Structural analysis of strained quantum dots using nuclear magnetic resonance

Is Wave Function Collapse Necessary? Explaining Quantum Nondemolition Measurement of a Spin Qubit within Linear Evolution

The measurement problem dates back to the dawn of quantum mechanics. Here, we measure a quantum dot electron spin qubit through off-resonant coupling with a highly redundant ancilla, consisting of thousands of nuclear spins. Large redundancy allows for single-shot measurement with high fidelity ≈99.85%. Repeated measurements enable heralded initialization of the qubit and backaction-free detection of electron spin quantum jumps, attributed to burstlike fluctuations in a thermally populated phonon bath. Based on these results we argue that the measurement, linking quantum states to classical observables, can be made without any "wave function collapse" in agreement with the Quantum Darwinism concept.

Approaching a fully-polarized state of nuclear spins in a solid

Magnetic noise of atomic nuclear spins is a major source of decoherence in solid-state spin qubits. In theory, near-unity nuclear spin polarization can eliminate decoherence of the electron spin qubit, while turning the nuclei into a useful quantum information resource. However, achieving sufficiently high nuclear polarizations has remained an evasive goal. Here we implement a nuclear spin polarization protocol which combines strong optical pumping and fast electron tunneling. Nuclear polarizations well above 95% are generated in GaAs semiconductor quantum dots on a timescale of 1 minute. The technique is compatible with standard quantum dot device designs, where highly-polarized nuclear spins can simplify implementations of qubits and quantum memories, as well as offer a testbed for studies of many-body quantum dynamics and magnetism.

Cooling of the Nuclear Spin System of a Nanostructure by Oscillating Magnetic Fields

We propose a method of cooling nuclear spin systems of solid-state nanostructures by applying a time-dependent magnetic field synchronized with spin fluctuations. Optical spin noise spectroscopy is considered a method of fluctuation control. Depending on the mutual orientation of the oscillating magnetic field and the probe light beam, cooling might be either provided by dynamic spin polarization in an external static field or result from population transfer between spin levels without build-up of a net magnetic moment ("true cooling").

Nuclear spin diffusion in the central spin system of a GaAs/AlGaAs quantum dot

The spin diffusion concept provides a classical description of a purely quantum-mechanical evolution in inhomogeneously polarized many-body systems such as nuclear spin lattices. The central spin of a localized electron alters nuclear spin diffusion in a way that is still poorly understood. Here, spin diffusion in a single GaAs/AlGaAs quantum dot is witnessed in the most direct manner from oscillatory spin relaxation dynamics. Electron spin is found to accelerate nuclear spin relaxation, from which we conclude that the long-discussed concept of a Knight-field-gradient diffusion barrier does not apply to GaAs epitaxial quantum dots. Our experiments distinguish between non-diffusion relaxation and spin diffusion, allowing us to conclude that diffusion is accelerated by the central electron spin. Such acceleration is observed up to unexpectedly high magnetic fields - we propose electron spin-flip fluctuations as an explanation. Diffusion-limited nuclear spin lifetimes range between 1 and 10 s, which is sufficiently long for quantum information storage and processing.

All-Optical Noise Spectroscopy of a Solid-State Spin

Noise spectroscopy elucidates the fundamental noise sources in spin systems, thereby serving as an essential tool toward developing spin qubits with long coherence times for quantum information processing, communication, and sensing. But existing techniques for noise spectroscopy that rely on microwave fields become infeasible when the microwave power is too weak to generate Rabi rotations of the spin. Here, we demonstrate an alternative all-optical approach to performing noise spectroscopy. Our approach utilizes coherent Raman rotations of the spin state with controlled timing and phase to implement Carr-Purcell-Meiboom-Gill pulse sequences. Analyzing the spin dynamics under these sequences enables us to extract the noise spectrum of a dense ensemble of nuclear spins interacting with a single spin in a quantum dot, which has thus far been modeled only theoretically. By providing spectral bandwidths of over 100 MHz, our approach enables studies of spin dynamics and decoherence for a broad range of solid-state spin qubits.

Nuclear spin quantum register in an optically active semiconductor quantum dot

Epitaxial quantum dots (QDs) have long been identified as promising charge spin qubits offering an efficient interface to quantum light and advanced semiconductor nanofabrication technologies. However, charge spin coherence is limited by interaction with the nanoscale ensemble of atomic nuclear spins, which is particularly problematic in strained self-assembled dots. Here, we use strain-free GaAs/AlGaAs QDs, demonstrating a fully functioning two-qubit quantum register using the nanoscale ensemble of arsenic quadrupolar nuclear spins as its hardware. Tailored radio-frequency pulses allow quantum state storage for up to 20 ms, and are used for few-microsecond single-qubit and two-qubit control gates with fidelities exceeding 97%. Combining long coherence and high-fidelity control with optical initialization and readout, we implement benchmark quantum computations such as Grover's search and the Deutsch-Jozsa algorithm. Our results identify QD nuclei as a potential quantum information resource, which can complement charge spins and light particles in future QD circuits.

Pulse control protocols for preserving coherence in dipolar-coupled nuclear spin baths

Coherence of solid state spin qubits is limited by decoherence and random fluctuations in the spin bath environment. Here we develop spin bath control sequences which simultaneously suppress the fluctuations arising from intrabath interactions and inhomogeneity. Experiments on neutral self-assembled quantum dots yield up to a five-fold increase in coherence of a bare nuclear spin bath. Numerical simulations agree with experiments and reveal emergent thermodynamic behaviour where fluctuations are ultimately caused by irreversible conversion of coherence into many-body quantum entanglement. Simulations show that for homogeneous spin baths our sequences are efficient with non-ideal control pulses, while inhomogeneous bath coherence is inherently limited even under ideal-pulse control, especially for strongly correlated spin-9/2 baths. These results highlight the limitations of self-assembled quantum dots and advantages of strain-free dots, where our sequences can be used to control the fluctuations of a homogeneous nuclear spin bath and potentially improve electron spin qubit coherence.

Fluctuating nuclear spin ensembles are a significant decoherence mechanism for solid-state spin qubits. Here the authors introduce an approach to controlling and extending the coherence of a nuclear spin bath around self-assembled quantum dots and gain insight into the many-body dynamics.

Direct Measurement of Hyperfine Shifts and Radio Frequency Manipulation of Nuclear Spins in Individual CdTe/ZnTe Quantum Dots

We achieve direct detection of electron hyperfine shifts in individual CdTe/ZnTe quantum dots. For the previously inaccessible regime of strong magnetic fields B_{z}≳0.1  T, we demonstrate robust polarization of a few-hundred-particle nuclear spin bath, with an optical initialization time of ∼1  ms and polarization lifetime exceeding ∼1  s. Nuclear magnetic resonance spectroscopy of individual dots reveals strong electron-nuclear interactions characterized by Knight fields |B_{e}|≳50  mT, an order of magnitude stronger than in III-V semiconductor quantum dots. Our studies confirm II-VI semiconductor quantum dots as a promising platform for hybrid electron-nuclear spin qubit registers, combining the excellent optical properties comparable to III-V dots and the dilute nuclear spin environment similar to group-IV semiconductors.

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.

Nuclear spins in solids can be implemented into quantum devices but their manipulation usually requires microwave irradiation. Here instead the authors show that they can shift the NMR frequency and drive the nuclear spins into the resolved-sideband regime by using the tunable phonon states from an electromechanical resonator.

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.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Role of the electron spin in determining the coherence of the nuclear spins in a quantum dot

A huge effort is underway to develop semiconductor nanostructures as low-noise qubits. A key source of dephasing for an electron spin qubit in GaAs and in naturally occurring Si is the nuclear spin bath. The electron spin is coupled to each nuclear spin by the hyperfine interaction. The same interaction also couples two remote nuclear spins via a common coupling to the delocalized electron. It has been suggested that this interaction limits both electron and nuclear spin coherence, but experimental proof is lacking. We show that the nuclear spin decoherence time decreases by two orders of magnitude on occupying an empty quantum dot with a single electron, recovering to its original value for two electrons. In the case of one electron, agreement with a model calculation verifies the hypothesis of an electron-mediated nuclear spin-nuclear spin coupling. The results establish a framework to understand the main features of this complex interaction in semiconductor nanostructures.

Quantum dot spin coherence governed by a strained nuclear environment

The interaction between a confined electron and the nuclei of an optically active quantum dot provides a uniquely rich manifestation of the central spin problem. Coherent qubit control combines with an ultrafast spin–photon interface to make these confined spins attractive candidates for quantum optical networks. Reaching the full potential of spin coherence has been hindered by the lack of knowledge of the key irreversible environment dynamics. Through all-optical Hahn echo decoupling we now recover the intrinsic coherence time set by the interaction with the inhomogeneously strained nuclear bath. The high-frequency nuclear dynamics are directly imprinted on the electron spin coherence, resulting in a dramatic jump of coherence times from few tens of nanoseconds to the microsecond regime between 2 and 3 T magnetic field and an exponential decay of coherence at high fields. These results reveal spin coherence can be improved by applying large magnetic fields and reducing strain inhomogeneity.

Spins confined to quantum dots are a possible qubit, but the mechanism that limits their coherence is unclear. Here, the authors use an all-optical Hahn-echo technique to determine the intrinsic coherence time of such spins set by its interaction with the inhomogeneously strained nuclear bath.

Nonlocal Nuclear Spin Quieting in Quantum Dot Molecules: Optically Induced Extended Two-Electron Spin Coherence Time

We demonstrate the extension of coherence between all four two-electron spin ground states of an InAs quantum dot molecule (QDM) via nonlocal suppression of nuclear spin fluctuations in two vertically stacked quantum dots (QDs), while optically addressing only the top QD transitions. Long coherence times are revealed through dark-state spectroscopy as resulting from nuclear spin locking mediated by the exchange interaction between the QDs. Line shape analysis provides the first measurement of the quieting of the Overhauser field distribution correlating with reduced nuclear spin fluctuations.

Quadrupolar and anisotropy effects on dephasing in two-electron spin qubits in GaAs

Understanding the decoherence of electron spins in semiconductors due to their interaction with nuclear spins is of fundamental interest as they realize the central spin model and of practical importance for using them as qubits. Interesting effects arise from the quadrupolar interaction of nuclear spins with electric field gradients, which have been shown to suppress diffusive nuclear spin dynamics and might thus enhance electron spin coherence. Here we show experimentally that for gate-defined GaAs quantum dots, quadrupolar broadening of the nuclear Larmor precession reduces electron spin coherence by causing faster decorrelation of transverse nuclear fields. However, this effect disappears for appropriate field directions. Furthermore, we observe an additional modulation of coherence attributed to an anisotropic electronic g-tensor. These results complete our understanding of dephasing in gated quantum dots and point to mitigation strategies. They may also help to unravel unexplained behaviour in self-assembled quantum dots and III–V nanowires.

Electron spins in semiconductors form a potential basis for quantum information technology however they are strongly affected by interactions with nuclear spins. Here, the authors show how quadrupolar interactions, although suppressing nuclear dynamics, can result in an anisotropic enhancement of electronic decoherence.

Influence of the Nuclear Electric Quadrupolar Interaction on the Coherence Time of Hole and Electron Spins Confined in Semiconductor Quantum Dots

The real-time spin dynamics and the spin noise spectra are calculated for p and n-charged quantum dots within an anisotropic central spin model extended by additional nuclear electric quadrupolar interactions and augmented by experimental data. Using realistic estimates for the distribution of coupling constants including an anisotropy parameter, we show that the characteristic long time scale is of the same order for electron and hole spins strongly determined by the quadrupolar interactions even though the analytical form of the spin decay differs significantly consistent with our measurements. The low frequency part of the electron spin noise spectrum is approximately 1/3 smaller than those for hole spins as a consequence of the spectral sum rule and the different spectral shapes. This is confirmed by our experimental spectra measured on both types of quantum dot ensembles in the low power limit of the probe laser.

Suppression of nuclear spin bath fluctuations in self-assembled quantum dots induced by inhomogeneous strain

Interaction with nuclear spins leads to decoherence and information loss in solid-state electron-spin qubits. One particular, ineradicable source of electron decoherence arises from decoherence of the nuclear spin bath, driven by nuclear-nuclear dipolar interactions. Owing to its many-body nature nuclear decoherence is difficult to predict, especially for an important class of strained nanostructures where nuclear quadrupolar effects have a significant but largely unknown impact. Here, we report direct measurement of nuclear spin bath coherence in individual self-assembled InGaAs/GaAs quantum dots: spin-echo coherence times in the range 1.2-4.5 ms are found. Based on these values, we demonstrate that strain-induced quadrupolar interactions make nuclear spin fluctuations much slower compared with lattice-matched GaAs/AlGaAs structures. Our findings demonstrate that quadrupolar effects can potentially be used to engineer optically active III-V semiconductor spin-qubits with a nearly noise-free nuclear spin bath, previously achievable only in nuclear spin-0 semiconductors, where qubit network interconnection and scaling are challenging.

Determination of gradient elastic tensors: stress and strain dependencies of electric field gradients in cubic and hexagonal systems

We present ab-initio calculations of the independent components of gradient elastic tensors, so-called gradient elastic constants, which relate electric field gradient tensors to stress or strain tensors. The constants of cubic and hexagonal metals, MAX phases, and zinc oxide were determined within the framework of density functional theory by using the augmented plane waves plus local orbitals method implemented in the WIEN2k code. Comparison with experimental gradient elastic constants and electric field gradients' stress dependencies suggest an accuracy of about 30% of the calculated constants, independent of the probe that detects the field gradient being self- or foreign-atom. Changes in the electric field gradient take place by strain-induced asymmetric occupations of the p and d states in the valence region for all investigated materials. Volume and structural dependencies of the electric field gradient can directly be determined from this fundamental approach and are, for hexagonal closed packed metals, consistent with vanishing electric field gradients around ideal close packing and volume dependencies larger than one. The concept of these calculations is applicable in any hyperfine interaction method and, thus, can be used to gain information about intrinsic strains in systems where the experimental gradient elastic constants are inaccessible.

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.

Nuclear magnetization in gallium arsenide quantum dots at zero magnetic field

Optical and electrical control of the nuclear spin system allows enhancing the sensitivity of NMR applications and spin-based information storage and processing. Dynamic nuclear polarization in semiconductors is commonly achieved in the presence of a stabilizing external magnetic field. Here we report efficient optical pumping of nuclear spins at zero magnetic field in strain-free GaAs quantum dots. The strong interaction of a single, optically injected electron spin with the nuclear spins acts as a stabilizing, effective magnetic field (Knight field) on the nuclei. We optically tune the Knight field amplitude and direction. In combination with a small transverse magnetic field, we are able to control the longitudinal and transverse components of the nuclear spin polarization in the absence of lattice strain--that is, in dots with strongly reduced static nuclear quadrupole effects, as reproduced by our model calculations.

Nuclear spin effects in semiconductor quantum dots

The interaction of an electronic spin with its nuclear environment, an issue known as the central spin problem, has been the subject of considerable attention due to its relevance for spin-based quantum computation using semiconductor quantum dots. Independent control of the nuclear spin bath using nuclear magnetic resonance techniques and dynamic nuclear polarization using the central spin itself offer unique possibilities for manipulating the nuclear bath with significant consequences for the coherence and controlled manipulation of the central spin. Here we review some of the recent optical and transport experiments that have explored this central spin problem using semiconductor quantum dots. We focus on the interaction between 10(4)-10(6) nuclear spins and a spin of a single electron or valence-band hole. We also review the experimental techniques as well as the key theoretical ideas and the implications for quantum information science.