Bohr Frequency Research Articles

Analyzing coherent and incoherent optical susceptibilities in four-wave mixing: stochasticity, symmetry, and intramolecular coupling

The nonlinear optical susceptibilities are analyzed in their optical propagation length considering the incoherent-coherent contributions with the dependence on the relaxation times. In addition, some symmetry properties of the Four-Wave mixing (FWM) signal concerning the frequency detuning exchange are used in the study, without restricting ourselves to the maxima of population oscillations. We analyze the behaviors of these optical responses in a vibronic coupling scheme using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in position and nuclear energies. The solvent effect in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Our results for both FWM signal propagation and nonlinear optical susceptibilities are sensitive to the intramolecular coupling parameters, solvent stochasticity, and perturbation order for the treatment of the weak probe beam. The consideration of a second-order probe beam in FWM would not represent a significant contribution to the predicted results, since its percentage contribution is negligible within the model development framework; however, this contribution becomes important when increasing the ratio between longitudinal and transverse relaxation times.

Stochastic Nature and Intramolecular Coupling in Optical Response Profiles: Critical Analysis through Semiclassical Models.

We have studied the nonlinear absorptive and dispersive responses considering a molecular system consisting of two-levels, where aspects of the vibrational internal structure and intramolecular coupling are inserted, in addition to the considerations of interaction with the thermal reservoir. The Born-Oppenheimer electronic energy curve for this molecular model consists of two-intercrossing harmonic oscillator potentials with minima displaced in energy and nuclear coordinate. The results obtained show how these optical responses are sensitive to explicit considerations of both intramolecular coupling and the presence of the solvent through their stochastic interaction. Our study shows that the permanent dipoles of the system and the transition dipoles induced by electromagnetic field effects represent critical quantities for the analysis. The solvent action in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Significant variations in the nonlinear optical properties for cases of perturbative and saturative treatments, relaxation times, and optical propagation, mainly due to changes in the probe and pump intensities, are studied. Our studies relating the intramolecular effects with those generated by the presence of the solvent and its stochastic interaction with the solute of study, have allowed not only to analyze the influence of these in the profile of the optical responses, but they could also provide some insights into the analysis and characterization of molecular systems through nonlinear optical properties.

Geometric-arithmetic master equation in large and fast open quantum systems

Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages, and find that it can improve the second order perturbation theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics. The characteristic frequency scale that governs the approximation is the minimax frequency: the minimum of the maximum system oscillation frequency and the bath relaxation rate; this needs to be larger than the dissipation rate for it to be valid. The concepts are illustrated on the Heisenberg ferromagnetic spin-chain model. To study the accuracy of the approximation, a Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate the fourth order time-convolutionless master equation, in the Ohmic bath at zero temperature. Enforcing the geometric average, decreases the trace distance to the exact solution. Dynamical decoupling of a qubit is examined by applying the Redfield and the geometric-arithmetic master equations, in the interaction picture of the time dependent system Hamiltonian, and the results are compared to the exact path integral solution. The geometric-arithmetic approach is significantly simpler and can be super-exponentially faster compared to the Redfield approach.

Quantum feedback control in quantum photosynthesis

A model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons is introduced. Quantum feedback in this approach describes the Landau--Zener transition with decoherence. The model explains irreversibility in the process of charge separation for quantum photosynthesis -- direct transitions for this quantum control model will have probabilities close to one and reverse transitions will have probabilities close to zero. This can be considered as a model of quantum ratchet. Also this model explains coincidence of energy of the vibron paired to the transition and Bohr frequency of the transition.

Nonlinear optical responses of molecular systems with vibronic coupling in fluctuating environments

The topological profiles of the nonlinear optical properties of a two-level molecular system involving simplified versions of intramolecular coupling immersed in a thermal reservoir have been studied in four-wave mixing (FWM) spectroscopy. Solvent effects have been explicitly considered by modeling the nonradiative interaction with the solute as a random variable. To formulate a solution, it is necessary to introduce stochastic considerations. We assume that system–solvent interactions induce random shifts in the Bohr frequency of the adiabatic states, and their manifestation corresponds to the broadening of the upper level. The Born–Oppenheimer (BO) electronic energy curves for this molecular model consist of two intertwined harmonic oscillator potentials shifted in both their position and their minimum equilibrium energy. The critical quantities for this analysis are the transition and permanent dipole moments, which depend strongly on intramolecular coupling. Our results show how absorption and refractive index are affected by vibronic coupling and solvent stochasticity.

Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.

Photon wave-mechanical theory of single-photon diffraction from a mesoscopic hole

A quantum electrodynamical theory for single-photon diffraction of light from a mesoscopic hole in a quantum well (QW) screen with (Schrödinger) electron dynamics is established. Photon wave mechanics (PWM) is used to extend and bridge the gap between hitherto used semiclassical and quantum optical theoretical approaches for analyses of diffraction of light. An essentially complete calculation is carried out for a paradigm example: (i) a single-photon point-like electric-dipole (ED) primary source, emitting (ii) a wave packet photon toward (iii) a two-level QW screen possessing (iv) in-plane jellium electrodynamics with (v) a single mesoscopic ED hole. The PWM description is based on the, in this context attractive, Riemann–Silberstein–Oppenheimer–Bialynicki formulation. The effective size of the hole is determined on the basis of a quantum mechanical extinction theorem for the in-plane jellium electron dynamics in the vicinity of the hole. The incident electrodynamic field induced current density in the screen (with hole) allows one to obtain the single-photon probabilities for scattering from the hole and the screen. A one-photon wave train emitted by the primary ED point-like source is assumed to drive the scattering process. The far-field hole-screen diffraction pattern is calculated paying particular attention to the spectral diffraction (correlation) pattern, which illustrates the interplay between the wave-train frequency, the screen/hole local-field resonance frequency, and the Bohr frequency. Our theory shows that the ED hole polarizability is close to that of a one-dimensional single harmonic oscillator with resonance frequency coinciding with the local-field resonance in the two-level QW screen.

The Collapse Before a Quantum Jump Transition

We may infer a transition $|n \rangle \to |m \rangle$ between energy eigenstates of an open quantum system by observing the emission of a photon of Bohr frequency $\omega_{mn} = (E_n-E_m) / \hbar$. In addition to the "collapses" to the state $|m\rangle$, the measurement must also have brought into existence the pre-measurement state $|n \rangle$. As quantum trajectories are based on past observations, the condition state will jump to $| m \rangle$, but the state $|n\rangle$ does not feature in any essential way. We resolve this paradox by looking at quantum smoothing and derive the time-symmetric model for quantum jumps.

Graviatom of Superheavy Dark Matter as a Source of Gravitational Radiation

The nature of dark matter (DM) in modern physics is an important problem. We consider a quantum system consisting of two identical particles which are candidates for the role of DM.We call them graviatoms, and they could be formed in the early Universe. We find the energy spectrum of the gravitatom from DM particles, the Bohr radius, the intensity and frequency of gravitational radiation, and the lifetime of a state. This lifetime is large for superheavy particles. Estimates of these values for different masses of DM particles are given. The amplitude of a gravitational wave from a cloud of dark matter in the Milky Way is also estimated.

On the structure of quantum Markov semigroups of weak coupling limit type

We discuss some recent results on the structure of quantum Markov semigroups of weak coupling limit type and their stationary states. In particular, we identify the minimal central projection in the fixed point algebra where they act in a trivial way and show, when they admit a single Bohr frequency, that all invariant states are convex combinations of equilibrium states and arbitrary states supported in the above minimal central projection.

Induced two-body scattering resonances from a square-well potential with oscillating depth

In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length a has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.

Entropy Production and Detailed Balance for a Class of Quantum Markov Semigroups

We give an explicit entropy production formula for a class of quantum Markov semigroups, arising in the weak coupling limit of a system coupled with reservoirs, whose generators [Formula: see text] are sums of other generators [Formula: see text] associated with positive Bohr frequencies [Formula: see text] of the system. As a consequence, we show that any such semigroup satisfies the quantum detailed balance condition with respect to an invariant state if and only if all semigroups generated by each [Formula: see text] do so with respect to the same invariant state.

Excitation spectra of a quantum ring embedded in a photon cavity

We explore the response of a quantum ring system coupled to a photon cavity with a single mode when excited by a classical dipole field. We find that the energy oscillates between the electronic and photonic components of the system. The contribution of the linear and the quadratic terms in the vector potential to the electron–photon interaction energy are of similar magnitude, but opposite signs stressing the importance of retaining both in the model. Furthermore, we find different Fourier spectra for the oscillations of the center of charge and the oscillations of the mean photon number in time. The Fourier spectra are compared to the spectrum of the many-body (MB) states and selection rules discussed. In case of the center of charge oscillations, the dipole matrix elements preselect the allowed Bohr frequencies of the transitions, while for the oscillations of the mean photon number, the difference of the photon content of the MB states influences the selection rules.

Weak and strong coupling of a quantum emitter with a meta-surface

Meta-surfaces are the bidimensional analogs of metamaterials. They are made on resonant elements periodically disposed on a surface. They have the ability of controlling the polarization of light and to generalized refraction laws as well. They have also been used to enhance the generation of the second harmonic. It seems however that their near-field properties have not been investigated. In this work, the coupling of an emitter with a meta-surface made of a periodic set of resonant linear dipoles was studied. Bloch surface modes localized on the meta-surface exist due the resonance of the dipoles. The strong coupling regime with a emitter can be reached when the Bohr frequency of the emitter is in resonance with the Bloch modes of the meta-surface.

Study of the absorptive and dispersive responses of molecular systems under stochastic considerations

Absorptive and dispersive nonlinear optical properties have been studied considering a two-level molecular system with permanent dipole moments immersed in a thermal reservoir interacting with a classical electromagnetic field. Our model is based in a stochastic description, where the system–solvent interaction induces random shifts in the Bohr frequency (ω0) that transforms ω0 into a stochastic variable ξ(t). Our results show that it is necessary to neglect the rotating-wave approximation in order to measure the effect of the permanent dipole moments. The two-photon transitions over those with one-photon are favored when the permanent dipole moments are considered.

Convergence of Numbers of Synapses and Quantum Foci within Human Brain Space: Quantitative Implications of the Photon as the Source of Cognition

Quantitative solutions involving classical methods indicated that the numbers of quantum foci within the human cerebrum are the same order of magnitude as the numbers of synapses in the cerebral cortices. The Bohr frequency for the magnitude of the quantum associated with the removal of one nucleus from another is within the range of the width of synapse (~1 µm) while the recoil energy from a rest mass photon is equivalent to the energy produced by the entire field of dynamic neurons per second. The intrinsic energy (10-20 J) associated with each action potential is similar to the gravitational potential energy from Planck’s mass applied across 1 µm. Both the endogenous cerebral magnetic field strength which is similar in magnitude to intergalactic intensities and the interaction between weak geomagnetic variations and the cerebrum’s electric dipole current are associated with photon flux densities in the order (10-11 W∙m-2) that have been measured in the laboratory. The perspective of the human cerebral volume as a field of foci of photon quanta offers different perspectives for the intrinsic nature of consciousness and cognition and their influence by phenomena from astronomical origins.

Convergence of Numbers of Synapses and Quantum Foci within Human Brain Space: Quantitative Implications of the Photon as the Source of Cognition

Quantitative solutions involving classical methods indicated that the numbers of quantum foci within the human cerebrum are the same order of magnitude as the numbers of synapses in the cerebral cortices. The Bohr frequency for the magnitude of the quantum associated with the removal of one nucleus from another is within the range of the width of synapse (~1 µm) while the recoil energy from a rest mass photon is equivalent to the energy produced by the entire field of dynamic neurons per second. The intrinsic energy (10-20 J) associated with each action potential is similar to the gravitational potential energy from Planck’s mass applied across 1 µm. Both the endogenous cerebral magnetic field strength which is similar in magnitude to intergalactic intensities and the interaction between weak geomagnetic variations and the cerebrum’s electric dipole current are associated with photon flux densities in the order (10-11 W∙m-2) that have been measured in the laboratory. The perspective of the human cerebral volume as a field of foci of photon quanta offers different perspectives for the intrinsic nature of consciousness and cognition and their influence by phenomena from astronomical origins.

Astronomical, Chemical, and Biological Implications of 10-20 Joules as a Fundamental Quantum Unit of Information for Neurofunction

: The persistence of 10-20 J as the fundamental unit of interaction between the most fundamental electromagnetic and molecular interactions within physical-chemical and biological systems reflects a universal origin. This quantity becomes apparent when the energetic parameters associated with the future (final) epoch of the universe are applied at the level of the smallest length. The quantum is a primary solution for the Bohr frequency for specific electron shells and the integrative quantity between the action potential of the neuron and the bulk velocity of the entire cerebral electromagnetic field when applied to the equations for de Broglie waves and Heisenberg uncertainty. The continuous and serial transformation of the 10-20 J quanta within cellular and brain space could replace the myriad of molecular pathways to a single and fundamental operator. Because the difference between the energy equivalence for an electron’s classic and Compton wavelength width by a Lorentz transform is about 10-20 J, this quantity, when applied appropriately, could facilitate the collapse of wave functions within brain space.

SYMMETRY PROPERTIES IN THE STUDY OF THE RAYLEIGH-TYPE OPTICAL MIXING SIGNAL IN PRESENCE OF A THERMAL BATH

In this work are studied the symmetry properties of the Rayleigh-type optical mixing signal of a two-level molecular system immersed in a thermal bath and irradiated by a classical electromagnetic field. The solvent induces a random shift of the Bohr frequency in the molecular system. A methodology based in cumulant expansions is employed to obtain the average of the coherences, populations, and susceptibilities of Fourier components associated, calculated by the optical stochastic Bloch equations. These symmetry properties show the dependence of the measured spectra with the variations in the frequencies of the incident fields. Our results show that the inclusion of the thermal bath diminishes the intensity response as well it promotes the loss of the symmetry properties, compared with the same results in the absence of the bath.

Convergence to equilibrium under a random Hamiltonian

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.