Dynamic Dephasing Research Articles

Experimental demonstration of suppressing residual geometric dephasing

The geometric phase is regarded as a promising strategy in fault tolerance quantum information processing (QIP) domain due to its phase only depending on the geometry of the path executed. However, decoherence caused by environmental noise will destroy the geometric phase. Traditional dynamic decoupling sequences can eliminate dynamic dephasing but can not reduce residual geometric dephasing, which is still vital for high-precision quantum manipulation. In this work, we experimentally demonstrate effective suppression of residual geometric dephasing with modified dynamic decoupling schemes, using a single trapped 171Yb+ ion. The experimental results show that the modified schemes can reduce dephasing rate up to more than one order of magnitude compared with traditional dynamic decoupling schemes, where residual geometric dephasing dominates. Besides, we also investigate the impact of intensity and correlation time of the low-frequency noise on coherence of the quantum system. And we confirm these methods can be used in many cases.

Non-Abelian Geometric Dephasing.

We study the adiabatic dynamics of degenerate quantum states induced by loop paths in a control parameter space. The latter correspond to noisy trajectories if the system is weakly coupled to environmental modes. On top of conventional dynamic dephasing, we find a universal non-Abelian geometric dephasing (NAGD) contribution and express it in terms of the non-Abelian Berry connection and curvature. We show that NAGD implies either decay or amplification of coherences as compared to the coherences when only dynamic dephasing is present. The full NAGD matrix structure can be probed through interference experiments. We outline such a detection scheme for modified Majorana braiding setups.

Non-Abelian Berry phase for open quantum systems: Topological protection versus geometric dephasing

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protocols proposed in this work for the detection of NAGD. In particular, we formulate interference measurements providing full access to NAGD. Apart from a factor due to the dynamic phase and its fluctuations, the averaged evolution operator contains the averaged Berry matrix. A polar decomposition of this non-unitary matrix into the product of a unitary, $V$, and a positive semi-definite Hermitian matrix, $R$, reveals the physics of the NAGD contributions. Unlike the conventional dynamic dephasing rate, the NAGD eigenrates encoded by $R$ depend on the loop orientation sense and, in particular, change sign under a reversal of the direction. A negative rate then implies amplification of coherences as compared to the ones when only dynamic dephasing is present. The non-Abelian character of geometric dephasing is rooted in the non-commutativity of $V$ and $R$ and causes smoking-gun signatures in interference experiments. We also clarify why systems subject to topological protection do not show geometric dephasing. Without full protection, however, geometric dephasing can arise and has to be taken into account. As concrete application, we propose spin-echo NAGD detection protocols for modified Majorana braiding setups.

Suppressing the geometric dephasing of Berry phase by using modified dynamical decoupling sequences

Even though traditional dynamical decoupling methods have the ability to resist dynamic dephasing caused by low frequency noise, they are not appropriate for suppressing the residual geometric dephasing, which arises from the disturbance of the geometric loop in the parameter space. This prevents the precision of quantum manipulation-based geometric quantum gates from being promoted further. In this paper, we design two kinds of modified dynamical decoupling schemes to suppress the residual geometric dephasing. The further numerical simulation demonstrates the validity of our schemes.

Phase coherence and energy relaxation in epitaxial graphene under microwave radiation

We have performed low-temperature magnetotransport measurements on monolayer epitaxial graphene under microwave radiation and extracted the radiation-induced effective temperatures, energy relaxation, and the dephasing times. We established that the response of the graphene sample is entirely bolometric at least up to 170 GHz. Dynamic dephasing, i.e., the time-reversal symmetry breaking effect of the ac electromagnetic field rather than mediated by heating, may become significant in the terahertz frequency range and in samples with longer phase coherence time.

Dynamic dephasing of magnetization precession in arrays of thin magnetic elements

We present a systematic micromagnetic simulation to demonstrate how the static and dynamic behaviors of single nanomagnets are modified in an array. We examine the precessional frequency and damping as a function of the width to separation $(w/s)$ ratio in arrays of square and circular magnetic elements and compare it with the single nanomagnet dynamics. Both frequency and damping are significantly modified by the interelement interaction. The precessional frequency shows a general trend of increase with $w/s$ ratio due to the increase in the dipolar magnetic field in the array and split into multiple modes when the $w/s$ ratio becomes greater than 1. The damping of precession increases with increase in $w/s$ ratio, i.e., with decrease in the separation between the elements. The increase in damping is found to be due to the mutual dephasing of precession of elements in an array. For larger square nanomagnets, $(\text{width}=150\text{ }\text{nm},\text{thickness}=50\text{ }\text{nm})$, where the single nanomagnet dynamics is inherently nonuniform, the effect of the array only increases the incoherence in the precession. For larger circular nanomagnets, $(\text{width}=150\text{ }\text{nm},\text{thickness}=50\text{ }\text{nm})$, where the single nanomagnet shows slow vortex core oscillation, the array modifies the dynamics into incoherent spin-wave dynamics whose coherence increases with the increase in $w/s$ ratio. Analysis of static and dynamic magnetic images reveals that the dynamics is strongly dependent on the static magnetization in the arrays. The results presented here show that the dynamics of arrays of nanomagnets is significantly or entirely different from that of individual elements, and hence measurements from arrays may not be considered as the single nanomagnet dynamics. We also evaluate the role of dynamic dephasing in the increased damping coefficient.

Enhanced diffusion weighting generated by selective adiabatic pulse trains

A theoretical description and experimental validation of the enhanced diffusion weighting generated by selective adiabatic full passage (AFP) pulse trains is provided. Six phantoms (Ph-1–Ph-6) were studied on a 4 T Varian/Siemens whole body MRI system. Phantoms consisted of 2.8 cm diameter plastic tubes containing a mixture of 10 μm ORGASOL polymer beads and 2 mM Gd-DTPA dissolved in 5% agar (Ph-1) or nickel(II) ammonium sulphate hexahydrate doped (56.3–0.8 mM) water solutions (Ph-2–Ph-6). A customized localization by adiabatic selective refocusing (LASER) sequence containing slice selective AFP pulse trains and pulsed diffusion gradients applied in the phase encoding direction was used to measure 1H 2O diffusion. The b-value associated with the LASER sequence was derived using the Bloch–Torrey equation. The apparent diffusion coefficients measured by LASER were comparable to those measured by a conventional pulsed gradient spin-echo (PGSE) sequence for all phantoms. Image signal intensity increased in Ph-1 and decreased in Ph-2–Ph-6 as AFP pulse train length increased while maintaining a constant echo-time. These experimental results suggest that such AFP pulse trains can enhance contrast between regions containing microscopic magnetic susceptibility variations and homogeneous regions in which dynamic dephasing relaxation mechanisms are dominant.

Assessment of brain iron and neuronal integrity in patients with Parkinson's disease using novel MRI contrasts

Postmortem demonstration of increased iron in the substantia nigra (SN) is a well-appreciated finding in Parkinson's disease (PD). Iron facilitates generation of free radicals, which are thought to play a role in dopamine neuronal loss. To date, however, magnetic resonance imaging (MRI) has failed to show significant in vivo differences in SN iron levels in subjects with PD versus control subjects. This finding may be due to the limitations in tissue contrasts achievable with conventional T(1)- and T(2)-weighted MRI sequences that have been used. With the recent development of novel rotating frame transverse (T(2rho)) and longitudinal (T(1rho)) relaxation MRI methods that appear to be sensitive to iron and neuronal loss, respectively, we embarked on a study of 8 individuals with PD (Hoehn & Yahr, Stage II) and 8 age-matched control subjects. Using these techniques with a 4T MRI magnet, we assessed iron deposits and neuronal integrity in the SN. First, T(2rho) MRI, which is reflective of iron-related dynamic dephasing mechanisms (e.g., chemical exchange and diffusion in the locally different magnetic susceptibilities), demonstrated a statistically significant difference between the PD and control group, while routine T(2) MRI did not. Second, T(1rho) measurements, which appear to reflect upon neuronal count, indicated neuronal loss in the SN in PD. We show here that sub-millimeter resolution T(1rho) and T(2rho) MRI relaxation methods can provide a noninvasive measure of iron content as well as evidence of neuronal loss in the midbrain of patients with PD.

Principles of magnetic resonance assessment of brain function

MRI has advanced to being one of the major tools for the assessment of brain function. This review article examines the basic principles that underpin these measurements. The main emphasis is on the characteristics and detection of blood oxygen level dependent (BOLD) contrast. In the first part of the article the relationship between BOLD, blood flow, blood oxygen, and the rate of metabolic consumption of oxygen is described. The four contrast mechanisms that contribute to the BOLD signal change, namely extravascular static and dynamic dephasing, intravascular T2-like changes, and the intravascular frequency offset effect are described in terms of their spatial localization and relative contributions to the BOLD signal. The current model of changes in blood flow being an indirect consequence of synaptic input to a region is presented. The second section of the article deals with the imaging characteristics of BOLD in terms of the attainable spatial resolution and linear system characteristics. In the third section, practical BOLD imaging is examined for choice of pulse sequence, resolution, echo time (TE), repetition time (TR), and flip angle. The final section touches on other MRI approaches that are relevant to cognitive neuroimaging, in particular the measurement of blood flow, blood volume, resting state fluctuations in the BOLD signal, and measures of connectivity using diffusion tensor imaging and fiber-tracking.

Dynamic dephasing changes in developing ischemic cerebral infarction in rats studied by Carr–Purcell T2 magnetic resonance imaging

Carr-Purcell (CP) T(2) MRI with adiabatic pulses, acquired with varying interecho interval (tau(CP)), was used to study the time course of T(2) and relative dynamic-dephasing contrast in the rat brain. Exposure to 30 min of middle cerebral artery occlusion (MCAo) resulted in an irreversible increase in absolute CP-T(2) relaxation times. This was not associated with signal change in the relative dynamic-dephasing images, as computed by subtracting short tau(CP) CP-T(2) images from long tau(CP) images and normalizing for long tau(CP) images. A day after MCAo strong CP-T(2) hyperintensity and low apparent diffusion coefficient were evident in the striatum with a decline in relative dynamic-dephasing contrast. Low dynamic dephasing contrast prevailed in striatum until day 5 post-MCAo, returning to control levels with similar time course to normalizing T(2) and diffusion. The present results show a novel behavior of dynamic-dephasing contrast in poststroke brain tissue, providing data to assess the age of infarction in association to T(2) images.

Proton T2 relaxation study of water, N-acetylaspartate, and creatine in human brain using Hahn and Carr-Purcell spin echoes at 4T and 7T.

Carr-Purcell and Hahn spin-echo (SE) measurements were used to estimate the apparent transverse relaxation time constant (T2) of water and metabolites in human brain at 4T and 7T. A significant reduction in the T2 values of proton resonances (water, N-acetylaspartate, and creatine/phosphocreatine) was observed with increasing magnetic field strength and was attributed mainly to increased dynamic dephasing due to increased local susceptibility gradients. At high field, signal loss resulting from T2 decay can be substantially reduced using a Carr-Purcell-type SE sequence.

Exciton states in quantum dot solids: excitation transfer and dynamic decorrelation

Coherent exciton transport in quantum dot solids is determined by electron and hole interdot tunneling and dipole–dipole interdot excitation transfer. We present a tight-binding theory of coupled dots to understand the interdot coupling and hybridization of states in dot solids. Results show that significant coupling is possible. Exciton dynamics in a dot solid is simulated by use of a Hubbard model that includes interdot carrier tunneling, electron–hole attraction and Forster exciton excitation transfer. Dynamic exciton decorrelation is driven by carrier tunneling. Dynamic exciton dephasing is driven by excitation transfer.

Solvent-induced dynamic polarization and vibrational dephasing of electronically excited molecules

In order to account for the extra vibrational Raman bandwidths observed specifically for electronically excited molecules in solution, a new model, the dynamic polarization model, has been introduced. In this model, the vibrational frequency of a highly polarizable electronically excited molecule in solution is stochastically modulated by the solvent-induced polarization. An olefinic C = C double bond is considered as the simplest prototype, for which the carbon-carbon stretch frequency can take values between the unpolarized (C = C) and the completely polarized (C+-C-) frequencies. The two-frequency exchange model is first introduced, followed by more general models. A focus is placed on the asymmetric exchange limit in which the solvent-induced polarization can be treated as a perturbation, so that the effect of the dynamic polarization manifests as a shift of the peak position and an increase in the bandwidth of the original unperturbed C = C stretch vibrational band. The experimental results on S1 trans-stilbene are discussed, based on the formulae derived.

Static and dynamic vibrational dephasing in a dense fluid

We present a theory of the statically broadened vibrational line shape of a molecule in liquid solution. In this limit of static broadening, the molecule vibrates in a static potential posed by fixed solvent molecules in a configuration chosen from the equilibrium distribution of fluid configurations. The line shape is calculated within the instantaneous normal mode approximation, in which the solute’s potential is approximated by a harmonic surface whose curvature agrees with that of the exact potential at the solute’s initial configuration. Within this approximation, the line shape is related to a configuration-averaged phonon Green’s function, which is calculated approximately with an analytical procedure. This theory represents a modification of our previous treatment of vibrational line shapes [J. Chem. Phys. 102, 2326 (1995)], in which the solvent dynamics were included. Comparison of the line shapes for static and dynamic solvents permits determination of the relative importance of static (inhomogeneous) and dynamic (homogeneous) contributions to line broadening. We carry out such comparisons for a harmonic diatomic in a Lennard-Jones solvent over a wide range of temperature and density.

Binary theory of dephasing in liquid solutions. II. Motion-transformed isotropic Raman spectra

Abstract The non-markovian theory of encounters is applied to calculations of impurity dephasing kinetics, corresponding Raman spectra and their moments. The theory is checked against the model of suddenly switched interactions and then applied to linewidth calculations under dynamic and stochastic dephasing. The former occurs for isotropic short- or long-range interactions. The latter takes place in the case of anisotropic dipole—dipole interactions modulated by fast rotation. Within perturbation theory the line is stated to be motion-narrowed in the former case and independent of translational motion in the latter case. If the interaction is strong, the line is motion-broadened in both cases but in different ways depending on whether the interaction was switched on by a jump or by continual diffusion. Perturbation theory becomes inapplicable to impurity dephasing much earlier than is conventionally assumed.