Nuclear Spin Ensemble Research Articles

Leakage and dephasing in Si28 -based exchange-only spin qubits

Exchange-only spin qubits hosted in $^{28}$Si-based triple quantum dots do not suffer from decoherence caused by randomly fluctuating nuclear-spin ensembles and can be relatively robust against electrical noise when operated at a sweet spot. Remaining sources of decoherence are qubit relaxation, leakage out of the qubit subspace, and dephasing due to residual effects of charge noise, the latter two of which are the focus of this work. We investigate spin-orbit-mediated leakage rates to the three-spin ground state accompanied by virtual (i) tunneling, (ii) orbital excitation, and (iii) valley excitation of an electron. We find different power-law dependencies on the applied magnetic field $B$ for the three mechanisms as well as for the two leakage rates, ranging from $\propto B^5$ to $\propto B^{11}$, and identify the sweet spot as a point of minimal leakage. We also revisit the role of electrical noise at the sweet spot, and show that it causes a decay of coherent qubit oscillations that follows a power law $\propto 1/t$ (as opposed to the more common exponential decay) and introduces a $\pi/2$ phase shift.

Dynamical coupling between a nuclear spin ensemble and electromechanical phonons

Dynamical coupling with high-quality factor resonators is essential in a wide variety of hybrid quantum systems such as circuit quantum electrodynamics and opto/electromechanical systems. Nuclear spins in solids have a long relaxation time and thus have the potential to be implemented into quantum memories and sensors. However, state manipulation of nuclear spins requires high-magnetic fields, which is incompatible with state-of-the-art quantum hybrid systems based on superconducting microwave resonators. Here we investigate an electromechanical resonator whose electrically tunable phonon state imparts a dynamically oscillating strain field to the nuclear spin ensemble located within it. As a consequence of the dynamical strain, we observe both nuclear magnetic resonance (NMR) frequency shifts and NMR sidebands generated by the electromechanical phonons. This prototype system potentially opens up quantum state engineering for nuclear spins, such as coherent coupling between sound and nuclei, and mechanical cooling of solid-state nuclei.

Parahydrogen-Based Hyperpolarization for Biomedicine.

Magnetic resonance (MR) is one of the most versatile and useful physical effects used for human imaging, chemical analysis, and the elucidation of molecular structures. However, its full potential is rarely used, because only a small fraction of the nuclear spin ensemble is polarized, that is, aligned with the applied static magnetic field. Hyperpolarization methods seek other means to increase the polarization and thus the MR signal. A unique source of pure spin order is the entangled singlet spin state of dihydrogen, parahydrogen (pH2 ), which is inherently stable and long-lived. When brought into contact with another molecule, this "spin order on demand" allows the MR signal to be enhanced by several orders of magnitude. Considerable progress has been made in the past decade in the area of pH2 -based hyperpolarization techniques for biomedical applications. It is the goal of this Review to provide a selective overview of these developments, covering the areas of spin physics, catalysis, instrumentation, preparation of the contrast agents, and applications.

Characterization ofYb3+171:YVO4for photonic quantum technologies

Rare-earth ions in crystals are a proven solid-state platform for quantum technologies in the ensemble regime and attractive for new opportunities at the single ion level. Among the trivalent rare earths, ${}^{171}\mathrm{Yb}^{3+}$ is unique in that it possesses a single 4f excited-state manifold and is the only paramagnetic isotope with a nuclear spin of 1/2. In this work, we present measurements of the optical and spin properties of $^{171}$Yb$^{3+}$:YVO$_4$ to assess whether this distinct energy level structure can be harnessed for quantum interfaces. The material was found to possess large optical absorption compared to other rare-earth-doped crystals owing to the combination of narrow inhomogeneous broadening and a large transition oscillator strength. In moderate magnetic fields, we measure optical linewidths less than 3 kHz and nuclear spin linewidths less than 50 Hz. We characterize the excited-state hyperfine and Zeeman interactions in this system, which enables the engineering of a $\Lambda$-system and demonstration of all-optical coherent control over the nuclear spin ensemble. Given these properties, $^{171}$Yb$^{3+}$:YVO$_4$ has significant potential for building quantum interfaces such as ensemble-based memories, microwave-to-optical transducers, and optically addressable single rare-earth-ion spin qubits.

Microwave-Assisted Cross-Polarization of Nuclear Spin Ensembles from Optically Pumped Nitrogen-Vacancy Centers in Diamond.

The ability to optically initialize the electronic spin of the nitrogen-vacancy (NV) center in diamond has long been considered a valuable resource to enhance the polarization of neighboring nuclei, but efficient polarization transfer to spin species outside the diamond crystal has proven challenging. Here we demonstrate variable-magnetic-field, microwave-enabled cross-polarization from the NV electronic spin to protons in a model viscous fluid in contact with the diamond surface. Further, slight changes in the cross-relaxation rate as a function of the wait time between successive repetitions of the transfer protocol suggest slower molecular dynamics near the diamond surface compared to that in bulk. This observation is consistent with present models of the microscopic structure of a fluid and can be exploited to estimate the diffusion coefficient near a solid-liquid interface, of importance in colloid science.

Many-body kinetics of dynamic nuclear polarization by the cross effect

Dynamic nuclear polarization (DNP) is an out-of-equilibrium method for generating non-thermal spin polarization which provides large signal enhancements in modern diagnostic methods based on nuclear magnetic resonance. A particular instance is cross effect DNP, which involves the interaction of two coupled electrons with the nuclear spin ensemble. Here we develop a theory for this important DNP mechanism and show that the non-equilibrium nuclear polarization build-up is effectively driven by three-body incoherent Markovian dissipative processes involving simultaneous state changes of two electrons and one nucleus. Our theoretical approach allows for the first time simulations of the polarization dynamics on an individual spin level for ensembles consisting of hundreds of nuclear spins. The insight obtained by these simulations can be used to find optimal experimental conditions for cross effect DNP and to design tailored radical systems that provide optimal DNP efficiency.

Nuclear spin cooling by helicity-alternated optical pumping at weak magnetic fields in n -GaAs

The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in $n$-doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed build-up of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warm-up in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time $T_2$ determined from nuclear magnetic resonance.

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.

Improving a Solid-State Qubit through an Engineered Mesoscopic Environment.

A controlled quantum system can alter its environment by feedback, leading to reduced-entropy states of the environment and to improved system coherence. Here, using a quantum-dot electron spin as a control and probe, we prepare the quantum-dot nuclei under the feedback of coherent population trapping and observe their evolution from a thermal to a reduced-entropy state, with the immediate consequence of extended qubit coherence. Via Ramsey interferometry on the electron spin, we directly access the nuclear distribution following its preparation and measure the emergence and decay of correlations within the nuclear ensemble. Under optimal feedback, the inhomogeneous dephasing time of the electron, T_{2}^{*}, is extended by an order of magnitude to 39ns. Our results can be readily exploited in quantum information protocols utilizing spin-photon entanglement and represent a step towards creating quantum many-body states in a mesoscopic nuclear-spin ensemble.

Measurement of the spin temperature of optically cooled nuclei and GaAs hyperfine constants in GaAs/AlGaAs quantum dots.

Deep cooling of electron and nuclear spins is equivalent to achieving polarization degrees close to 100% and is a key requirement in solid-state quantum information technologies. While polarization of individual nuclear spins in diamond and SiC (ref.) reaches 99% and beyond, it has been limited to 50-65% for the nuclei in quantum dots. Theoretical models have attributed this limit to formation of coherent 'dark' nuclear spin states but experimental verification is lacking, especially due to the poor accuracy of polarization degree measurements. Here we measure the nuclear polarization in GaAs/AlGaAs quantum dots with high accuracy using a new approach enabled by manipulation of the nuclear spin states with radiofrequency pulses. Polarizations up to 80% are observed-the highest reported so far for optical cooling in quantum dots. This value is still not limited by nuclear coherence effects. Instead we find that optically cooled nuclei are well described within a classical spin temperature framework. Our findings unlock a route for further progress towards quantum dot electron spin qubits where deep cooling of the mesoscopic nuclear spin ensemble is used to achieve long qubit coherence. Moreover, GaAs hyperfine material constants are measured here experimentally for the first time.

Purification of an unpolarized spin ensemble into entangled singlet pairs

Dynamical polarization of nuclear spin ensembles is of central importance for magnetic resonance studies, precision sensing and for applications in quantum information theory. Here we propose a scheme to generate long-lived singlet pairs in an unpolarized nuclear spin ensemble which is dipolar coupled to the electron spins of a Nitrogen Vacancy center in diamond. The quantum mechanical back-action induced by frequent spin-selective readout of the NV centers allows the nuclear spins to pair up into maximally entangled singlet pairs. Counterintuitively, the robustness of the pair formation to dephasing noise improves with increasing size of the spin ensemble. We also show how the paired nuclear spin state allows for enhanced sensing capabilities of NV centers in diamond.

Inertial rotation measurement with atomic spins: From angular momentum conservation to quantum phase theory

Rotation measurement in an inertial frame is an important technology for modern advanced navigation systems and fundamental physics research. Inertial rotation measurement with atomic spin has demonstrated potential in both high-precision applications and small-volume low-cost devices. After rapid development in the last few decades, atomic spin gyroscopes are considered a promising competitor to current conventional gyroscopes—from rate-grade to strategic-grade applications. Although it has been more than a century since the discovery of the relationship between atomic spin and mechanical rotation by Einstein [Naturwissenschaften, 3(19) (1915)], research on the coupling between spin and rotation is still a focus point. The semi-classical Larmor precession model is usually adopted to describe atomic spin gyroscope measurement principles. More recently, the geometric phase theory has provided a different view of the rotation measurement mechanism via atomic spin. The theory has been used to describe a gyroscope based on the nuclear spin ensembles in diamond. A comprehensive understanding of inertial rotation measurement principles based on atomic spin would be helpful for future applications. This work reviews different atomic spin gyroscopes and their rotation measurement principles with a historical overlook. In addition, the spin-rotation coupling mechanism in the context of the quantum phase theory is presented. The geometric phase is assumed to be the origin of the measurable rotation signal from atomic spins. In conclusion, with a complete understanding of inertial rotation measurements using atomic spin and advances in techniques, wide application of high-performance atomic spin gyroscopes is expected in the near future.

Quantum state transfer between an optomechanical cavity and a diamond nuclear spin ensemble

We explore an efficient scheme for transferring quantum state between an optomechanical cavity and nuclear spins of nitrogen-vacancy centers in diamond, where quantum information can be efficiently stored (retrieved) into (from) the nuclear spin ensemble assisted by a mechanical resonator in a dispersive regime. Our scheme works for a broad range of cavity frequencies and might have potential applications in employing the nuclear spin ensemble as a memory in quantum information processing. The feasibility of our protocol is analyzed using currently available parameters.

Symmetric-cycle pulse sequence for dynamical decoupling of local fields and dipole–dipole interactions

We have proposed a new pulse sequence for the dynamical decoupling of decoherence effects in the ensemble of nuclear spins. The sequence provides a symmetric cycle that offers a strong suppression of the decoherence effects caused by the dipole–dipole interactions and the inhomogeneous local magnetic fields in nuclear spin ensemble dynamics. We have discussed a potential of the proposed pulse sequence for the long-lived storage of the multi-qubit quantum states.

Accelerated nanoscale magnetic resonance imaging through phase multiplexing

We report a method for accelerated nanoscale nuclear magnetic resonance imaging by detecting several signals in parallel. Our technique relies on phase multiplexing, where the signals from different nuclear spin ensembles are encoded in the phase of an ultrasensitive magnetic detector. We demonstrate this technique by simultaneously acquiring statistically polarized spin signals from two different nuclear species (1H, 19F) and from up to six spatial locations in a nanowire test sample using a magnetic resonance force microscope. We obtain one-dimensional imaging resolution better than 5 nm, and subnanometer positional accuracy.

Feedback control of nuclear spin bath of a single hole spin in a quantum dot

For a III--V semiconductor quantum dot charged with a single hole, we investigate the feedback control of the nuclear spin bath through dynamical nuclear spin polarization. The scheme utilizes the hole-nuclear flip-flop by their anisotropic hyperfine interaction, where the flip direction of the nuclear spin can be conditioned on the sign of the overall hyperfine field through initialization processes that do not involve explicit measurement. We show that a negative feedback can be implemented to suppress the statistical fluctuations of the nuclear hyperfine field for enhancing the coherence time of the hole spin qubit. Positive feedback can prepare the nuclear spin ensemble into states where the nuclear hyperfine field distribution has two well separated peaks, realizing a quantum heat bath that cannot be described by a single effective temperature.

Nuclear magnetometry studies of spin dynamics in quantum Hall systems

We performed a nuclear magnetometry study on quantum Hall ferromagnet with a bilayer total filling factor of $\nu_{\rm{tot}} = 2$. We found not only a rapid nuclear relaxation but also a sudden change in the nuclear spin polarization distribution after a one-second interaction with a canted antiferromagnetic phase. We discuss the possibility of observing cooperative phenomena coming from nuclear spin ensemble triggered by electrons with collective spin interactions.

Experimental heat-bath cooling of spins

Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The algorithmic cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with selective reset, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process “heat-bath” cooling, rather than algorithmic cooling. We experimentally implemented two consecutive steps of selective reset, thus transferring entropy from two selected spins to the environment. We performed such cooling experiments, with commercially available labeled molecules, on standard liquid-state NMR spectrometers. We report in particular on our original experiment, unpublished until now except on the arXiv (quant-ph/0511156) in 2005, which was, to the best of our knowledge, the world’s first experiment that yielded polarizations results that bypassed Shannon’s entropy-conservation bound, so that the entire spin-system was cooled.

Dynamics of a mesoscopic nuclear spin ensemble interacting with an optically driven electron spin

The ability to discriminate between simultaneously occurring noise sources in the local environment of semiconductor InGaAs quantum dots, such as electric and magnetic field fluctuations, is key to understanding their respective dynamics and their effect on quantum dot coherence properties. We present a discriminatory approach to all-optical sensing based on two-color resonance fluorescence of a quantum dot charged with a single electron. Our measurements show that local magnetic field fluctuations due to nuclear spins in the absence of an external magnetic field are described by two correlation times, both in the microsecond regime. The nuclear spin bath dynamics show a strong dependence on the strength of resonant probing, with correlation times increasing by a factor of four as the optical transition is saturated. We interpret the behavior as motional averaging of both the Knight field of the resident electron spin and the hyperfine-mediated nuclear spin-spin interaction due to optically-induced electron spin flips.

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

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