Density-matrix Calculations Research Articles

Second-order quadrupole interaction based detection of ultra-slow motions: Tensor operator framework for central-transition spectroscopy and the dynamics in hexagonal ice as an experimental example

The second-order quadrupolar broadening of the central transition of nuclear probes with half-integer spins I is demonstrated to be useful to detect ultraslow molecular motions. On the basis of density matrix calculations explicit expressions are derived for quadrupolarly modulated sin–sin and cos–cos signals of selectively excited nuclei with I=3/2, 5/2, 7/2, and 9/2. These correlation functions are suitable for implementation in two-dimensional exchange spectroscopy as well as for stimulated-echo experiments. As an application, 17O measurements of the reorientational correlation function of water molecules in hexagonal ice are presented.

Four-wave mixing in a ring cavity

We investigate a four-wave-mixing process in an N interaction scheme in Rb vapor placed inside a low-finesse ring cavity. We observe strong amplification and generation of a probe signal, circulating in the cavity, in the presence of two strong optical pump fields. We study the variations in probe field gain and dispersion as functions of experimental parameters with an eye on the potential application of such a system for enhanced rotation measurements. Density-matrix calculations are performed to model the system and are shown to provide good qualitative agreement with the experiment.

Coherent Electronic Coupling in Atomically ThinMoSe2

We report the first direct spectroscopic evidence for coherent electronic coupling between excitons and trions in atomically thin transition metal dichalcogenides, specifically monolayer MoSe2. Signatures of coupling appear as isolated cross-peaks in two-color pump-probe spectra, and the lineshape of the peaks reveals that the coupling originates from many-body interactions. Excellent agreement between the experiment and density matrix calculations suggests the formation of a correlated exciton-trion state due to their coupling.

A New Graphical User Interface for Teaching NMR

The classical Nuclear Magnetic Resonance (NMR) vector model is known to be very effective and useful in teaching basic NMR 1D pulse sequences such as spin echo. For more complicated spin systems, density matrix calculation is often used. This method is known to be very complicated and not easy to follow after couple steps. Students usually get lost within the calculation and loose the physical meaning of the effect of different NMR pulses and other operations (chemical shifts, scalar-couplings) on the spin-system under investigation. As a compromise, another methodology has been developed which depends on the spin angular momentum operators. This is known as product operator formalism which involves less mathematical calculations, but still requires the user to know the correct outcome of different NMR pulses, scalar couplings and chemical shifts on different spin operators. We have developed product operator graphical user interface (OP-GUI) using MATLAB software that is capable of calculating product operators of up to four-coupled ½ spin systems. The effect of NMR pulses, scalar- coupling and chemical shifts on the spin system under investigation can be easily calculated. In this paper, several examples are given as prove of concept to show the capability and flexibility of the obtained OP-GUI in dealing with spin systems. We believe the obtained calculator is an effective teaching tool for new students in NMR and will help them to better understand and interpret complicated NMR pulse sequences applied on up to four weakly coupled ½ spin systems.

Coherent Coupling of Excitons and Trions in a Photoexcited CdTe/CdMgTe Quantum Well

We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

Local-field approximation of homonuclear dipolar interactions in 7Li-NMR: Density-matrix calculations and random-walk simulations tested by echo experiments on borate glasses

NMR echo techniques have proven to be important to study dynamics in ion conductors and other solid materials. Using the spin-3/2 nucleus 7Li as a probe, both the quadrupolar and the often neglected homonuclear dipolar interactions modulate the NMR frequency as the ion performs jump processes. Retaining only the local-field term of the many-body Hamiltonian, the impact of the dipolar interaction on various echo experiments was studied using spin dynamics calculations yielding products of dipolar and quadrupolar correlation functions. Using a simple stochastic model these functions were simulated with particular emphasis on the impact of ionic motions and on the conditions under which the dipolar and quadrupolar contributions factorize. The results of the computations and of the random-walk simulations are compared with experimental data obtained for various lithium borate and lithium borophosphate glasses. It is concluded that the local-field approximation is a useful means of treating the Li–Li dipole interactions and that the simple model that we introduce is capable of describing many experimentally observed features. Furthermore, because the dipolar and quadrupolar contributions essentially factorize, a selective determination of the corresponding correlation functions becomes possible.

Coherent Excitonic Coupling in an Asymmetric Double InGaAs Quantum Well Arises from Many-Body Effects

We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum, and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the double well coherent optical response. Coherent and incoherent contributions to the coupling between the two quantum well excitons are clearly separated. An excellent agreement with density matrix calculations reveals that coherent interwell coupling originates from many-body interactions.

Spin transport in buckled bilayer silicene

In this article, we have theoretically studied and investigated spin polarized electronic transport in buckled bilayer silicene (BLS) using semi-classical Monte–Carlo approach. Monte Carlo simulations are used to model spin transport along with spin density matrix calculations in the semiconductor devices. Dephasing of the spin vectors in the buckled bilayer silicene is due to Elliott–Yafet (EY) and D’yakonov–Perel (DP) relaxation mechanisms. The spin dephasing length is estimated in the range of 2μm for buckled bilayer silicene. Next, we investigated the ensemble averaged spin vector variation in buckled bilayer silicene along the length of the device with varying temperature. We observe a negligible variation in the spin dephasing length in the temperature range of 4–77K. As the temperature increases from 77K to 373K, we find a monotonous decrease in the spin dephasing length. In our study, we found buckled bilayer silicene to be a promising candidate for next generation spintronic devices.

The DQF-COSY NMR Experiment, a Way to Detect Small J Couplings in the Case of Fast Relaxing Nuclei: Application to <sup>59</sup>Co in the Tetrahedral Mixed-Metal Cluster HRuCo<sub>3</sub>(CO)<sub>11</sub>(PPh<sub>3</sub>)

The first investigation and analysis of 59Co 2D NMR homonuclear chemical shift correlation spectra for a ruthenium-based tetrahedral mixed-metal cluster HRuCo3(CO)11(PPh3) are reported. For this cluster in solution and by contrast to the conventional COSY NMR experiment, the double-quantum filtered (DQF) COSY NMR spectrum proves the existence of a scalar coupling constant between 59Co nuclei. In order to obtain a value of this coupling, the 2D COSY spectrum for a three-spin 7/2 AX2 system has been simulated by numerical density matrix calculations. The comparison between experimental and theoretical 2D NMR COSY spectra gives a spin-coupling constant |1J(59Co-59Co)| ＜ 300 Hz for this cluster.

Radio-frequency spectroscopy in the dark

We demonstrate a technique for investigation of a strongly perturbed atomic system, which is an extension of standard radio-frequency spectroscopy. Analogous to ``relaxation in the dark'' experiments, this technique allows a reconstruction of the population distribution of the unperturbed atomic state by observing the rf spectroscopy signal after an abrupt switch-off of the perturbing light. The evolution and relaxation dynamics of the individual magnetic sublevels is investigated. Experimental observations are supported with numerical modeling based on a full density-matrix calculation performed in the presence of spin-exchange collisions and homogeneous relaxation.

Spin transport in N-armchair-edge silicene nanoribbons

In this article, we have investigated spin polarized electronic transport in N-armchair-edge silicene nanoribbons (N-ASiNRs, where N is the number of atoms in armchair edge) using semi-classical Monte-Carlo approach. Monte Carlo simulations are used to model spin transport along with spin density matrix calculations in the semiconductor devices. The spin vector dephasing in the silicene nanoribbons are due to Elliott-Yafet (EY) and D'yakonov-Perel (DP) relaxation mechanisms. In this article, we theoretically studied spin polarized transport along the length of the N-armchair-edge silicene nanoribbons structure and the spin dephasing length is estimated to be in the range of 3 μm for N-ASiNRs. Next, we have investigated the ensemble averaged spin vector variation in N-ASiNRs along the length of the nanoribbons with varying temperature. We observe a negligible variation in the spin dephasing length in the temperature range of 4 K to 373 K. As the localized temperature increases from 373 K to 1000 K, we observe a decrease in the spin dephasing length by extrapolating the curve up to 1000 K and in these higher temperature ranges spin dephasing length decrease due to hot electron/phonon effects and higher scattering rates. We have also studied the ensemble averaged spin vector variation in N-ASiNRs along the length of the nanoribbons with varying width (N) of the nanoribbons and found negligible effect of width (N) on the spin dephasing length in N-ASiNRs. In our study, we finally find N-armchair-edge silicene nanoribbons to be the promising candidates for next generation spintronics devices.

The Quantum Coherent Mechanism for Singlet Fission: Experiment and Theory

The absorption of one photon by a semiconductor material usually creates one electron-hole pair. However, this general rule breaks down in a few organic semiconductors, such as pentacene and tetracene, where one photon absorption may result in two electron-hole pairs. This process, where a singlet exciton transforms to two triplet excitons, can have quantum yields as high as 200%. Singlet fission may be useful to solar cell technologies to increase the power conversion efficiency beyond the so-called Shockley-Queisser limit. Through time-resolved two-photon photoemission (TR-2PPE) spectroscopy in crystalline pentacene and tetracene, our lab has recently provided the first spectroscopic signatures in singlet fission of a critical intermediate known as the multiexciton state (also called a correlated triplet pair). More importantly, we found that population of the multiexciton state rises at the same time as the singlet state on the ultrafast time scale upon photoexcitation. This observation does not fit with the traditional view of singlet fission involving the incoherent conversion of a singlet to a triplet pair. However, it provides an experimental foundation for a quantum coherent mechanism in which the electronic coupling creates a quantum superposition of the singlet and the multiexciton state immediately after optical excitation. In this Account, we review key experimental findings from TR-2PPE experiments and present a theoretical analysis of the quantum coherent mechanism based on electronic structural and density matrix calculations for crystalline tetracene lattices. Using multistate density functional theory, we find that the direct electronic coupling between singlet and multiexciton states is too weak to explain the experimental observation. Instead, indirect coupling via charge transfer intermediate states is two orders of magnitude stronger, and dominates the dynamics for ultrafast multiexciton formation. Density matrix calculation for the crystalline tetracene lattice satisfactorily accounts for the experimental observations. It also reveals the critical roles of the charge transfer states and the high dephasing rates in ensuring the ultrafast formation of multiexciton states. In addition, we address the origins of microscopic relaxation and dephasing rates, and adopt these rates in a quantum master equation description. We show the need to take the theoretical effort one step further in the near future by combining high-level electronic structure calculations with accurate quantum relaxation dynamics for large systems.

Numerical Simulations of Photon Echoes for both Space and Time using Density Matrix and Iterative Approach

We present a three-dimensional computational tool for atom-field interactions such as optically locked photon echoes in a three level system for both space and time axes, where time-dependent density matrix calculations are combined with iterative methods. We provide an exact numerical simulation tool without any approximations. To the best of our knowledge, this is the first computational tool for short-pulse light interactions with an optical medium, whose space dimension along the pulse propagation direction is simultaneously cared for density matrix calculations.

Spin transport in silicene and germanene

In this article, we have investigated spin polarized electronic transport in two dimensional sheet materials of silicon and germanium, such as, monolayer silicene and germanene, using semi-classical Monte-Carlo approach. Monte-Carlo simulations are used to model spin transport along with spin density matrix calculations in the devices. Dephasing of the spin vectors in silicene and germanene are due to primarily D'yakonov–Perel (DP) and Elliott–Yafet (EY) relaxation mechanisms. But, as silicene and germanene has high carrier mobility the latter one is not the dominant relaxation mechanism. In this work, we studied spin polarized transport along the length of the planar monolayer silicene, buckled monolayer silicene and germanene monolayer structure and the spin dephasing length is estimated to be in the range of 0.5 μm for silicene and 1.5 μm for germanene. We also investigated the ensemble averaged spin vector variation along the length of the planar and buckled monolayer silicene and germanene with varying temperature. Finally, we studied the effect of variation of vertical electric field (Ez) on spin dephasing length in silicene buckled monolayer structure. Silicene and germanene show significant potential for future nanoelectronics devices.

Magnon scattering in single and bilayer graphene intercalates

Semi-classical Monte Carlo simulation is used to determine the effect of magnetic substance as intercalated layer in single layer and bilayer graphene intercalates on spin relaxation length. Spin relaxation lengths are studied with spin density matrix calculation under the effect of one magnon scattering mechanisms. Spin relaxation lengths are simulated and made comparisons by including magnon scattering with phonon scattering. The results are simulated with varying temperatures below Curie temperature.

Optimized purification for density matrix calculation

We present an optimized linear-scaling purification method for calculation of the density matrix. Traditional purification polynomials, including those proposed by McWeeny and Holas, are monotonic and have stable fixed points at 0 and 1. We relax these conditions and develop optimized purification polynomials which achieve maximum reduction in the LUMO eigenvalue and maximum increase in the HOMO eigenvalue, while heading towards idempotency. We demonstrate that optimized purification achieves appreciable speedup over traditional purification, which increases with decreasing band-gap. We also show improvement over non-monotonic purification proposed by Rubensson, while having identical performance for polynomials of degree 3.

Impulsive optical spin orientation by Zeeman state mixing in ruby

Optical excitation of electron spin orientation and spin coherence is studied associated with the state-mixing due to the coupling of the anisotropic fine-structure and Zeeman energies. An adiabatically-induced magnetization is none of the consequence of either the angular-momentum transfer from light to matter or the Boltzmann population difference in the presence of magnetic field. Different types of the state-mixings are described with respect to the combination of the Zeeman sublevels. Experiment has been carried out for a sample of ruby at room temperature. Dependences of the intensity of the induced magnetization on wide ranges of the strength and direction of the magnetic field have shown excellent agreement with density-matrix calculation of the spin expectation values. Consideration of the spin state-mixing also accounts for the polarization-insensitive optical excitation of electron spin orientation previously reported for spin ensembles in poly-crystal and solution.

Spin Relaxation in Germanium Nanowires

We use semiclassical Monte Carlo approach along with spin density matrix calculations to model spin polarized electron transport. The model is applied to germanium nanowires and germanium two-dimensional channels to study and compare spin relaxation between them. Spin dephasing in germanium occurs because of Rashba Spin Orbit Interaction (structural inversion asymmetry) which gives rise to the D’yakonov-Perel (DP) relaxation. In germanium spin flip scattering due to the Elliot-Yafet (EY) mechanism also leads to spin relaxation. The spin relaxation tests for both 1D and 2D channels are carried out at different values of temperature and driving electric field, and the variation in spin relaxation length is recorded. Spin relaxation length in a nanowire is found to be much higher than that in a 2D channel due to suppression of DP relaxation in a nanowire. At lower temperatures the spin relaxation length increases. This suggests that spin relaxation in germanium occurs slowly in a 1D channel (nanowires) and at lower temperatures. The electric field dependence of spin relaxation length was found to be very weak.

Quantum Interference between Three Two-Spin States in a Double Quantum Dot

Qubits based on the singlet (S) and the triplet (T(0), T(+)) states in double quantum dots have been demonstrated in separate experiments. It has been recently proposed theoretically that under certain conditions a quantum interference could occur from the interplay between these two qubit species. Here we report experiments and modeling that confirm these theoretical predictions and identify the conditions under which this interference occurs. Density matrix calculations show that the interference pattern manifests primarily via the occupation of the common singlet state. The S/T(0) qubit is found to have a much longer coherence time as compared to the S/T(+) qubit.

Variational Two-Particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-Adapted Lifting Conditions

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.