Nuclear Spin Noise Research Articles

Ultra-low charge and spin noise in self-assembled quantum dots

Self-assembled InxGa1−xAs quantum dots (QDs) are promising hosts for spin qubits with excellent coupling to photons. Nuclear spin and charge fluctuations lead to dephasing and limit the applicability of QDs as qubits. We show that charge noise can be minimized by high quality MBE growth of well-designed heterostructures yielding natural optical linewidths down to 1.15µeV. To minimize the nuclear spin noise, one direction would be to reduce the wave function overlap with the nuclei. We show that this is indeed the case for a single hole spin in a QD that we embedded in the intrinsic region of an n-i-p-diode. For random nuclei, the heavy-hole limit is achieved down to neV energies, equivalent to dephasing times of microseconds.

Decoupling a hole spin qubit from the nuclearspins.

A huge effort is underway to develop semiconductor nanostructures as low-noise hosts for qubits. The main source of dephasing of an electron spin qubit in a GaAs-based system is the nuclear spin bath. A hole spin may circumvent the nuclear spin noise. In principle, the nuclear spins can be switched off for a pure heavy-hole spin. In practice, it is unknown to what extent this ideal limit can be achieved. A major hindrance is that p-type devices are often far too noisy. We investigate here a single hole spin in an InGaAs quantum dot embedded in a new generation of low-noise p-type device. We measure the hole Zeeman energy in a transverse magnetic field with 10 neV resolution by dark-state spectroscopy as we create a large transverse nuclear spin polarization. The hole hyperfine interaction is highly anisotropic: the transverse coupling is <1% of the longitudinal coupling. For unpolarized, randomly fluctuating nuclei, the ideal heavy-hole limit is achieved down to nanoelectronvolt energies; equivalently dephasing times up to a microsecond. The combination of large and strong optical dipole makes the single hole spin in a GaAs-based device an attractive quantum platform.

Use of Nuclear Spin Noise Spectroscopy to Monitor Slow Magnetization Buildup at Millikelvin Temperatures.

At ultralow temperatures, longitudinal nuclear magnetic relaxation times become exceedingly long and spectral lines are very broad. These facts pose particular challenges for the measurement of NMR spectra and spin relaxation phenomena. Nuclear spin noise spectroscopy is used to monitor proton spin polarization buildup to thermal equilibrium of a mixture of glycerol, water, and copper oxide nanoparticles at 17.5 mK in a static magnetic field of 2.5 T. Relaxation times determined in such a way are essentially free from perturbations caused by excitation radiofrequency pulses, radiation damping, and insufficient excitation bandwidth. The experimental spin‐lattice relaxation times determined on resonance by saturation recovery with spin noise detection are consistently longer than those determined by using pulse excitation. These longer values are in better accordance with the expected field dependence trend than those obtained by on‐resonance experiments with pulsed excitation.

Screening Nuclear Field Fluctuations in Quantum Dots for Indistinguishable Photon Generation.

A semiconductor quantum dot can generate highly coherent and indistinguishable single photons. However, intrinsic semiconductor dephasing mechanisms can reduce the visibility of two-photon interference. For an electron in a quantum dot, a fundamental dephasing process is the hyperfine interaction with the nuclear spin bath. Here, we directly probe the consequence of the fluctuating nuclear spins on the elastic and inelastic scattered photon spectra from a resident electron in a single dot. We find the in-plane component of the nuclear Overhauser field leads to detuned Raman scattered photons, broadened over experimental time scales by field fluctuations, which are distinguishable from both the elastic and incoherent components of the resonance fluorescence. This significantly reduces two-photon interference visibility. However, we demonstrate successful screening of the nuclear spin noise, which enables the generation of coherent single photons that exhibit high visibility two-photon interference.

Strongly polarizing weakly coupled (13)C nuclear spins with optically pumped nitrogen-vacancy center.

Enhancing the polarization of nuclear spins surrounding the nitrogen-vacancy (NV) center in diamond has recently attracted widespread attention due to its various applications. Here we present an analytical formula that not only provides a clear physical picture for the recently observed polarization reversal of strongly coupled13C nuclei over a narrow range of magnetic field [H. J. Wang et al., Nat. Commun. 4, 1940 (2013)], but also demonstrates the possibility to strongly polarize weakly coupled13C nuclei. This allows sensitive magnetic field control of the 13C nuclear spin polarization for NMR applications and significant suppression of the 13C nuclear spin noise to prolong the NV spin coherence time.

Interplay of Electron and Nuclear Spin Noise in n-Type GaAs.

We present spin-noise spectroscopy measurements on an ensemble of donor-bound electrons in ultrapure GaAs:Si covering temporal dynamics over 6 orders of magnitude from milliseconds to nanoseconds. The spin-noise spectra detected at the donor-bound exciton transition show the multifaceted dynamical regime of the ubiquitous mutual electron and nuclear spin interaction typical for III-V-based semiconductor systems. The experiment distinctly reveals the finite Overhauser shift of an electron spin precession at zero external magnetic field and a second contribution around zero frequency stemming from the electron spin components parallel to the nuclear spin fluctuations. Moreover, at very low frequencies, features related with time-dependent nuclear spin fluctuations are clearly resolved making it possible to study the intricate nuclear spin dynamics at zero and low magnetic fields. The findings are in agreement with the developed model of electron and nuclear spin noise.

Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Whether a quantum bath can be approximated as classical noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock-transitions (CTs). This system is therefore ideal for studying the quantum/classical nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a classical noise model. We develop a Gaussian noise model with noise correlations determined by quantum calculations and compare the classical noise approximation to the full quantum bath theory. We experimentally test our model through dynamical decoupling sequence of up to 128 pulses, finding good agreement with simulations and measuring electron spin coherence times approaching one second - notably using natural silicon. Our theoretical and experimental study demonstrates that the noise from a nuclear spin bath is analogous to classical Gaussian noise if the back-action of the qubit on the bath is small compared to the internal bath dynamics, as is the case close to CTs. However, far from the CTs, the back-action of the central spin on the bath is such that the quantum model is required to accurately model spin decoherence.

A nitrogen-vacancy spin based molecular structure microscope using multiplexed projection reconstruction

Methods and techniques to measure and image beyond the state-of-the-art have always been influential in propelling basic science and technology. Because current technologies are venturing into nanoscopic and molecular-scale fabrication, atomic-scale measurement techniques are inevitable. One such emerging sensing method uses the spins associated with nitrogen-vacancy (NV) defects in diamond. The uniqueness of this NV sensor is its atomic size and ability to perform precision sensing under ambient conditions conveniently using light and microwaves (MW). These advantages have unique applications in nanoscale sensing and imaging of magnetic fields from nuclear spins in single biomolecules. During the last few years, several encouraging results have emerged towards the realization of an NV spin-based molecular structure microscope. Here, we present a projection-reconstruction method that retrieves the three-dimensional structure of a single molecule from the nuclear spin noise signatures. We validate this method using numerical simulations and reconstruct the structure of a molecular phantom β-cyclodextrin, revealing the characteristic toroidal shape.

Nuclear spin noise in NMR revisited.

The theoretical shapes of nuclear spin-noise spectra in NMR are derived by considering a receiver circuit with finite preamplifier input impedance and a transmission line between the preamplifier and the probe. Using this model, it becomes possible to reproduce all observed experimental features: variation of the NMR resonance linewidth as a function of the transmission line phase, nuclear spin-noise signals appearing as a "bump" or as a "dip" superimposed on the average electronic noise level even for a spin system and probe at the same temperature, pure in-phase Lorentzian spin-noise signals exhibiting non-vanishing frequency shifts. Extensive comparisons to experimental measurements validate the model predictions, and define the conditions for obtaining pure in-phase Lorentzian-shape nuclear spin noise with a vanishing frequency shift, in other words, the conditions for simultaneously obtaining the spin-noise and frequency-shift tuning optima.

Dynamical decoupling design for identifying weakly coupled nuclear spins in a bath

Identifying weakly coupled nuclear spins around single electron spins is a key step toward implementing quantum information processing using coupled electron-nuclei spin systems or sensing like single-spin nuclear magnetic resonance detection using diamond defect spins. Dynamical decoupling control of the center electron spin with periodic pulse sequences [e.g., the Carre-Purcell-Meiboom-Gill (CPMG) sequence] has been successfully used to identify single nuclear spins and to resolve structure of nuclear spin clusters. Here, we design a type of pulse sequence by replacing the repetition unit (a single $\ensuremath{\pi}$ pulse) of the CPMG sequence with a group of nonuniformly spaced $\ensuremath{\pi}$ pulses. Using the nitrogen-vacancy center system in diamond, we theoretically demonstrate that the designed pulse sequence improves the resolution of nuclear spin noise spectroscopy, and more information about the surrounding nuclear spins is extracted. The principle of dynamical decoupling design proposed in this paper is useful in many systems (e.g., defect spin qubit in solids, trapped ion, and superconducting qubit) for high-resolution noise spectroscopy.

Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses.

The nuclear spins in nanostructured semiconductors play a central role in quantum applications. The nuclear spins represent a useful resource for generating local magnetic fields but nuclear spin noise represents a major source of dephasing for spin qubits. Controlling the nuclear spins enhances the resource while suppressing the noise. NMR techniques are challenging: the group III and V isotopes have large spins with widely different gyromagnetic ratios; in strained material there are large atom-dependent quadrupole shifts; and nanoscale NMR is hard to detect. We report NMR on 100,000 nuclear spins of a quantum dot using chirped radiofrequency pulses. Following polarization, we demonstrate a reversal of the nuclear spin. We can flip the nuclear spin back and forth a hundred times. We demonstrate that chirped NMR is a powerful way of determining the chemical composition, the initial nuclear spin temperatures and quadrupole frequency distributions for all the main isotopes. The key observation is a plateau in the NMR signal as a function of sweep rate: we achieve inversion at the first quantum transition for all isotopes simultaneously. These experiments represent a generic technique for manipulating nanoscale inhomogeneous nuclear spin ensembles and open the way to probe the coherence of such mesoscopic systems.

Preparation of nonequilibrium nuclear spin states in double quantum dots

We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots.

Non-linearity and frequency shifts of nuclear magnetic spin-noise

We have systematically investigated the line shapes observed in proton nuclear spin-noise spectra which depend in a complex way on the properties of the resonance circuit, the number of spins present, transverse relaxation, inhomogeneous broadening, and radiation damping. Using highly sensitive high resolution probes these dependencies are investigated by way of high resolution 1H noise power NMR spectra of liquid samples. Significant deviations from intuitive expectations are observed. Simulations based on an adapted Nyquist noise equation are used to understand and interpret the experimental findings.

Dangling-bond spin relaxation and magnetic1∕fnoise from the amorphous-semiconductor/oxide interface: Theory

We propose a model for magnetic noise based on spin flips (not electron trapping) of paramagnetic dangling bonds at the amorphous-semiconductor/oxide interface. A wide distribution of spin-flip times is derived from the single-phonon cross-relaxation mechanism for a dangling bond interacting with the tunneling two-level systems of the amorphous interface. The temperature and frequency dependence is sensitive to three energy scales: The dangling-bond spin Zeeman energy $(\ensuremath{\delta})$, as well as the minimum $({E}_{\mathrm{min}})$ and maximum $({E}_{\mathrm{max}})$ values for the energy splittings of the tunneling two-level systems. At the highest temperatures, ${k}_{B}T⪢\mathrm{max}$ $(\ensuremath{\delta},{E}_{\mathrm{max}})$, the noise spectral density is independent of temperature and has a $1∕f$ frequency dependence. At intermediate temperatures, ${k}_{B}T⪢\ensuremath{\delta}$ and ${E}_{\mathrm{min}}⪡{k}_{B}T⪡{E}_{\mathrm{max}}$, the noise is proportional to a power law in temperature and possesses a $1∕{f}^{p}$ spectral density, with $p=1.2--1.5$. At the lowest temperatures, ${k}_{B}T⪡\ensuremath{\delta}$, or ${k}_{B}T⪡{E}_{\mathrm{min}}$, the magnetic noise is exponentially suppressed. We compare and fit our model parameters to a recent experiment probing spin coherence of antimony donors implanted in nuclear-spin-free silicon [T. Schenkel et al., Appl. Phys. Lett. 88, 112101 (2006)], and conclude that a dangling-bond area density of the order of ${10}^{14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ is consistent with the data. This enables the prediction of single spin qubit coherence times as a function of the distance from the interface and the dangling-bond area density in a real device structure. We apply our theory to calculations of magnetic flux noise affecting superconducting quantum interference devices (SQUIDs) due to their $\mathrm{Si}∕\mathrm{Si}{\mathrm{O}}_{2}$ substrate. Our explicit estimates of flux noise in SQUIDs lead to a noise spectral density of the order of ${10}^{\ensuremath{-}12}\phantom{\rule{0.3em}{0ex}}{\ensuremath{\Phi}}_{0}^{2}{(\mathrm{Hz})}^{\ensuremath{-}1}$ at $f=1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. This value might explain the origin of flux noise in some SQUIDs. Finally, we consider the suppression of these effects using surface passivation with hydrogen, and the residual nuclear-spin noise resulting from a perfect silicon-hydride surface.

STM NMR and nuclear spin noise

Fluctuations of an electronic spin can be revealed in the tunneling current fluctuations of a scanning tunneling microscope (STM). We consider fluctuations of the electronic spin due to coupling to nuclear spin. We argue that the noise spectroscopy of electronic spin can reveal the nuclear spin dynamics due to hyperfine coupling. We find that the STM tunneling current power spectrum develops hyperfine split satellites of the main lines at Larmor frequency and at zero frequency. We also address the role of the rf field that is at or near the resonance with the nuclear hyperfine field. This approach is similar to electron nuclear double resonance in that is allows one to detect nuclear spin dynamics indirectly through its effect on electronic spin.

NMR of water protons. The detection of their nuclear-spin noise, and a simple determination of absolute probe sensitivity based on radiation damping

NMR of water protons. The detection of their nuclear-spin noise, and a simple determination of absolute probe sensitivity based on radiation damping

Nuclear spin noise at room temperature

It is demonstrated that it is possible to observe nuclear spin noise at room temperature using a conventional NMR spectrometer. The noise spectrum shows the impedance characteristics of the receiver circuit modified by the presence of the nuclear spins and manifests spontaneous emission of spin noise. The experimental findings are compared with analytical results derived from a simple electronic circuit model. The role of radiation damping in determining the features of spin noise is discussed.

Nuclear magnetic resonance with DC SQUID preamplifiers

Describes five experiments illustrating the application of DC SQUID (superconducting quantum interference device) amplifiers to magnetic resonance experiments. The first experiment involved the observation of nuclear spin noise, that is the spontaneous emission of photons from an ensemble of /sup 35/Cl nuclei in the zero polarization state. The second experiment involved the use of the Q-spoiler in conventional NQR (nuclear quadrupole resonance) and NMR measurements in which one applies a large RF pulse to the nuclei to make them precess. The Q-spoiler was then used in an experiment to detect the oscillating electric polarization induced by /sup 35/Cl nuclear quadrupole moments. The fourth experiment involved the extension of the use of the Q-spoiler and SQUID amplifier to NMR, detecting the signal from /sup 119/Sn nuclei at 30 MHz. Finally, a SQUID amplifier was used with an untuned input circuit to detect the low-frequency NMR signal at 55 kHz from /sup 195/Pt nuclei in an applied field of 60 Gauss. >

Nuclear-spin noise and spontaneous emission.

Spontaneous emission from nuclear spins is measured for the first time, we believe. This is possible because of the use of a low-noise SQUID amplifier with noise temperature (~0.2 K) less than that of the 1.5 K helium bath. The spontaneous emission power is ~5-10% of the background circuit Nyquist noise, which corresponds to the ratio of the effective spin resistance Rs (proportional to the nuclear susceptibility) and circuit resistance R. Although only one spin flip occurs per 108 yr due to spontaneous omission, the effect is magnified, because all 1022 spins in the sample contribute independent of the temperature. This technique implies that spectra of spins can be measured without the requirement of a net polarization and might be useful for samples where spin lattice relaxation times are impracticaily long. Radiation damping terms which are added to the Bloch equations allow for spin noise analysis of power flow between the spin system and cavity. The equivalence is obtained of predictions of Nyquist's theorem at all spin temperatures Ts and bath temperatures T in conformity with the predictions of the Einstein detailed balance equation for spontaneous emission. The model of a macroscopic spin pendulum applies where fluctuation through a mean square angle 〈θ2〉 from magnetization alignment along the polarizing field accounts for coupling of the fluctuating spins to the single-cavity mode. Several aspects of the model for spin noise analysis are applicable to inverted two-level systems.

Nuclear-spin noise.

The spectral density of the Nyquist noise current in a tuned circuit coupled to a sample of nuclear spins has been measured at $^{4}\mathrm{He}$ temperatures with a dc SQUID used as a rf amplifier. When the sample is in thermal equilibrium, a dip is observed in the spectral density at the Larmor frequency. For zero spin polarization, on the other hand, a bump in the spectral density is observed. This bump is due to temperature-independent fluctuations in the transverse component of magnetization, and represents spontaneous emission from the spins into the circuit.