Laser cooling and real-time measurement of the nuclear spin environment of a solid-state qubit

Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level ^{73}Ge Vacancy Nuclear Spin Qudit in Diamond

A high-spin nucleus coupled to a color center can act as a long-lived memory qudit in a spin-photon interface. The germanium vacancy (GeV) in diamond has attracted recent attention due to its excellent spectral properties and provides access to the ten-dimensional Hilbert space of the I=9/2 ^{73}Ge nucleus. Here, we observe the ^{73}GeV  hyperfine structure, perform nuclear spin readout, and optically initialize the ^{73}Ge spin into any eigenstate on a μs timescale and with a fidelity of up to ∼84%. Our results establish ^{73}GeV as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.

Non-Gaussian Dynamics of Quantum Fluctuations and Mean-Field Limit in Open Quantum Central Spin Systems

Central spin systems, in which a central spin is singled out and interacts nonlocally with several bath spins, are paradigmatic models for nitrogen-vacancy centers and quantum dots. They show complex emergent dynamics and stationary phenomena which, despite the collective nature of their interaction, are still largely not understood. Here, we derive exact results on the emergent behavior of open quantum central spin systems. The latter crucially depends on the scaling of the interaction strength with the bath size. For scalings with the inverse square root of the bath size (typical of one-to-many interactions), the system behaves, in the thermodynamic limit, as an open quantum Jaynes-Cummings model, whose bosonic mode encodes the quantum fluctuations of the bath spins. In this case, non-Gaussian correlations are dynamically generated and persist at stationarity. For scalings with the inverse bath size, the emergent dynamics is instead of mean-field type. Our Letter provides a fundamental understanding of the different dynamical regimes of central spin systems and a simple theory for efficiently exploring their nonequilibrium behavior. Our findings may become relevant for developing fully quantum descriptions of many-body solid-state devices and their applications.

The squeezed dark nuclear spin state in lead halide perovskites

Coherent many-body states are highly promising for robust quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr3 (FA = formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping after its build-up. Via optical orientation of localized hole spins we drive the nuclear many-body system into this entangled state, requiring a weak magnetic field of only a few milli-Tesla strength at cryogenic temperatures. During its fast establishment, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with ξs < 0.5. The dark state corresponds to an ~35-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.

Stabilization of spin states of an open system: bichromatic driving of resonance transitions in NV ensembles in diamond

We apply a laser and two nearly degenerate microwave fields upon an ensemble of nitrogen-vacancy centers in diamond and observe magnetic resonance structures with two-component, composite shapes of nested Lorentzians with different widths. One component of them undergoes regular power-broadening, whereas the linewidth of the other one becomes power-independent and undergoes field-induced stabilization. We show that the observed width stabilization is a general phenomenon that results from competition between coherent driving and non-conservation of populations that occur in open systems. The phenomenon is interpreted in terms of specific combinations of state populations that play the role of bright and dark states.

Optical Control of a Single Nuclear Spin in the Solid State

We demonstrate a novel method for coherent optical manipulation of individual nuclear spins in the solid state, mediated by the electronic states of a proximal quantum emitter. Specifically, using the nitrogen-vacancy (NV) color center in diamond, we demonstrate control of a proximal ^{14}N nuclear spin via an all-optical Raman technique. We evaluate the extent to which the intrinsic physical properties of the NV center limit the performance of coherent control, and we find that it is ultimately constrained by the relative rates of transverse hyperfine coupling and radiative decay in the NV center's excited state. Possible extensions and applications to other color centers are discussed.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

Controlling the coherence of a diamond spin qubit through its strain environment

The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. For quantum bits in the solid state, decoherence from thermal vibrations of the surrounding lattice can typically only be suppressed by lowering the temperature of operation. Here, we use a nano-electro-mechanical system to mitigate the effect of thermal phonons on a spin qubit - the silicon-vacancy colour centre in diamond - without changing the system temperature. By controlling the strain environment of the colour centre, we tune its electronic levels to probe, control, and eventually suppress the interaction of its spin with the thermal bath. Strain control provides both large tunability of the optical transitions and significantly improved spin coherence. Finally, our findings indicate the possibility to achieve strong coupling between the silicon-vacancy spin and single phonons, which can lead to the realisation of phonon-mediated quantum gates and nonlinear quantum phononics.

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 39 ns. 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.

Transfer of Phase Information between Microwave and Optical Fields via an Electron Spin

We demonstrate the coherent coupling and the resulting transfer of phase information between microwave and optical fields in a single nitrogen vacancy center in diamond. The relative phase of two microwave fields is encoded in a coherent superposition spin state. This phase information is then retrieved with a pair of optical fields. A related process is also used for the transfer of phase information from optical to microwave fields. These studies show the essential role of dark states, including optical pumping into the dark states, in the coherent microwave-optical coupling and open the door to the full quantum state transfer between microwave and optical fields in a solid-state spin ensemble.

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.

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.

Spin-photon entanglement interfaces in silicon carbide defect centers

Optically active spins in solid-state systems can be engineered to emit photons that are entangled with the spin in the solid. This allows for applications such as quantum communications, quantum key distribution, and distributed quantum computing. Recently, there has been a strong interest in silicon carbide defects, as they emit very close to the telecommunication wavelength, making them excellent candidates for long range quantum communications. In this work we develop explicit schemes for spin-photon entanglement in several SiC defects: the silicon monovacancy, the silicon divacancy, and the NV center in SiC. Distinct approaches are given for (i) single-photon and spin entanglement and (ii) the generation of long strings of entangled photons. The latter are known as cluster states and comprise a resource for measurement-based quantum information processing.

Heralded Control of Mechanical Motion by Single Spins

We propose a method to achieve a high degree of control of nanomechanical oscillators by coupling their mechanical motion to single spins. Manipulating the spin alone and measuring its quantum state heralds the cooling or squeezing of the oscillator even for weak spin-oscillator couplings. We analytically show that the asymptotic behavior of the oscillator is determined by a spin-induced thermal filter function whose overlap with the initial thermal distribution of the oscillator determines its cooling, heating, or squeezing. Counterintuitively, the rate of cooling dependence on the instantaneous thermal occupancy of the oscillator renders robust cooling or squeezing even for high initial temperatures and damping rates. We further estimate how the proposed scheme can be used to control the motion of a thin diamond cantilever by coupling it to its defect centers at low temperature.

Optomechanical Quantum Control of a Nitrogen-Vacancy Center in Diamond

We demonstrate optomechanical quantum control of the internal electronic states of a diamond nitrogen-vacancy (NV) center in the resolved-sideband regime by coupling the NV to both optical fields and surface acoustic waves via a phonon-assisted optical transition and by taking advantage of the strong excited-state electron-phonon coupling of a NV center. Optomechanically driven Rabi oscillations as well as quantum interferences between the optomechanical sideband and the direct dipole-optical transitions are realized. These studies open the door to using resolved-sideband optomechanical coupling for quantum control of both the atomlike internal states and the motional states of a coupled NV-nanomechanical system, leading to the development of a solid-state analog of trapped ions.

Coherent Population Trapping of a Single Nuclear Spin Under Ambient Conditions

We demonstrate coherent population trapping of a single nuclear spin in a room-temperature solid. To this end, we exploit a three-level system with a Λ configuration in the microwave domain, which consists of nuclear spin states addressed through their hyperfine coupling to the electron spin of a single nitrogen-vacancy defect in diamond. Moreover, the Λ-scheme relaxation is externally controlled through incoherent optical pumping and separated in time from consecutive coherent microwave excitations. Such a scheme allows us (i) to monitor the sequential accumulation of population into the dark state and (ii) to reach a novel regime of coherent population trapping dynamics for which periodic arrays of dark resonances can be observed, owing to multiple constructive interferences. This Letter offers new prospects for quantum state preparation, information storage in hybrid quantum systems, and metrology.

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 coupled(13)C 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 coupled (13)C nuclei. This allows sensitive magnetic field control of the (13)C nuclear spin polarization for NMR applications and significant suppression of the (13)C nuclear spin noise to prolong the NV spin coherence time.

All-Optical Preparation of Coherent Dark States of a Single Rare Earth Ion Spin in a Crystal

All-optical addressing and coherent control of single solid-state based quantum bits is a key tool for fast and precise control of ground-state spin qubits. So far, all-optical addressing of qubits was demonstrated only in a very few systems, such as color centers and quantum dots. Here, we perform high-resolution spectroscopic of native and implanted single rare earth ions in solid, namely, a cerium ion in yttrium aluminum garnet (YAG) crystal. We find narrow and spectrally stable optical transitions between the spin sublevels of the ground and excited optical states. Utilizing these transitions we demonstrate the generation of a coherent dark state in electron spin sublevels of a single Ce^{3+} ion in YAG by coherent population trapping.

All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond

The silicon-vacancy (SiV-) color center in diamond has attracted attention because of its unique optical properties. It exhibits spectral stability and indistinguishability that facilitate efficient generation of photons capable of demonstrating quantum interference. Here we show optical initialization and readout of electronic spin in a single SiV- center with a spin relaxation time of T1=2.4±0.2  ms. Coherent population trapping (CPT) is used to demonstrate coherent preparation of dark superposition states with a spin coherence time of T2⋆=35±3  ns. This is fundamentally limited by orbital relaxation, and an understanding of this process opens the way to extend coherence by engineering interactions with phonons. Hyperfine structure is observed in CPT measurements with the 29Si isotope which allows access to nuclear spin. These results establish the SiV- center as a solid-state spin-photon interface.

Protecting a solid-state spin from decoherence using dressed spin states

We report experimental studies of dressing an electron spin in diamond with resonant and continuous microwave fields to protect the electron spin from magnetic fluctuations induced by the nuclear spin bath. We use optical coherent population trapping (CPT) to probe the energy level structure, optically induced spin transitions, and spin decoherence rates of the dressed spin states. Dressing an electron spin with resonant microwaves at a coupling rate near 1 MHz leads to a 50 times reduction in the linewidth of the spin transition underlying the CPT process, limited by transit-time broadening. Compared with dynamical decoupling, where effects of the bath are averaged out at specific times, the dressed spin state provides a continuous protection from decoherence.

Probing the dynamics of a nuclear spin bath in diamond through time-resolved central spin magnetometry

Using fast electron spin resonance spectroscopy of a single nitrogen-vacancy defect in diamond, we demonstrate real-time readout of the Overhauser field produced by its nuclear spin environment under ambient conditions. These measurements enable narrowing the Overhauser field distribution by postselection, corresponding to a conditional preparation of the nuclear spin bath. Correlations of the Overhauser field fluctuations are quantitatively inferred by analyzing the Allan deviation over consecutive measurements. This method allows us to extract the dynamics of weakly coupled nuclear spins of the reservoir.

Ultrafast optical control of orbital and spin dynamics in a solid-state defect

Atom-scale defects in semiconductors are promising building blocks for quantum devices, but our understanding of their material-dependent electronic structure, optical interactions, and dissipation mechanisms is lacking. Using picosecond resonant pulses of light, we study the coherent orbital and spin dynamics of a single nitrogen-vacancy center in diamond over time scales spanning six orders of magnitude. We develop a time-domain quantum tomography technique to precisely map the defect's excited-state Hamiltonian and exploit the excited-state dynamics to control its ground-state spin with optical pulses alone. These techniques generalize to other optically addressable nanoscale spin systems and serve as powerful tools to characterize and control spin qubits for future applications in quantum technology.

Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator

We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling.

Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond

Rabi oscillations and adiabatic passage of single electron spins in a diamond nitrogen vacancy center are demonstrated with two Raman-resonant optical pulses that are detuned from the respective dipole optical transitions. We show that the optical spin control is nuclear-spin selective and can be robust against rapid decoherence, including radiative decay and spectral diffusion, of the underlying optical transitions. A direct comparison between the Rabi oscillation and the adiabatic passage, along with a detailed theoretical analysis, provides significant physical insights into the connections and differences between these coherent spin processes and also elucidates the role of spectral diffusion in these processes. The optically driven coherent spin processes enable the use of nitrogen vacancy excited states to mediate coherent spin-phonon coupling, opening the door to combining optical control of both spin and mechanical degrees of freedom.

Fast optical cooling of nanomechanical cantilever with the dynamical Zeeman effect

We propose an efficient optical electromagnetically induced transparency (EIT) cooling scheme for a cantilever with a nitrogen-vacancy center attached in a non-uniform magnetic field using dynamical Zeeman effect. In our scheme, the Zeeman effect combined with the quantum interference effect enhances the desired cooling transition and suppresses the undesired heating transitions. As a result, the cantilever can be cooled down to nearly the vibrational ground state under realistic experimental conditions within a short time. This efficient optical EIT cooling scheme can be reduced to the typical EIT cooling scheme under special conditions.

Bulk nuclear polarization enhanced at room temperature by optical pumping

Bulk (13)C polarization can be strongly enhanced in diamond at room temperature based on the optical pumping of nitrogen-vacancy color centers. This effect was confirmed by irradiating single crystals at a ~50 mT field promoting anticrossings between electronic excited-state levels, followed by shuttling of the sample into an NMR setup and by subsequent (13)C detection. A nuclear polarization of ~0.5%--equivalent to the (13)C polarization achievable by thermal polarization at room temperature at fields of ~2000 T--was measured, and its bulk nature determined based on line shape and relaxation measurements. Positive and negative enhanced polarizations were obtained, with a generally complex but predictable dependence on the magnetic field during optical pumping. Owing to its simplicity, this (13)C room temperature polarizing strategy provides a promising new addition to existing nuclear hyperpolarization techniques.

Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing

We use electromagnetically induced transparency (EIT) to probe the narrow electron-spin resonance of nitrogen-vacancy centers in diamond. Working with a multipass diamond chip at temperatures 6-30 K, the zero-phonon absorption line (637 nm) exhibits an optical depth of 6 and inhomogeneous linewidth of ~30 GHz FWHM. Simultaneous optical excitation at two frequencies separated by the ground-state zero-field splitting (2.88 GHz) reveals EIT resonances with a contrast exceeding 6% and FWHM down to 0.4 MHz. The resonances provide an all-optical probe of external electric and magnetic fields with a projected photon-shot-noise-limited sensitivity of 0.2 V/cm/√[Hz] and 0.1 nT/√[Hz], respectively. Operation of a prototype diamond-EIT magnetometer measures a noise floor of ~/<1 nT/√[Hz] for frequencies above 10 Hz and Allan deviation of 1.3±1.1 nT for 100 s intervals. The results demonstrate the potential of diamond-EIT devices for applications ranging from quantum-optical memory to precision measurement and tests of fundamental physics.

All-optical control of a solid-state spin using coherent dark states

The study of individual quantum systems in solids, for use as quantum bits (qubits) and probes of decoherence, requires protocols for their initialization, unitary manipulation, and readout. In many solid-state quantum systems, these operations rely on disparate techniques that can vary widely depending on the particular qubit structure. One such qubit, the nitrogen-vacancy (NV) center spin in diamond, can be initialized and read out through its special spin-selective intersystem crossing, while microwave electron spin resonance techniques provide unitary spin rotations. Instead, we demonstrate an alternative, fully optical approach to these control protocols in an NV center that does not rely on its intersystem crossing. By tuning an NV center to an excited-state spin anticrossing at cryogenic temperatures, we use coherent population trapping and stimulated Raman techniques to realize initialization, readout, and unitary manipulation of a single spin. Each of these techniques can be performed directly along any arbitrarily chosen quantum basis, removing the need for extra control steps to map the spin to and from a preferred basis. Combining these protocols, we perform measurements of the NV center's spin coherence, a demonstration of this full optical control. Consisting solely of optical pulses, these techniques enable control within a smaller footprint and within photonic networks. Likewise, this unified approach obviates the need for both electron spin resonance manipulation and spin addressability through the intersystem crossing. This method could therefore be applied to a wide range of potential solid-state qubits, including those which currently lack a means to be addressed.

Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing

We propose and analyze a novel mechanism for long-range spin-spin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogen-vacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phonon-mediated effective spin-spin interactions that can be used to generate squeezed states of a spin ensemble. We show that spin dephasing and relaxation can be largely suppressed, allowing for substantial spin squeezing under realistic experimental conditions. Our approach has implications for spin-ensemble magnetometry, as well as phonon-mediated quantum information processing with spin qubits.