Nonperturbative Treatment Research Articles

Ground state excitation of an atom strongly coupled to a free quantum field

This paper presents a nonperturbative treatment of strong-coupling induced effects in atom-field systems which cannot be seen in traditional perturbative treatments invoking compromising assumptions such as the Born-Markov, rotating wave or Fermi Golden rule. We consider an atom whose internal degrees of freedom are modeled by a harmonic oscillator, bilinearly coupled to a scalar quantum field, representing one of the two polarizations of an electromagnetic field. Because the whole system is Gaussian we can solve this problem exactly. Using the open quantum system conceptual framework and the influence functional formalism we derive the dynamics of the reduced density matrix for the atom which enables the calculation of atomic transition probability and other relevant physical quantities. Finding an exact solution to this problem has the distinct advantage of enabling one to capture fully the strong coupling regime and discover interesting effects such as spontaneous ground state excitation which is unfathomable in perturbative treatments. The conventional description of atomic-optical activities is predicated on the assumption that the state of the total atom-field system is a product state of the atomic excitations and the photon number states, an assumption which is valid only for vanishingly weak coupling. The correct energy eigenfunctions to use should be that of the Hamiltonian of the combined atom-field system. Other features associated with finite to strong coupling effects such as resonance peak broadening and transition from a gapped to a gapless spectrum can all be understood from this perspective. Finally, to put the issues in a proper perspective we take the perturbative limit of the exact results and compare them with those from conventional TDPT. This enables one to pin-point where the deficiencies of TDPT lie as one removes the ultra-weak coupling assumption.

Toward an accurate strongly coupled many-body theory within the equation-of-motion framework

Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with non-perturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons (2q$\otimes$2phonon), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of $^{42,48}$Ca and $^{68}$Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.

Numerical Approach to Nonequilibrium Quantum Thermodynamics: Nonperturbative Treatment of the Driven Resonant Level Model Based on the Driven Liouville von-Neumann Formalism.

Nonequilibrium thermodynamics of the driven resonant-level model is studied using numerical simulations based on the driven Liouville von-Neumann formalism. The approach is first validated against recently obtained analytical results for quasistatic level shifts and the corresponding first-order corrections. The numerical approach is then used to study far-from-equilibrium thermodynamic properties of the system under finite level shift rates. The proposed methodology allows the study of unexplored nonequilibrium thermodynamic regimes in open quantum systems.

Phase jump in resonance harmonic emission driven by strong laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504288, 11534008, and 91536115) and the Fundamental Research Funds for the Central Universities of China.

We present a theoretical investigation of the multiphoton resonance dynamics in the high-order-harmonic generation (HHG) process driven by a strong driving continuous wave (CW) field along with a weak control harmonic field. The Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the combined laser field. Multiple multiphoton-transition paths for the harmonic emission are coherently summed. The phase information about paths can be extracted via the Fourier transform analysis of the harmonic signals which oscillate as a function of the relative phase between driving and control fields. Phase jumps are observed when sweeping across the resonance by varying the frequency or intensity of the driving field. The phase variation as a function of driving frequency at a fixed intensity and as a function of the intensity at a fixed driving frequency allows us to determine the intensity dependence of the transition energy of quantum systems.

Simulating Magnetic Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory in Gauge Including Atomic Orbitals.

Magnetic circular dichroism (MCD) spectra are able to provide insights into the geometric, electronic, and magnetic properties of chemical systems. However, they can be challenging to understand and simulate given the need to simultaneously treat both the finite magnetic and optical fields. Thus, efficient simulations are desired to understand the spectra and resolve the molecular electronic states. Real-time dynamics are used widely in the simulation of electronic spectroscopies such as absorption as well as electronic circular dichroism, but simulating MCD with real-time dynamics is technically and theoretically challenging. In this work, we introduce a real-time dynamics-based ab initio method with a nonperturbative treatment of a static magnetic field with London orbitals for simulating the MCD spectra of closed shell systems. Effects of a magnetic field are included variationally in the spin-free nonrelativistic Hamiltonian. Real-time time-dependent density functional theory dynamics are then performed, from which we compute the response function in the presence of the external magnetic field, giving the MCD spectrum. The method developed in this paper is applied to simulate the MCD spectra for pyrimidine, pyrazine, and 1,4-naphthoquinone. Results are discussed and compared to the experiment.

On the Role of Local Many-Body Interactions on the Thermoelectric Properties of Fullerene Junctions.

The role of local electron–vibration and electron–electron interactions on the thermoelectric properties of molecular junctions is theoretically analyzed focusing on devices based on fullerene molecules. A self-consistent adiabatic approach is used in order to obtain a non-perturbative treatment of the electron coupling to low frequency vibrational modes, such as those of the molecule center of mass between metallic leads. The approach also incorporates the effects of strong electron–electron interactions between molecular degrees of freedom within the Coulomb blockade regime. The analysis is based on a one-level model which takes into account the relevant transport level of fullerene and its alignment to the chemical potential of the leads. We demonstrate that only the combined effect of local electron–vibration and electron–electron interactions is able to predict the correct behavior of both the charge conductance and the Seebeck coefficient in very good agreement with available experimental data.

Dissipative dynamics in a tunable Rabi dimer with periodic harmonic driving.

Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D2 ansatz, is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created, thanks to the resonance between the periodic driving field and the photon frequency. In the presence of the phonon bath, one can still change the photon numbers in two resonators and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states.

Interference effect and Autler-Townes splitting in coherent blue light generated by four-wave mixing

An unexpected interference effect between four-wave mixing excitation routes in rubidium vapor is observed using a combination of a cw diode laser and a 1 GHz femtosecond pulse train. The generated coherent blue light is analyzed by scanning the diode frequency and the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler-Townes splitting and a large separation is observed in the doublet structure due to the configuration of copropagating fields. Remarkably, by scanning the repetition rate, a narrow peak appears as a signature of the interfering pathways. A non-perturbative treatment of the Bloch equations achieves good agreement with the experimental data, and demonstrates that the interfering effect appears only when both lasers are resonant with one- and two-photon transitions for the same atomic velocity group.

Note on the conjectured breakdown of QED perturbation theory in strong fields

Strong background fields require a non-perturbative treatment, which is afforded in QED by the Furry expansion of scattering amplitudes. It has been conjectured that this expansion breaks down for sufficiently strong fields, based on the asymptotic growth of loop corrections with increasing "quantum nonlinearity", essentially the product of field strength and particle energy. However, calculations to date have assumed that the background is constant. We show here, using general plane waves of finite duration, that observables at high quantum nonlinearity scale differently depending on whether intensity or energy is large. We find that, at high energy, loop contributions to observables tend to fall with increasing quantum nonlinearity, rather than grow.

An ab Initio Linear Response Method for Computing Magnetic Circular Dichroism Spectra with Nonperturbative Treatment of Magnetic Field.

Magnetic circular dichroism (MCD) experiments provide a sensitive tool for exploring geometric, magnetic, and electronic properties of chemical complexes and condensed matter systems. They are also challenging to simulate because of the need to simultaneously treat the perturbations of a finite magnetic field as well as an optical field. In this work, we introduce an ab initio approach that treats the external magnetic field nonperturbatively with London orbitals for simulating the MCD spectra of closed-shell systems. Effects of a magnetic field are included variationally in the spin-free nonrelativistic Hamiltonian, followed by a linear response formalism to directly calculate the difference in absorption between the left and right circularly polarized light. In addition to the presentation of underlying mathematical formalism and implementation, the method developed in this paper has been applied to simulations of MCD spectra of the sodium anion, 2,2,6,6-tetramethylcyclohexanone, and 3-methyl-2-hexanone. Results are discussed and compared to experiments.

A perturbative perspective on self-supporting wormholes

We describe a class of wormholes that generically become traversable after incorporating gravitational back-reaction from linear quantum fields satisfying appropriate (periodic or anti-periodic) boundary conditions around a non-contractible cycle, but with natural boundary conditions at infinity (i.e. without additional boundary interactions). The class includes both asymptotically flat and asymptotically AdS examples. Related constructions can also be performed in asymptotically de Sitter space or in other closed cosmologies. Simple asymptotically AdS3 or asymptotically AdS examples with a single periodic scalar field are then studied in detail. When the examples admit a smooth extremal limit, our perturbative analysis indicates the back-reacted wormhole remains traversable at later and later times as this limit is approached. This suggests that a fully non-perturbative treatment would find a self-supporting eternal traversable wormhole. While the general case remains to be analyzed in detail, the likely relation of the above effect to other known instabilities of extreme black holes may make the construction of eternal traversable wormholes more straightforward than previously expected.

Vacuum Condensate Picture of Quantum Gravity

In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge–Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale ξ in many ways analogous to the scaling violation parameter Λ M ¯ S of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.

The Expansion in Hadron Effective Field Theory**Supported by the National Natural Science Foundation of China under Grant No. 11305137

We study the Nc scalings of pion-nucleon and nucleon-nucleon scatterings in hadron effective field theory. By assuming Wittenʼs counting rules are applied to matrix elements or scattering amplitudes, which use the relativistic normalization for the nucleons, we find that the nucleon axial coupling is of order , and a consistent large Nc counting can be established for the pion-nucleon and nucleon-nucleon scatterings. We also justify the nonperturbative treatment of the low energy nucleon-nucleon interaction with the large Nc analysis and find that the deuteron binding energy is of order .

Generalized Hartree-Fock with Nonperturbative Treatment of Strong Magnetic Fields: Application to Molecular Spin Phase Transitions.

In this work, we present a framework of an ab initio variational approach to effectively explore electronic spin phase transitions in molecular systems inside of a homogeneous magnetic field. In order to capture this phenomenon, the complex generalized Hartree-Fock ([Formula: see text]) method is used in the spinor formalism with London orbitals. Recursive algorithms for computing the one- and two-electron integrals of London orbitals are also provided. A Pauli matrix representation of the [Formula: see text] method is introduced to separate spin contributions from the scalar part of the Fock matrix. Next, spin phase transitions in two different molecular systems are investigated in the presence of a strong magnetic field. Noncollinear spin configurations are observed during the spin phase transitions in H2 and a dichromium complex, [(H3N)4Cr(OH)2Cr(NH3)4]4+, with an increase in magnetic field strength. The competing driving forces of exchange coupling and the spin Zeeman effect have been shown to govern the spin phase transition and its transition rate. Additionally, the energetic contributions of the spin Zeeman, orbital Zeeman, and diamagnetic terms to the potential energy surface are also analyzed.

Classical and semiclassical non-perturbative treatments of the electron transfer process in the collisional system proton-hydrogen involving initial excited states

We investigate the total cross sections of the electron transfer process in the proton-hydrogen collisional system involving initial excited states at impact energies in the 2.5 eV/u–100 keV/u range. The calculations are based on two non-perturbative treatments, namely the semiclassical atomic orbitals close-coupling (SC-AOCC) approach and the classical trajectory Monte Carlo method. The results are presented and discussed for the collisions taking into account the degeneracy of each level in orbital momentum ℓ. We find that the SC-AOCC results show empirical n3 and n4 scaling laws at low and high impact velocities, respectively.

Next-to-Next-to-Next-to-Leading Order Pressure of Cold Quark Matter: Leading Logarithm.

At high baryon chemical potential μ_{B}, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling α_{s}. The result is currently known up to and including the full next-to-next-to-leading order α_{s}^{2}. Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates nonperturbative treatment of the scale α_{s}^{1/2}μ_{B}. We apply a hard-thermal-loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and we use it to determine the leading-logarithm contribution to next-to-next-to-next-to-leading order: α_{s}^{3}ln^{2}α_{s}. This result is the first improvement to the equation of state of massless cold quark matter in 40years. The new term is negligibly small and thus significantly increases our confidence in the applicability of the weak-coupling expansion.

Density Estimation on Small Data Sets.

How might a smooth probability distribution be estimated with accurately quantified uncertainty from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one dimension, providing an exact nonparametric Bayesian posterior without relying on tunable parameters or large-data approximations. Strong non-Gaussian constraints, which require a nonperturbative treatment, are found to play a major role in reducing distribution uncertainty. A software implementation of this method is provided.

Stochastic decoupling approach to the spin-boson dynamics: Perturbative and nonperturbative treatments

We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the hierarchical functional derivatives, one can recover the second order Nakajima-Zwanzig quantum master equation. Taking into account the higher-order corrections, our method can be implemented as a highly efficient numerical scheme for a general quantum dissipative system beyond the usual Markovian, rotating-wave, and weak-coupling approximations.

Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals.

We extend the vibronic exciton theory introduced in our previous work to study singlet fission dynamics, in particular addressing recent indications of the importance of vibronic coupling in this process. A microscopic and non-perturbative treatment of electronic and selected vibrational degrees of freedom in combination with Redfield theory allows us to dynamically consider clusters of molecules under conditions close to those in molecular crystals that exhibit fission. Using bulk pentacene as a concrete example, our results identify a number of factors that render fission rapid and effective. Strong coupling to high-frequency Holstein modes generates resonances between the photo-prepared singlet and product triplet states. We furthermore find the large number of triplet combinations associated with bulk periodic systems to be critical to the fission process under such vibronically resonant conditions. In addition, we present results including, in an approximate manner, the effects of Peierls coupling, indicating that this factor can both enhance and suppress fission depending on its interplay with vibronic resonance and thermodynamics.

Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504288, 11374239, 11534008, and 91536115) and the Fundamental Research Funds for the Central Universities, China.

The frequency-comb structure in the extreme ultraviolet (XUV) and vacuum ultraviolet (VUV) regions can be realized by the high-order harmonic generation (HHG) process driven by frequency-comb fields, providing an alternative approach for the measurement of an unknown frequency in XUV or VUV. We consider the case of two driving frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental- and third-harmonics, respectively. The many-mode Floquet theorem (MMFT) is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the frequency-comb laser fields. Multiphoton transition paths involving both fundamental- and third-harmonic photons are opened due to the coupling of the third-harmonic frequency-comb field. The multiphoton transition paths are superpositioned when the carrier-envelope-phase shifts (CEPs) fulfill the matching condition. And the interference of the multiphoton transition paths can be controlled by tuning the relative envelope delay between the fields. We find that the quasienergy structure, as well as the multiphoton resonant high-order harmonic generation (HHG) spectra, driven by the two frequency-comb fields can be coherently controlled via the interference of multiphoton transition paths. It is also found that the spectral intensities of the generated harmonics can be modulated, and the modulation behavior is harmonic-sensitive.