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On the application of theoretical multi-dimensional coherence spectroscopy techniques to discrete quantum systems

David J. Ing

Published May 28, 2018• 0 citations
Publisher

Abstract

Multi-dimensional coherence spectroscopy (MDCS) is a powerful technique that allows insight about the energy dynamics of quantum systems, on the timescale in which they occur. This work focuses on the application of this technique to predict quantum noise characteristics of some known systems. It begins with an explanation of what noise is, and follows with a derivation of the equations used throughout the rest of the work. Chapter 3 explores the possibility of determining the spatial correlations of noise, via the use of the Bloch-Redfield equation - which quantifies the degree of correlation as a continuous variable - on a photosynthetic-inspired model. Not only is there a possibility to determine the degree of spatial correlation in the noise, it shows that the secular approximation – where small perturbations on the coherent dynamics of the system are discarded – is not valid when considering multi-dimensional (MD) spectra. The techniques are applied to the nitrogen-vacancy centre in chapter 4, with a focus on the temperature-dependent noise processes associated with the system. A prediction is made that this temperature-dependent noise – and the associated averaging processes – should be visible when conducting MDCS on the nitrogen-vacancy centre. Utilising noise, instead of suppressing it, is investigated in chapter 5, via the use of the decoherence probe system. In this set up, the noise experienced by a probe is measured, and a map is created. This chapter shows that not only does MDCS remove ambiguity in measuring a single probe, but when moving to a dual-probe system, it is possible to estimate the dipole orientation of quantum systems in the environment.

DOI
10.25439/rmt.27591045

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Multi-dimensional coherence spectroscopy (MDCS) is a powerful technique that allows insight about the energy dynamics of quantum systems, on the timescale in which they occur. This work focuses on the application of this technique to predict quantum noise characteristics of some known systems. It begins with an explanation of what noise is, and follows with a derivation of the equations used throughout the rest of the work. Chapter 3 explores the possibility of determining the spatial correlations of noise, via the use of the Bloch-Redfield equation - which quantifies the degree of correlation as a continuous variable - on a photosynthetic-inspired model. Not only is there a possibility to determine the degree of spatial correlation in the noise, it shows that the secular approximation – where small perturbations on the coherent dynamics of the system are discarded – is not valid when considering multi-dimensional (MD) spectra. The techniques are applied to the nitrogen-vacancy centre in chapter 4, with a focus on the temperature-dependent noise processes associated with the system. A prediction is made that this temperature-dependent noise – and the associated averaging processes – should be visible when conducting MDCS on the nitrogen-vacancy centre. Utilising noise, instead of suppressing it, is investigated in chapter 5, via the use of the decoherence probe system. In this set up, the noise experienced by a probe is measured, and a map is created. This chapter shows that not only does MDCS remove ambiguity in measuring a single probe, but when moving to a dual-probe system, it is possible to estimate the dipole orientation of quantum systems in the environment.
Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.
This work covers two main results united by multidimensional coherent spectroscopy (MDCS): one experimental and one theoretical. MDCS is a nonlinear optical technique in which a sample is probed using a series of ultrashort pulses. Measurements are made while varying the relative time delays between the pulses, and the resulting spectra yield a much richer set of information compared to traditional linear spectroscopies. The experimental work concerns the negatively charged silicon-vacancy (SiV) center in diamond. We use two-pulse correlation (TPC) spectroscopy and rephasing MDCS to probe a diamond sample with a high density of implanted SiV centers. These spectra reveal a large number of spectral peaks, which can be grouped into two families of SiV centers using the MDCS spectra. By comparing spectra from two polarizations of the incident light, we associate the two families with two orientation groups within the diamond. We link the differences in the frequencies of the spectral peaks to strain intrinsic to our sample, and use the peak locations from both families to solve for the full strain tensor local to the laser spot. By measuring TPC spectra at multiple points on the sample, we track changes in the measured strain. We observe non-zero strain on the order or 1e-5 at every measured location, and observe variation in both the normal and shear strain in the sample. We interpret the strain as likely to be due to the high implantation density of silicon in the diamond. These results could be useful when using SiV centers as a strain gauge. The theoretical work uses simulations to calculate spectra. The simulations developed here begin by recursively generating a list of Feynman diagrams for a given signal pathway and system. The contributions due to each Feynman diagram are calculated and combined to find the complete spectrum. The code is designed to be very flexible, and can be used to simulate arbitrary types of MDCS spectra and energy level diagrams. We then apply the simulations to investigate the effects of correlated dephasing due to scattering events in the Markovian limit on MDCS of interacting systems. We derive a mathematical expression to represent the dephasing rate of a coherence in terms of the dephasing rates of the coherences from the constituent energy transitions and the correlation matrix of these transitions. This expression is applied to simulate double-quantum and higher-order n-quantum spectra of multiple interacting systems. For double-quantum spectra, correlated dephasing results in a higher double-quantum dephasing rate, and anticorrelated dephasing results in a lower double-quantum dephasing rate. Similar results are found for the n-quantum dephasing rate. Generally, for certain configurations, the many-body dephasing rate can be arbitrarily low, and the n-quantum linewidth can be arbitrarily narrow, although this requires some form of anticorrelation. These results could be useful in creating quantum sensors with higher sensitivities, since one limit of the sensitivity is the decoherence time of the system.
Abstract Interpretation of multi-dimensional coherent spectra is presented in this chapter. Results are presented with the Bloch model. We begin by discussing the characteristic features of an MDCS rephasing plot corresponding to a two-level system. We then discuss the characteristics of inhomogeneous ensembles of two-level systems. We go on to discuss the origins of cross-peaks in MDCS, and then some of the signatures in MDCS that arise as a result of many-body effects. Double-quantum spectra, zero-quantum spectra, three-dimensional spectra, and nonrephasing single-quantum spectra are discussed. Finally, we discuss the impact that finite pulse effects can have on a multidimensional spectrum.
Noise spectroscopy with quantum sensors is a powerful tool for characterising the properties of the sensor environment and detecting critical magnetic phenomena. While replacing single sensors with large ensembles promises substantial gains in measurement sensitivity and field of view, the output becomes difficult to interpret when there is a variable coupling to targets across the sensing ensemble. In this work we present an analysis procedure for accessing the true source noise spectrum using ensemble coherence from dynamical decoupling measurements. We show that sequence timing plays a dual role in ensemble noise spectroscopy, setting both the frequency selectivity and the weighted collection of signal across the ensemble, and demonstrate how incorporation of the coupling distribution allows accurate parameter extraction of the noise. We apply this procedure to a model system, shallow nitrogen-vacancy centres in diamond, and show that consistent information about the spectral character of MHz-range surface noise can be obtained from two sensing ensembles featuring distinct depth distributions. Our results pave the way for using large quantum sensor ensembles for quantitative, broadband noise spectroscopy, with straightforward extension to other solid-state and molecular sensing platforms.
Multidimensional coherent spectroscopy (MDCS) has been established in quantum chemistry as a powerful tool for studying the nonlinear response and nonequilibrium dynamics of molecular systems. More recently, the technique has also been applied to correlated electron materials, where the interplay of localized and itinerant states makes the interpretation of the spectra more challenging. Here we use the Keldysh contour representation of effective models and nonequilibrium dynamical mean field theory to systematically study the MDCS signals of prototypical correlated lattice systems. By analyzing the current induced by sequences of ultrashort laser pulses we demonstrate the usefulness of MDCS as a diagnostic tool for excitation pathways and coherent processes in correlated solids. We also show that this technique allows to extract detailed information on the nature and evolution of photo-excited nonequilibrium states.