recombination

Photoexcited dynamics of electrons and holes in semiconductor quantum dots (QD), including phonon-induced relaxation, multiple exciton generation, and recombination (MEG and MER), were simulated by combining ab initio time-dependent density functional theory and non-adiabatic (NA) molecular dynamics. These nonequilibrium phenomena govern the optical properties and photoexcited dynamics of QDs, determining the branching between electronic processes and thermal energy losses. Our approach accounts for QD size and shape as well as defects, core-shell distribution, surface ligands and charge trapping, which significantly influence the properties of photoexcited QDs. The method creates an explicit time-domain representation of photoinduced processes and describes various kinetic regimes owing to the non-perturbative treatment of NA couplings in the quantum dynamics. QDs of different sizes and materials, with and without ligands, are considered. The simulations provide direct evidence that the high-frequency ligand modes on the QD surface play a pivotal role in the electron-phonon relaxation, MEG, and MER. The insights reported here suggest novel routes for controlling the photoinduced processes in semiconductor QDs and lead to new design principles for increasing efficiencies of photovoltaic devices.

Generation and coherent control of even-order harmonics driven by intense frequency-comb and cavity-mode fields inside a fsEC

We present a theoretical investigation of the multiphoton resonance dynamics driven by intense frequency-comb and cavity-mode fields inside a femtosecond enhancement cavity (fsEC). The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and laser fields. The quasienergy structure driven by the frequency-comb laser field is modified by coupling the cavity-mode field and the multiphoton resonance processes between modified quasienergy states, resulting in the generation of even-order harmonics. The high-order harmonic generation (HHG) from a two-level system driven by the laser fields can be coherently controlled by tuning the laser parameters. In particular, the tuning intensity of the cavity-mode field allows one to coherently control the HHG power spectra without changing the absolute positions of comb frequencies.

Detectors for probing relativistic quantum physics beyond perturbation theory

We develop a general formalism for a nonperturbative treatment of harmonic-oscillator particle detectors in relativistic quantum field theory using continuous-variable techniques. By means of this we forgo perturbation theory altogether and reduce the complete dynamics to a readily solvable set of first-order, linear differential equations. The formalism applies unchanged to a wide variety of physical setups, including arbitrary detector trajectories, any number of detectors, arbitrary time-dependent quadratic couplings, arbitrary Gaussian initial states, and a variety of background spacetimes. As a first set of concrete results, we prove nonperturbatively---and without invoking Bogoliubov transformations---that an accelerated detector in a cavity evolves to a state that is very nearly thermal with a temperature proportional to its acceleration, allowing us to discuss the universality of the Unruh effect. Additionally we quantitatively analyze the problems of considering single-mode approximations in cavity field theory and show the emergence of causal behavior when we include a sufficiently large number of field modes in the analysis. Finally, we analyze how the harmonic particle detector can harvest entanglement from the vacuum. We also study the effect of noise in time-dependent problems introduced by suddenly switching on the interaction versus ramping it up slowly (adiabatic activation).

CONTROLLABILITY OF ELECTROMAGNETICALLY INDUCED TRANSPARENCY IN A DOPPLER BROADENED FOUR-LEVEL ATOMIC SYSTEM

The influence of Doppler broadening on a four-level N-type atomic system has been investigated in the presence of spontaneous generating coherence. The atomic system interacting with three electromagnetic fields and includes the nonradiative decay, the effect of co- and counter-propagation of the fields is considered. The probe susceptibility behaviors can be modified by Doppler broadening via nonperturbative treatments of the density matrix elements solution in the absence and presence of the spontaneous generating coherence. Some interesting features are enhanced for the spectral behaviors and controllability of electromagnetically induced transparency, which were found to be in good agreement to some experimental results without including Zeeman sublevels to the system.

Solution of a model for the two-channel electronic Mach-Zehnder interferometer

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at Landau level filling factor \nu = 2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of dephasing and non-equlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short-range. In particular, this approach allows a non-perturbative treatment of electron tunneling at the quantum point contacts that act as beam-splitters. We find an exact analytic expression at arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length, and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones, and with observations.

Observables in a lattice Universe: the cosmological fitting problem

We explore observables in a lattice Universe described by a recently found solution to Einstein field equations. This solution models a regular lattice of evenly distributed objects of equal masses. This inhomogeneous solution is perturbative, and, up to second order in a small parameter, it expands at a rate exactly equal to the one expected in a dust dominated Friedmann–Lemaître–Robertson–Walker (FLRW) model with the equivalent, smoothed energy density. Therefore, the kinematics of both cosmologies are identical up to the order of perturbation studied. Looking at the behaviour of the redshift and angular distance, we find a condition on the compactness of the objects at the centre of each cell under which corrections to the FLRW observables remain small, i.e. of order of a few percents at most. Nevertheless, we show that, if this condition is violated, i.e. if the objects are too compact, our perturbative scheme breaks down as far as the calculations of observables are concerned, even though the kinematics of the lattice remains identical to its FLRW counterpart (at the perturbative order considered). This may be an indication of an actual fitting problem, i.e. a situation in which the FLRW model obtained from lightcone observables does not correspond to the FLRW model obtained by smoothing the spatial distribution of matter. Fully non-perturbative treatments of the observables will be necessary to answer that question.

Density Functional Theory and Bose Statistics for the Freezing of Superfluid 4He

Density functional theory so far has experienced pathological results in the description of the freezing of superfluid 4He, even with the use of accurate inputs, namely the density response function, χ(q), and the equation of state of the superfluid. In fact, while the second order approximation of Ramakrishnan-Yussouff type gives a too much stable solid phase (Likos et al. in Phys. Rev. B 55:8867, 1997; Minoguchi and Galli in J. Law Temp. Phys. 162:160, 2011), a non-perturbative treatment called modified weighted density approximation (MWDA) gives, on the other hand, a too stable superfluid phase (Minoguchi et al. in J. Phys. Conf. Ser. 2012). We have preliminarily performed a MWDA calculation for a specific Gaussian distortion α=0.387 A−2 of liquid 4He. By using χ(q) and the equation of state of a system of liquid 4He in which Bose statistics has been suppressed, we have found that the calculation provides a lower energy. This indicates that the solid may be better described by a distorted normal liquid. The input data has been obtained via Path Integral Monte Carlo simulations of a system of distinguishable 4He atoms. The χ(q) has been obtained from the dynamic structure factors extracted, via the Genetic Inversion via Falsification of Theories (GIFT) method (Vitali et al. in Phys. Rev. B 82:174510, 2010) from imaginary time density–density correlation functions.