Off-diagonal Elements Of Density Matrix Research Articles

Coherence as an indicator to discern electromagnetically induced transparency and Autler–Townes splitting

Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are generally characterized and distinguished by the width of the transparency created in the absorption profile of a weak probe in presence of a strong control field. This often leads to ambiguities, as both phenomena yield similar spectroscopic signatures. However, an objective method based on Akaike’s information criterion (AIC) test offers a quantitative way to discern the two regimes when applied on the probe absorption profile. The obtained transition value of control field strength was found to be higher than the value given by pole analysis of the corresponding off-diagonal density matrix element. By contrast, we apply the test on ground state coherence and the measured coherence quantifier, which yields a distinct transition point around the predicted value even in presence of noise. Our test accurately captures the transition between two regimes, indicating that a proper measure of coherence is essential for making such distinctions.

High-frequency transport properties of a 2D electron gas with spin-orbit interaction under magnetic field driven topological transition

We study the transport properties of a two-dimensional electron system with an essential spin-orbit interaction under topological phase transition due to changing in-plane magnetic field. We have analyzed the contribution of diagonal and off-diagonal components of density matrix with respect to number of spin zone in the high-frequency conductivity. Analytical formulas for the conductivity tensor have been obtained. A numerical analysis giving full enough representation about the dependence of the conductivity on frequency and magnetic field is presented. We have shown that the contribution of the off-diagonal elements of density matrix is the greater than the higher the frequency of the alternating electromagnetic field. It has been established that for magnetic field value at which the minimum electron energy of upper spin zone exceeds the Fermi energy, the conductivity as a function of magnetic field change in discrete step.

Inversionless terahertz lasing in a four-level Raman-type scheme within mid-infrared quantum cascade structures

This paper applies the density matrix formalism to investigate a feasibility of inversionless terahertz (THz) lasing within a mid-infrared (mid-IR) quantum cascade laser (QCL). The proposed structure aims to use a mid-IR QCL as an efficient pump source that integrated with a four-level Raman-type scheme to generate THz radiation through strong coherence excited in the system. A key aspect of the design is that the THz generation is achieved by interplay between inversion-based lasing and coherent effects due to quantum interference between the microscopic polarizations of the dipole-allowed transitions in the four-level system. THz intensity gain arising from both the inversion-based lasing and coherent effects is derived from the off-diagonal density matrix elements in the four-level system. The simulation results indicate that the proposed design demonstrates the potential to achieve THz lasing with good temperature characteristics and without the need for population inversion.

Efficient quantum analytic nuclear gradients with double factorization.

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.

Coherence Amplification in Off-Diagonal Density Matrix Elements

We demonstrate coherence amplification in off-diagonal density matrix elements for a decoherence model for spin ½ particles with applied radio-frequency pulse without relaxation. The method of coherence amplification developed may be of general utility in applications in NMR/MRI.

Numerically efficient density-matrix technique for modeling electronic transport in mid-infrared quantum cascade lasers

We present a numerically efficient density-matrix model applicable to mid-infrared quantum cascade lasers. The model is based on a Markovian master equation for the density matrix that includes in-plane dynamics, preserves positivity of the density matrix and does not rely on phenomenologically introduced dephasing times. Nonparabolicity in the band structure is accounted for with a three-band $${\bf k}\cdot {\bf p}$$ model, which includes the conduction, light-hole, and spin-orbit split-off bands. We compare the model to experimental results for QCLs based on lattice-matched as well as strain-balanced InGaAs/InAlAs heterostructures grown on InP. We find that our density-matrix model is in quantitative agreement with experiment up to threshold and is capable of reproducing results obtained using the more computationally expensive nonequilibrium Green’s function formalism. We compare our density-matrix model to a semiclassical model where off-diagonal elements of the density matrix are ignored. We find that the semiclassical model overestimates the threshold current density by 29% for a 8.5- $$\upmu $$ m-QCL based on a lattice-matched heterostructure and 40% for a 4.6- $$\upmu $$ m-QCL based on a strain-balanced heterostructure, demonstrating the need to include off-diagonal density-matrix elements for accurate description of mid-infrared QCLs.

Novel cone-like and four-leaf-like optical rogue waves in a transient stimulated Raman scattering system

A new transient stimulated Raman scattering (TSRS) system in nonlinear optical fibers is studied. The analytical optical rogue wave solutions are constructed via the Lax–Darboux technique. Furthermore, novel cone-like rogue wave for the off-diagonal density-matrix element, four-leaf-like rogue waves for the pump and Stokes waves are observed. The results provide a new way to understand the propagation mechanism of the optical pulse in the stimulated Raman scattering media.

Breather phase transitions for a three-component transient stimulated Raman scattering system in nonlinear optics

A three-component transient stimulated Raman scattering system in nonlinear optics is investigated. By applying the Lax-Darboux scheme, analytical breather solutions are constructed. A detailed investigation was performed for the breathers of the off-diagonal density-matrix element, Stokes wave and pump wave. The system possesses both general and Kuznetsov-Ma breathers. Furthermore, an exact link is established between the phase states and spectrum parameter. Via adjusting the spectrum parameter, the breathers exhibit novel phase transitions. The amplitudes and densities of the wave envelopes also vary at the different phase states.

Implementation of Coherent Switching with Decay of Mixing into the SHARC Program.

Simulation of electronically nonadiabatic dynamics is an important tool for understanding the mechanisms of photochemical and photophysical processes. Two contrasting methods in which the electrons are treated quantum mechanically while the nuclei are treated classically are semiclassical Ehrenfest dynamics and trajectory surface hopping; neither method in its original form includes decoherence. Decoherence in the context of electronically nonadiabatic dynamics refers to the gradual collapse of a coherent quantum mechanical electronic state under the scrutiny of nuclear motion into a mixture of stable pointer states. This is modeled in the coherent switches with decay of mixing (CSDM) method by the decay of the off-diagonal elements of the electronic density matrix. Here, we present an implementation of CSDM in the SHARC program; a key element of the new implementation is the use of a different propagator than that used previously in the ANT program.

Nonadiabatic molecular dynamics with decoherence and detailed balance under a density matrix ensemble formalism

Author(s): Kang, J; Wang, LW | Abstract: The mixed quantum-classical nonadiabatic molecular dynamics (NAMD) is a powerful tool to study many phenomena, especially ultrafast carrier transport and cooling. Carrier decoherence and detailed balance are two major issues in NAMD. So far, there is no computationally inexpensive approach to incorporate both effects. While the decoherence effect can be easily included in the state density matrix formalism and the detailed balance can be included in surface hopping or the wave function collapse approach, it is difficult to include both of them in a unified formalism. In this work we introduce a state density matrix formalism (referred to as P-matrix) including both the decoherence and detailed balance effects for NAMD. This method is able to explicitly treat the decoherence between different pairs of adiabatic states. Moreover, the off-diagonal density matrix elements are divided into two parts, corresponding to energy-increasing and energy-decreasing transitions. The detailed balance is then enforced by a Boltzmann factor applied to the energy-increasing transition part. The P-matrix formalism is applied to study hot-hole cooling and transfer processes in Si quantum dot (QD) systems. The calculated hot-carrier relaxation time is consistent with experiments. In a QD-pair system, the hot-hole cooling time shows weak dependence on the QD spacing. However, the hot-carrier transfer rate from one QD to another is found to decrease exponentially with the QD-QD distance. When the QD spacing is small (∼1 nm), the hot-carrier transfer can be very efficient. It is also shown that the explicit treatment of decoherence time is important in order to treat this hot-carrier transfer correctly.

Spatio-temporal dynamics of shift current quantum pumping by femtosecond light pulse

Shift current—a photocurrent induced by light irradiating noncentrosymmetric materials in the absence of any bias voltage or built-in electric field—is one of the mechanisms of the so-called bulk photovoltaic effect. It has been traditionally described as a nonlinear optical response of a periodic solid to continuous wave light using a perturbative formula, which is linear in the intensity of light and which involves Berry connection describing the shift in the center of mass position of the Wannier wave function associated with the transition between the valence and conduction bands of the solid. Since shift current is solely due to off-diagonal elements of the nonequilibrium density matrix that encode quantum correlations, its peculiar space–time dynamics in response to femtosecond light pulse employed locally can be expected. To study such response requires to analyze realistic two-terminal devices, instead of traditional periodic solids, for which we choose paradigmatic Rice–Mele model sandwiched between two metallic electrodes and apply to it time-dependent nonequilibrium Green function algorithms scaling linearly in the number of time steps and capable of treating nonperturbative effects in the amplitude of external time-dependent fields. This reveals novel features: superballistic transport, signified by time dependence of the displacement, ∼tν with ν > 1, of the photoexcited charge carriers from the spot where the femtosecond light pulse is applied toward the electrodes; and photocurrent quadratic in light intensity at subgap frequencies of light due to two-photon absorption processes that were missed in previous perturbative analyses. Furthermore, frequency dependence of the DC component of the photocurrent reveals shift current as a realization of nonadiabatic quantum charge pumping enabled by breaking of left–right symmetry of the device structure. This demonstrates that a much wider class of systems, than the usually considered polar noncentrosymmetric bulk materials, can be exploited to generate nonzero DC component of photocurrent in response to unpolarized light and optimize shift-current-based solar cells and optoelectronic devices.

Plasmon-assisted two-photon Rabi oscillations in a semiconductor quantum dot – metal nanoparticle heterodimer

Tho-photon Rabi oscillations hold potential for quantum computing and quantum information processing, because during a Rabi cycle a pair of entangled photons may be created. We theoretically investigate the onset of this phenomenon in a heterodimer comprising a semiconductor quantum dot strongly coupled to a metal nanoparticle. Two-photon Rabi oscillations in this system occur due to a coherent two-photon process involving the ground-to-biexciton transition in the quantum dot. The presence of a metal nanoparticle nearby the quantum dot results in a self-action of the quantum dot via the metal nanoparticle, because the polatization state of the latter depends on the quantum state of the former. The interparticle interaction gives rise to two principal effects: (i) - enhancement of the external field amplitude and (ii) - renormalization of the quantum dot's resonance frequencies and relaxation rates of the off-diagonal density matrix elements, both depending on the populations of the quantum dot's levels. Here, we focus on the first effect, which results in interesting new features, in particular, in an increased number of Rabi cycles per pulse as compared to an isolated quantum dot and subsequent growth of the number of entangled photon pairs per pulse. We also discuss the destructive role of radiative decay of the excitonic states on two-photon Rabi oscillations for both an isolated quantum dot and a heterodimer.

Path integral Monte Carlo calculation of the momentum distribution of the homogeneous electron gas at finite temperature

Path integral Monte Carlo (PIMC) simulations are employed to calculate the momentum distribution of the homogeneous electron gas at finite temperature. Open paths are introduced to sample off-diagonal elements of the real-space density matrix. It is demonstrated how the restricted PIMC method can be extended to incorporate open paths in order to allow for the simulations in fermionic systems where a sign problem is present. The computed momentum distribution shows significant deviations from behavior of free fermions when strong correlations are present but agrees with predictions from variational methods.

Perturbative dissipation dynamics of a weakly driven cavity QED system: generalized microscopic master equation

We generalize a microscopic master equation method to study the dissipation dynamics of Jaynes–Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected Rabi oscillation and vacuum Rabi splitting analytically. The evolution of the decoherence factor of the weakly driven system reveals that the off-diagonal density matrix elements are oscillating at a frequency dependent on the driving strength and the initial population inversion. For highly inverted systems at the weak-driving limit, this frequency reduces to twice the value for the non-driven system, showing the dissipation dynamics unable to be discovered using more conventional approaches.

Measurement-Induced Strong Kerr Nonlinearity for Weak Quantum States of Light.

Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the single photon level. We probe the induced nonlinearity with weak coherent states and characterize the output non-Gaussian states with quantum state tomography. The strong nonlinearity is clearly witnessed as a change of sign of specific off-diagonal density matrix elements in the Fock basis.

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

The real-time broadening of density profiles starting from non-equilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum amplitude yield a broadening in perfect agreement with linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Relic neutrino decoupling with flavour oscillations revisited

We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, Neff. We find a value of Neff = 3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that Neff can be reduced down to 3.040 or enhanced up to 3.059.

Mixed Quantum-Classical Study of Nonadiabatic Curve Crossing in Condensed Phases.

We apply the mixed quantum-classical Liouville (MQCL) equation to investigate the nonadiabatic curve crossing in condensed phases. More specifically, electron transfer rate constants of the spin-Boson model are calculated by employing a rate constant expression using the collective solvent polarization as the reaction coordinate. In the calculation, classical nuclear degrees of freedom are initially sampled at the transition state configuration, and the initial state for the electronic degree of freedom is obtained from a mixed quantum-classical Boltzmann distribution. Different contributions to the electron transfer rate from the diagonal and off-diagonal elements of the initial density matrix, and contributions from trajectories with positive and negative initial velocities are analyzed. It is shown that the off-diagonal elements of the initial density matrix play an important role in the total electron transfer rate. The MQCL results are also compared with those calculated using Ehrenfest dynamics. It is found that, although the Ehrenfest dynamics is inaccurate when the reactive flux rate expression is used directly, it can give reasonably accurate results when individual contributions from the diagonal and off-diagonal elements of the initial density matrix are calculated.

Exact quantum Bayesian rule for qubit measurements in circuit QED.

Developing efficient framework for quantum measurements is of essential importance to quantum science and technology. In this work, for the important superconducting circuit-QED setup, we present a rigorous and analytic solution for the effective quantum trajectory equation (QTE) after polaron transformation and converted to the form of Stratonovich calculus. We find that the solution is a generalization of the elegant quantum Bayesian approach developed in arXiv:1111.4016 by Korotokov and currently applied to circuit-QED measurements. The new result improves both the diagonal and off-diagonal elements of the qubit density matrix, via amending the distribution probabilities of the output currents and several important phase factors. Compared to numerical integration of the QTE, the resultant quantum Bayesian rule promises higher efficiency to update the measured state, and allows more efficient and analytical studies for some interesting problems such as quantum weak values, past quantum state, and quantum state smoothing. The method of this work opens also a new way to obtain quantum Bayesian formulas for other systems and in more complicated cases.