Resonator-induced dissipation of transverse nuclear-spin signals in cold nanoscale samples

The back action of typical macroscopic resonators used for detecting nuclear magnetic resonance can cause a reversible decay of the signal, known as radiation damping. A mechanical resonator that is strongly coupled to a microscopic sample can in addition induce an irreversible dissipation of the nuclear-spin signal, distinct from radiation damping. We provide a theoretical description of resonator-induced transverse relaxation that is valid for samples of a few nuclear spins in the low-temperature regime, where quantum fluctuations play a significant role in the relaxation process, as well as for larger samples and at higher temperatures. Transverse relaxation during free evolution and during spin locking are analyzed, and simulations of relaxation in example systems are presented. In the case where an isolated spin 1/2 interacts with the resonator, transverse relaxation is exponential during free evolution, and the time constant for the relaxation is T_2=2/R_h, where R_h is the rate constant governing the exchange of quanta between the resonator and the spin. For a system of multiple spins, the time scale of transverse relaxation during free evolution depends on the spin Hamiltonian, which can modify the relaxation process through the following effects: (1) changes in the structure of the spin-spin correlations present in the energy eigenstates, which affect the rates at which these states emit and absorb energy, (2) frequency shifts that modify emission and absorption rates within a degenerate manifold by splitting the energy degeneracy and thus suppressing the development of resonator-induced correlations within the manifold, and (3) frequency shifts that introduce a difference between the oscillation frequencies of single-quantum coherences ρ_(ab) and ρ_(cd) and average to zero the transfers between them. This averaging guarantees that the spin transitions responsible for the coupling between ρ_(ab) and ρ_(cd) cause irreversible loss of order rather than a reversible interconversion of the coherences. In systems of a few spins, transverse relaxation is accelerated by a dipolar Hamiltonian that is either the dominant term in the internal spin Hamiltonian or a weak perturbation to the chemical-shift Hamiltonian. A pure chemical-shift Hamiltonian yields exponential relaxation with T_2=2/R_h in the case where the Larmor frequencies of the spins are distinct and sufficiently widely spaced. During spin locking with a nutation frequency fast enough to average the evolution under the internal spin Hamiltonian but not the interactions occurring during the correlation time of the resonator, relaxation of the spin-locked component is exponential with time constant T_(1ρ)=2/R_h

Communication: Partial polarization transfer for single-scan spectroscopy and imaging

A method is presented to partially transfer nuclear spin polarization from one isotope S to another isotope I by the way of heteronuclear spin couplings, while minimizing the loss of spin order to other degrees of freedom. The desired I spin polarization to be detected is a design parameter, while the sequence of pulses at the two Larmor frequencies is optimized to store the greatest unused S spin longitudinal polarization for subsequent use. The unitary evolution for the case of I_NS spin systems illustrates the potentially ideal efficiency of this strategy, which is of particular interest when the spin-lattice relaxation time of S greatly exceeds that of I. Explicit timing and pulses are tabulated for the cases for which M ≤ 10 partial transfers each result in equal final polarization of 1/M or more compared to the final I polarization expected in a single transfer for N = 1, 2, or 3 I spins. Advantages for the ratiometric study of reacting molecules and hyperpolarized initial conditions are outlined

Method for atomic-layer-resolved measurement of polarization fields by nuclear magnetic resonance

A nuclear magnetic resonance (NMR) method of probing the dielectric response to an alternating electric field is described, which is applicable to noncentrosymmetric sites with nuclear spin I>1/2. A radio-frequency electric field induces a linear quadrupole Stark effect at a multiple of the nuclear Larmor frequency. This perturbation is applied in the windows of an NMR multiple-pulse line-narrowing sequence in such a way that the resulting nonsecular spin interactions are observed as first-order quadrupole satellites, free of line broadening by the usual dominant static interactions. A simulation of the 69Ga spectrum for the nuclei within the two-dimensional electron gas of a 10 nm quantum well predicts resolution of individual atomic layers in single devices due to the spatial dependence of the polarization response of the quantum-confined carriers to the applied field. This method is part of a more general strategy, perturbations observed with enhanced resolution NMR. Experimentally realized examples in GaAs include spectrally resolving electron probability densities surrounding optically relevant point defects and probing the changes in radial electric field associated with the light-on and light-off states of these shallow traps. Adequate sensitivity for such experiments in individual epitaxial structures is achieved by optical nuclear polarization followed by time-domain NMR observed via nuclear Larmor-beat detection of luminescence

Polarization of nuclear spins by a cold nanoscale resonator

A cold nanoscale resonator coupled to a system of nuclear spins can induce spin relaxation. In the low-temperature limit where spin-lattice interactions are “frozen out,” spontaneous emission by nuclear spins into a resonant mechanical mode can become the dominant mechanism for cooling the spins to thermal equilibrium with their environment. We provide a theoretical framework for the study of resonator-induced cooling of nuclear spins in this low-temperature regime. Relaxation equations are derived from first principles, in the limit where energy donated by the spins to the resonator is quickly dissipated into the cold bath that damps it. A physical interpretation of the processes contributing to spin polarization is given. For a system of spins that have identical couplings to the resonator, the interaction Hamiltonian conserves spin angular momentum, and the resonator cannot relax the spins to thermal equilibrium unless this symmetry is broken by the spin Hamiltonian. The mechanism by which such a spin system becomes “trapped” away from thermal equilibrium can be visualized using a semiclassical model, which shows how an indirect spin-spin interaction arises from the coupling of multiple spins to one resonator. The internal spin Hamiltonian can affect the polarization process in two ways: (1) By modifying the structure of the spin-spin correlations in the energy eigenstates, and (2) by splitting the degeneracy within a manifold of energy eigenstates, so that zero-frequency off-diagonal terms in the density matrix are converted to oscillating coherences. Shifting the frequencies of these coherences sufficiently far from zero suppresses the development of resonator-induced correlations within the manifold during polarization from a totally disordered state. Modification of the spin-spin correlations by means of either mechanism affects the strength of the fluctuating spin dipole that drives the resonator. In the case where product states can be chosen as energy eigenstates, spontaneous emission from eigenstate populations into the resonant mode can be interpreted as independent emission by individual spins, and the spins relax exponentially to thermal equilibrium if the development of resonator-induced correlations is suppressed. When the spin Hamiltonian includes a significant contribution from the homonuclear dipolar coupling, the energy eigenstates entail a correlation specific to the coupling network. Simulations of dipole-dipole coupled systems of up to five spins suggest that these systems contain weakly emitting eigenstates that can trap a fraction of the population for time periods ≫100/R_0, where R_0 is the rate constant for resonator-enhanced spontaneous emission by a single spin 1/2. Much of the polarization, however, relaxes with rates comparable to R_0. A distribution of characteristic high-field chemical shifts tends to increase the relaxation rates of weakly emitting states, enabling transitions to states that can quickly relax to thermal equilibrium. The theoretical framework presented in this paper is illustrated with discussions of spin polarization in the contexts of force-detected nuclear-magnetic-resonance spectroscopy and magnetic-resonance force microscopy

Postmodernism Meets the Mopey Prince: Comparing the Ideologies of \u3cem\u3eHamlet\u3c/em\u3e and \u3cem\u3eRosencrantz and Guildenstern are Dead\u3c/em\u3e

It is often said that Hamlet’s tragic flaw was indecisiveness. Centuries of scholars and high school students have imperiously pointed at Hamlet, prescribing an oh-so-obvious solution to our dithering hero’s problems: just do something! Yet in his play Rosencrantz and Guildenstern are Dead, Tom Stoppard takes the opposite tack, introducing us to characters who are even more actionless and aimless than our troubled Danish prince. Stoppard’s main characters are an obvious homage to Vladimir and Estragon in Samuel Beckett’s Waiting For Godot: purely Postmodern men—clueless, directionless, and passionless. By juxtaposing Beckett-like uncertainty with the Bard’s iconic characters and setting, Stoppard is able to clearly illustrate the principle ideological change that has occurred during the centuries that separate Hamlet and Rosencrantz and Guildenstern are Dead: a transformation from caring for oneself and others to apathy, and a change from passion to indifference

Observation of force-detected nuclear magnetic resonance in a homogeneous field

We report the experimental realization of BOOMERANG (better observation of magnetization, enhanced resolution, and no gradient), a sensitive and general method of magnetic resonance. The prototype millimeter-scale NMR spectrometer shows signal and noise levels in agreement with the design principles. We present H-1 and F-19 NMR in both solid and liquid samples, including time-domain Fourier transform NMR spectroscopy, multiple-pulse echoes, and heteronuclear J spectroscopy. By measuring a H-1-F-19 J coupling, this last experiment accomplishes chemically specific spectroscopy with force-detected NMR. In BOOMERANG, an assembly of permanent magnets provides a homogeneous field throughout the sample, while a harmonically suspended part of the assembly, a detector, is mechanically driven by spin-dependent forces. By placing the sample in a homogeneous field, signal dephasing by diffusion in a field gradient is made negligible, enabling application to liquids, in contrast to other force-detection methods. The design appears readily scalable to µm-scale samples where it should have sensitivity advantages over inductive detection with microcoils and where it holds great promise for application of magnetic resonance in biology, chemistry, physics, and surface science. We briefly discuss extensions of the BOOMERANG method to the µm and nm scales

The IMSA-SF Paradigm: Why it’s All The Same to Me

On what must have been my third or fourth day of IMSA, I remember an upperclassman asking me, “You’ve read Ender’s Game, right? You have to read that book—everyone at IMSA does.” I had, in fact, read the book, and I immediately felt relieved. I felt had passed my first test at IMSA, plus I was geeked to learn that my taste in books wasn’t out of place here. I shouldn’t have been so surprised. IMSA is overflowing with science fiction fans of all varieties—we are a nerd school after all, even if the Admissions Office disapproves of my terminology. But reading David Hartwell’s “The Golden Age of Science Fiction is Twelve” has made me realize that IMSA’s association with science fiction runs even more deeply—IMSA is science fiction, or at least the reality TV show version of it. The main effects of science fiction upon its readers—to isolate readers from normal society, to introduce scientific ways of thinking, and to influence the way readers see the rest of the world—are, in my opinion, identical to the main effects IMSA has upon its student

Nanoscale Torsional Resonator for Polarization and Spectroscopy of Nuclear Spins

We propose a torsional resonator that couples to the transverse spin dipole of an attached sample. The absence of relative motion eliminates a source of friction that would otherwise hinder nanoscale implementation. Enhanced spontaneous emission induced by the resonator relaxes the longitudinal spin dipole at a rate of ~1  s^(-1) in the low-temperature limit. With signal averaging, single-proton magnetic resonance spectroscopy appears feasible at ~10  mK and a high magnetic field, while single-shot sensitivity is practical for samples with at least tens of protons in a volume of ~5  nm^3

Selling Education in the Shape of a Shuttle

At some point in the early- to mid-1980s, probably in 1983 or 1984 when he was about ten or eleven years old, my younger brother, Raymond, wrote a letter to the National Aeronautics and Space Administration (NASA), volunteering to be the first child in space. He wanted to fly as a passenger on NASA\u27s Space Transportation System, a vehicle known better as the Space Shuttle. In response, he received a large envelope from NASA stuffed with fact sheets and brochures as well as posters and stickers that soon decorated his bedroom and filled a scrapbook. Although Ray\u27s desire to volunteer may have been partially inspired by a family visit to the Kennedy Space Center in 1983, many other children followed the same impulse in the mid-1980s. The NASA historical reference collection contains numerous examples of letters received by the agency and the White House especially in the weeks and months after the announcement of the Teacher in Space Program on August 27, 1984. The connection seemed obvious: a teacher would need a student. More so, the rhetoric about the Shuttle program in the early 1980s suggested that ordinary people might soon participate in spaceflights. Even children made the connection. As 12-year-old Karen Rall of Kent, Washington reasoned in a letter to President Ronald Reagan, We have sent Senators, scientists, foreigners and soon a teacher into space; why not send a kid?