Single Quantum Transitions Research Articles

Single and double quantum transitions in spin-mixed states under photo-excitation

Electronic spins associated with the Nitrogen-Vacancy (NV) center in diamond offer an opportunity to study spin-related phenomena with extremely high sensitivity owing to their high degree of optical polarization. Here, we study both single- and double-quantum transitions (SQT and DQT) in NV centers between spin-mixed states, which arise from magnetic fields that are non-collinear to the NV axis. We demonstrate the amplification of the ESR signal from both these types of transition under laser illumination. We obtain hyperfine-resolved X-band ESR signal as a function of both excitation laser power and misalignment of static magnetic field with the NV axis. This, combined with our analysis using a seven-level model that incorporates thermal polarization and double quantum relaxation, allows us to comprehensively analyze the polarization of NV spins under off-axis fields. Such detailed understanding of spin-mixed states in NV centers under photo-excitation can help greatly in realizing NV-diamond platform’s potential in sensing correlated magnets and biological samples, as well as other emerging applications, such as masing and nuclear hyperpolarization.

High-resolution heteronuclear correlations between spin-1/2 and half-integer quadrupolar nuclei under fast MAS solid-state NMR

High isotropic resolution is essential for the structural elucidation of samples with multiple sites. In this study, utilizing the benefits of TRAPDOR-based heteronuclear multiple quantum coherence (T-HMQC) and a pair of one rotor period long cosine amplitude modulated low-power (cos-lp) pulse-based symmetric-split-t1 multiple-quantum magic angle spinning (MQMAS) methods, we have developed a proton-detected 2D 35Cl/1H T-HMQC-MQMAS pulse sequence under fast MAS (70 kHz) to achieve high-resolution in the indirect dimension of the spin-3/2 (35Cl) nuclei connected via protons. As T-HMQC polarizes not only single-quantum central transition (SQCT) but also triple-quantum (TQ) coherences, the proposed 2D pulse sequence is implemented via selection of two coherence pathways (SQCT→TQ →SQCT and TQ → SQCT→TQ) resulting in the 35Cl isotropic dimension and is superior to the existing double-quantum satellite-transition (DQST) T-HMQC in terms of resolution.

Hyperfine transition induced by atomic motion above a paraffin-coated magnetic film

We measured transitions between the hyperfine levels of the electronic ground state of potassium-39 atoms (transition frequency: 460 MHz) as the atoms moved through a periodic magneto-static field produced above the magnetic-stripe domains of a magnetic film. The period length of the magnetic field was 3.8 µm. The atoms were incident to the field as an impinging beam with the most probable velocity of 550 m s−1 and experienced a peak oscillating field of 20 mT. Unwanted spin relaxation caused by the collisions of the atoms with the film surface was suppressed by the paraffin coating on the film. We observed increasing hyperfine transition probabilities as the frequency of the field oscillations experienced by the atoms increased from 0 to 140 MHz for the atomic velocity of 550 m s−1, by changing the incident angle of the atomic beam with respect to the stripe domains. Numerical calculation of the time evolution of the hyperfine states revealed that the oscillating magnetic field experienced by the atoms induced the hyperfine transitions, and the main process was not a single-quantum transition but rather multi-quanta transitions.

Plasmonic Photoemission from Single-Crystalline Silver

Optical fields interacting with solids excite single particle quantum transitions and elicit collective screening responses that define their penetration, absorption, and reflection. The interplay of these interactions on the attosecond time scale defines how optical energy transforms to electronic, setting the limits of efficiency for processes such as solar energy harvesting or photocatalysis. Our understanding of light–matter interactions is primarily based on specifying the electronic structure of solids and initial particles or fields occupying well-defined states, and the outcome of their interaction culminating in photoelectron or photon emission and analysis, with scant ability to follow the transitional, ultrafast many-body interactions that define it. The optical properties of metals transubstantiate from metallic to dielectric when the real part of their dielectric response function, Re[ε(ω)], passes through zero: at low frequencies, Re[ε(ω)] < 0, and the collective free electron plasmonic response confers high reflectivity; at high frequencies, Re[ε(ω)] > 0, and the fields penetrate as charge-density or longitudinal plasmon waves. How such collective plasmonic responses decay on the femtosecond time scale into single particle excitations is cardinal to plasmonics, but not sufficiently well described by experiment or theory. We examine the spectroscopic signatures of the nonlinear single particle and collective excitations of the low index crystals of silver by nonlinear two-photon photoemission spectroscopy, at frequencies where the bulk dielectric response passes through zero. We find that the transition through zero dielectric region is reflected in the nonlinear photoemission spectra, and in particular, the bulk plasmons decay by giving rise to a non-Einsteinian plasmonic photoemission component. This response, where the energy of photoelectrons is not defined by the incoming photons, occurs when photons excite the longitudinal plasmons, which then decay by exciting photoelectrons selectively from the Fermi level. Such mode of plasmon decay into hot electrons is contrary to the general agreement, but confirms a theoretical prediction by J. J. Hopfield from 1965. Our experiment illuminates a more energy efficient optical-to-electronic energy flow in metals that so far has escaped scrutiny.

Acoustically Driving the Single-Quantum Spin Transition of Diamond Nitrogen-Vacancy Centers

Using a high quality factor 3 GHz bulk acoustic wave resonator device, we demonstrate the acoustically driven single quantum spin transition ($\left|m_{s}=0\right>\leftrightarrow\left|\pm1\right>$) for diamond NV centers and characterize the corresponding stress susceptibility. A key challenge is to disentangle the unintentional magnetic driving field generated by device current from the intentional stress driving within the device. We quantify these driving fields independently using Rabi spectroscopy before studying the more complicated case in which both are resonant with the single quantum spin transition. By building an equivalent circuit model to describe the device's current and mechanical dynamics, we quantitatively model the experiment to establish their relative contributions and compare with our results. We find that the stress susceptibility of the NV center spin single quantum transition is around $\sqrt{2}(0.5\pm0.2)$ times that for double quantum transition ($\left|+1\right>\leftrightarrow\left|-1\right>$). Although acoustic driving in the double quantum basis is valuable for quantum-enhanced sensing applications, double quantum driving lacks the ability to manipulate NV center spins out of the $\left|m_{s}=0\right>$ initialization state. Our results demonstrate that efficient all-acoustic quantum control over NV centers is possible, and is especially promising for sensing applications that benefit from the compact footprint and location selectivity of acoustic devices.

Extremely imbalanced two-dimensional electron-hole-photon systems

We investigate the phases of two-dimensional electron-hole systems strongly coupled to a microcavity photon field in the limit of extreme charge imbalance. Using variational wave functions, we examine the competition between different electron-hole paired states for the specific cases of semiconducting III-V single quantum wells, electron-hole bilayers, and transition metal dichalcogenide monolayers embedded in a planar microcavity. We show how the Fermi sea of excess charges modifies both the electron-hole bound state (exciton) properties and the dielectric constant of the cavity active medium, which in turn affects the photon component of the many-body polariton ground state. On the one hand, long-range Coulomb interactions and Pauli blocking of the Fermi sea promote electron-hole pairing with finite center-of-mass momentum, corresponding to an excitonic roton minimum. On the other hand, the strong coupling to the ultra-low-mass cavity photon mode favors zero-momentum pairs. We discuss the prospect of observing different types of electron-hole pairing in the photon spectrum.

Robust techniques for polarization and detection of nuclear spin ensembles

Highly sensitive nuclear spin detection is crucial in many scientific areas including nuclear magnetic resonance spectroscopy (NMR), imaging (MRI) and quantum computing. The tiny thermal nuclear spin polarization represents a major obstacle towards this goal which may be overcome by Dynamic Nuclear Spin Polarization (DNP) methods. The latter often rely on the transfer of the thermally polarized electron spins to nearby nuclear spins, which is limited by the Boltzmann distribution of the former. Here we demonstrate the polarization and read out of a nuclear spin bath consisting of $^{13}$C nuclear spins in diamond by using a single nitrogen-vacancy (NV) center. Our method utilizes microwave dressed states to transfer the NV's high ($>$~92~\%) non-equilibrium electron spin polarization induced by short laser pulses to the surrounding carbon nuclear spins, where the NV is repeatedly repolarized optically, thus providing an effectively infinite polarization reservoir. A saturation of the polarization in the nuclear "frozen core" is achieved, which is confirmed by the decay of the polarization transfer signal and shows an excellent agreement with theoretical simulations. Hereby we introduce the Polarization Read Out by Polarization Inversion (PROPI) method as a quantitative magnetization measure of the nuclear spin bath. Moreover, we show that using the integrated solid effect both for single and double quantum transitions a nuclear spin polarization can be achieved even when the static magnetic field is not aligned along the NV's crystal axis. This opens a path for the application of our DNP technique to spins in and outside of nanodiamonds, enabling their application as MRI tracers.

On the influence of multi-quantum transitions on gas-dynamic parameters in the relaxation zone behind shock waves

In this paper the influence of multi-quantum V T-exchanges on gas flow parameters in the relaxation zone behind a shock wave is studied. The set of equations of state-to-state vibrational-chemical kinetics coupled to the gas-dynamic equations is simulated numerically in the zero-order approximation of the Chapman— Enskog method. Rate coefficients of V T-transitions are calculated on the basis of Billing’s trajectory calculations. Distributions of fluid dynamic variables are obtained for the binary mixture N and N2 under various free stream conditions. Significant effect of multi-quantum transitions on the vibrational level populations and atom molar fractions is shown. The maximum error in temperature values calculated taking into account only single-quantum transitions is within 10–12%, and does not exceed 6–8% for the velocity. Refs 7. Figs 5.

Terahertz single conductance quantum and topological phase transitions in topological insulator Bi₂Se₃ ultrathin films.

Strong spin-orbit interaction and time-reversal symmetry in topological insulators generate novel quantum states called topological surface states. Their study provides unique opportunities to explore exotic phenomena such as spin Hall effects and topological phase transitions, relevant to the development of quantum devices for spintronics and quantum computation. Although ultrahigh-vacuum surface probes can identify individual topological surface states, standard electrical and optical experiments have so far been hampered by the interference of bulk and quantum well states. Here, with terahertz time-domain spectroscopy of ultrathin Bi₂Se₃ films, we give evidence for topological phase transitions, a single conductance quantum per topological surface state, and a quantized terahertz absorbance of 2.9% (four times the fine structure constant). Our experiment demonstrates the feasibility to isolate, detect and manipulate topological surface states in the ambient at room temperature for future fundamental research on the novel physics of topological insulators and their practical applications.

Three-dimensional analytic probabilities of coupled vibrational-rotational-translational energy transfer for DSMC modeling of nonequilibrium flows

A three-dimensional, nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, and between two rotating diatomic molecules (Forced Harmonic Oscillator–Free Rotation model) has been extended to incorporate rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. The model is based on analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential. The model predictions are compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential energy surface. The comparison demonstrates good agreement between analytic and numerical probabilities of rotational and vibrational energy transfer processes, over a wide range of total collision energies, rotational energies, and impact parameter. The model predicts probabilities of single-quantum and multi-quantum vibrational-rotational transitions and is applicable up to very high collision energies and quantum numbers. Closed-form analytic expressions for these transition probabilities lend themselves to straightforward incorporation into DSMC nonequilibrium flow codes.

Lineshape-based polarimetry of dynamically-polarized [formula omitted] in solid-state mixtures

Dynamic nuclear polarization (DNP) of 15N2O, known for its long-lived singlet-state order at low magnetic field, is demonstrated in organic solvent/trityl mixtures at ∼1.5K and 5T. Both 15N polarization and intermolecular dipolar broadening are strongly affected by the sample’s thermal history, indicating spontaneous formation of N2O clusters. In situ 15N NMR reveals four distinct powder-pattern spectra, attributed to the chemical-shift anisotropy (CSA) tensors of the two 15N nuclei, further split by the intramolecular dipolar coupling between their magnetic moments. 15N polarization is estimated by fitting the free-induction decay (FID) signals to the analytical model of four single-quantum transitions. This analysis implies (10.2±2.2)% polarization after 37h of DNP, and provides a direct, instantaneous probe of the absolute 15N polarization, without a need for time-consuming referencing to a thermal-equilibrium NMR signal.

Broadband excitation by chirped pulses: application to single electron spins in diamond

Pulsed excitation of broad spectra requires very high field strengths if monochromatic pulses are used. If the corresponding high power is not available or not desirable, the pulses can be replaced by suitable low-power pulses that distribute the power over a wider bandwidth. As a simple case, we use microwave pulses with a linear frequency chirp. We use these pulses to excite spectra of single nitrogen–vacancy centres in a Ramsey experiment. Compared to the conventional Ramsey experiment, our approach increases the bandwidth by at least an order of magnitude. Compared to the conventional continuous wave-ODMR experiment, the chirped Ramsey experiment does not suffer from power broadening and increases the resolution by at least an order of magnitude. As an additional benefit, the chirped Ramsey spectrum contains not only ‘allowed’ single quantum transitions, but also ‘forbidden’ zero- and double quantum transitions, which can be distinguished from the single quantum transitions by phase-shifting the readout pulse with respect to the excitation pulse or by variation of the external magnetic field strength.

ChemInform Abstract: Two‐Dimensional Higher Quantum Correlation and Resolved Techniques for the Analyses of Complex 1H NMR Spectra of Scalar‐Coupled Spins

AbstractReview: 94 refs.

Double-quantum homonuclear correlations of spin I = 5/2 nuclei

The challenges associated with acquiring double-quantum homonuclear Nuclear Magnetic Resonance correlation spectra of half-integer quadrupolar nuclei are described. In these experiments the radio-frequency irradiation amplitude is necessarily weak in order to selectively excite the central transition. In this limit only one out of the 25 double-quantum coherences possible for two coupled spin I=5/2 nuclei is excited. An investigation of all the 25 two spins double quantum transitions reveals interesting effects such as a compensation of the first-order quadrupolar interaction between the two single quantum transitions involved in the double quantum coherence. In this paper a full numerical study of a hypothetical two spin I=5/2 system is used to show what happens when the RF amplitude during recoupling is increased. In principle this is advantageous, since the required double quantum coherence should build up faster, but in practice it also induces adiabatic passage transfer of population and coherence which impedes any build up. Finally an optimized rotary resonance recoupling (oR3) sequence is introduced in order to decrease these transfers. This sequence consists of a spin locking irradiation whose amplitude is reduced four times during one rotor period, and allows higher RF powers to be used during recoupling. The sequence is used to measure 27Al DQ dipolar correlation spectra of Y3Al5O12 (YAG) and gamma alumina (γAl2O3). The results prove that aluminium vacancies in gamma alumina mainly occur in the tetrahedral sites.

Role of electronic friction during the scattering of vibrationally excited nitric oxide molecules from Au(111)

Some time ago, it has been observed that vibrationally highly excited $\text{NO}(v)$ molecules (with typical vibrational quantum numbers $v\ensuremath{\approx}15$) lose substantial amounts of vibrational energy when scattering off a Au(111) surface [H. Huang, C. Rettner, D. Auerbach, and A. Wodtke, Science 290, 111 (2000)]. This has been interpreted as a sign for the breakdown of the Born-Oppenheimer approximation due to vibration-electron coupling. It has been argued that this process cannot be understood on the basis of single-quantum transitions which are typical for ``electronic friction'' models based on a perturbative treatment of weak vibration-electron couplings. Rather, multiple-quanta transitions characteristic for strong nonadiabatic effects are needed according to recent classical surface hopping calculations involving multiple potential-energy surfaces and model Hamiltonians [N. Shenvi, S. Roy, and J. C. Tully, Science 326, 829 (2009)]. Here we address the importance and magnitude of electronic friction for $\text{NO}@\text{Au}(111)$ by using fully quantum-mechanical, parameter-free first-principles theories in reduced dimensions. Periodic density-functional theory calculations are performed to obtain a ground-state potential-energy surface along the desorption and NO-vibration coordinates, and coordinate-resolved, finite NO vibrational lifetimes due to vibration-electron coupling. Using this input, the scattering event is modeled by open-system density-matrix theory in the frame of the coupled-channel-density-matrix method, which allows for the inclusion of energy relaxation of the scattering NO molecules. It is found that within this model at least, electronic friction accounts for the observed vibrational deactivation of NO scattering from gold.

Vibrational overtone excitation in electron mediated energy transfer at metal surfaces

Vibrational overtone excitation is, in general, inefficiently stimulated by photons, but can under some circumstances be efficiently stimulated by electrons. Here, we demonstrate electron mediated vibrational overtone excitation in molecular collisions with a metal surface. Specifically, we report absolute vibrational excitation probabilities to ν = 1 and 2 for collisions of NO(ν = 0) with a Au(111) surface as a function of surface temperature from 300 to 985 K. In all cases, the observed populations of vibrationally excited NO are near those expected for complete thermalization with the surface, despite the fact that the scattering occurs through a direct “single bounce” mechanism of sub-ps duration. We present a state-to-state kinetic model, which accurately describes the case of near complete thermalization (a regime we call the strong coupling case) and use this model to extract state-to-state rate constants. This analysis unambiguously shows that direct vibrational overtone excitation dominates the production of ν = 2 and that, within the context of our model, the intrinsic strength of the overtone transition is of the same order as the single quantum transition, suggesting a possible way to circumvent optical selection rules in vibrational pumping of molecules. This result also suggests that previous measurements of vibrational relaxation of highly vibrationally excited NO exhibiting highly efficient multi-quantum jumps (Δν ∼ −8) are mechanistically similar to vibrational excitation of NO(ν = 0).

Direct Evidence for Nitrogen Ligation to the High Stability Semiquinone Intermediate in Escherichia coli Nitrate Reductase A

The membrane-bound heterotrimeric nitrate reductase A (NarGHI) catalyzes the oxidation of quinols in the cytoplasmic membrane of Escherichia coli and reduces nitrate to nitrite in the cytoplasm. The enzyme strongly stabilizes a menasemiquinone intermediate at a quinol oxidation site (Q(D)) located in the vicinity of the distal heme b(D). Here molecular details of the interaction between the semiquinone radical and the protein environment have been provided using advanced multifrequency pulsed EPR methods. (14)N and (15)N ESEEM and HYSCORE measurements carried out at X-band ( approximately 9.7 GHz) on the wild-type enzyme or the enzyme uniformly labeled with (15)N nuclei reveal an interaction between the semiquinone and a single nitrogen nucleus. The isotropic hyperfine coupling constant A(iso)((14)N) approximately 0.8 MHz shows that it occurs via an H-bond to one of the quinone carbonyl group. Using (14)N ESEEM and HYSCORE spectroscopies at a lower frequency (S-band, approximately 3.4 GHz), the (14)N nuclear quadrupolar parameters of the interacting nitrogen nucleus (kappa = 0.49, eta = 0.50) were determined and correspond to those of a histidine N(delta), assigned to the heme b(D) ligand His-66 residue. Moreover S-band (15)N ESEEM spectra enabled us to directly measure the anisotropic part of the nitrogen hyperfine interaction (T((15)N) = 0.16 MHz). A distance of approximately 2.2 Abetween the carbonyl oxygen and the nitrogen could then be calculated. Mechanistic implications of these results are discussed in the context of the peculiar properties of the menasemiquinone intermediate stabilized at the Q(D) site of NarGHI.

Proton NMR studies of dihalogenated phenyl benzamides: two‐dimensional higher quantum methodologies

The scalar coupled proton NMR spectra of many organic molecules possessing more than one phenyl ring are generally complex due to degeneracy of transitions arising from the closely resonating protons, in addition to several short- and long-range couplings experienced by each proton. Analogous situations are generally encountered in derivatives of halogenated benzanilides. Extraction of information from such spectra is challenging and demands the differentiation of spectrum pertaining to each phenyl ring and the simplification of their spectral complexity. The present study employs the blend of independent spin system filtering and the spin-state selective detection of single quantum (SQ) transitions by the two-dimensional multiple quantum (MQ) methodology in achieving this goal. The precise values of the scalar couplings of very small magnitudes have been derived by double quantum resolved experiments. The experiments also provide the relative signs of heteronuclear couplings. Studies on four isomers of dihalogenated benzanilides are reported in this work.

Direct estimation of an element of order matrix from 1H NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyses require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported.

Numerical Simulations of Ultrafast Charge Separation Dynamics from Second Excited State of Directly Linked Zinc−Porphyrin−Imide Dyads and Ensuing Hot Charge Recombination into the First Excited State

A model of the intramolecular charge separation from the second singlet excited-state of directly linked Zn-porphyrin-imide dyads and following charge recombination into the first singlet excited-state has been constructed and investigated. The model incorporates three electronic states (the first and the second singlet excited and charge separated states) as well as their vibrational sublevels. Dynamics of the transitions between these states are described in the framework of the stochastic point-transition approach. The relaxation of the intramolecular high frequency vibrational mode is supposed to occur as a single-quantum transition between nearest states with a time constant depending on the number of the vibrational state. The medium relaxation is characterized by two timescales. A good fitting to experimentally observed population dynamics of both the first and the second singlet excited states has been obtained. The calculations show the charge recombination into the first excited-state to proceed in a hot stage in parallel with the relaxation of both the medium and the intramolecular high-frequency vibrational mode.