Dynamical decoupling of spin ensembles with strong anisotropic interactions
Benjamin Merkel, Pablo Cova Fariña, Andreas Reiserer
备注：
Second version of the manuscript contains additional measurements, in which dynamical decoupling in the absence of strong spin-spin interactions is demonstrated
Ensembles of dopants have widespread applications in quantum technology. The miniaturization of corresponding devices is however hampered by dipolar interactions that reduce the coherence at increased dopant density. We theoretically and experimentally investigate this limitation. We find that dynamical decoupling can alleviate, but not fully eliminate, the decoherence in crystals with strong anisotropic spin-spin interactions. Our findings can be generalized to all quantum systems with anisotropic g-factor used for quantum sensing, microwave-to-optical conversion, and quantum memory.
Quantum non-demolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the build-up of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieve…
Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the overall efficiency of quantum operations, but at the same time also increases the collision rate and leads to faster decoherence. Here we report on experiments with optically trapped 87Rb atoms demonstrating a 20-fold increase of the coherence time when a dynamical decoupling sequence with more than 200 pi-pulses is applied. We perform quantum process tomography and demonstrate that using the decoupling scheme a dense ensemble…
We simulate the dynamics of varying density quasi-two-dimensional spin ensembles in solid-state systems, focusing on the nitrogen-vacancy centers in diamond. We consider the effects of various control sequences on the averaged dynamics of large ensembles of spins, under a realistic "spin-bath" environment. We reveal that spin locking is efficient for decoupling spins initialized along the driving axis, both from coherent dipolar interactions and from the external spin-bath environment, when the driving is two orders of magnitude stronger than the relevant coupling energies. Since the applicati…
Zero-field dipolar decoupling of color center ensembles via universal qutrit control
Universidad de Murcia（穆尔西亚大学）；Monodon, Navantia, S.A（Navantia公司Monodon部门）；Universidad Politécnica de Cartagena（卡塔赫纳理工大学）；European University of Technology EUT+（欧洲理工大学联盟EUT+）；Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja（拉里奥哈国际大学高等工程与技术学院）；Ulm University（乌尔姆大学）；Center for Integrated Quantum Science and Technology (IQST)（集成量子科学与技术中心）
提出 ZENITH 脉冲序列，通过三能级控制消除 V 型简并自旋-1 系统间的偶极相互作用，实现零场下的高保真度、兼容现有传感序列并提升直流检测能力。
Robust gigahertz-range ac magnetometry with an ensemble of NV centers in diamond using concatenated continuous dynamical decoupling
Ulm University（乌尔姆大学）；Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Advanced Materials Laboratory, Sumitomo Electric Industries Ltd.（住友电工株式会社先进材料实验室）；Quantum Materials and Applications Research Center, National Institutes for Quantum Science and Technology（量子科学和技术研究院量子材料与应用程序研究中心）；Faculty of Pure and Applied Sciences, University of Tsukuba（筑波大学理工学部）
We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation $T_1$ effects and DD microwave pulses are used to increase the transverse coherence time $T_2$ from $\sim 0.7$ ms up to $\sim 30$ ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance o…
Ensembles of nitrogen-vacancy (NV) centers in diamond are widely used as AC magnetometers. While such measurements are usually performed using standard (XY) dynamical decoupling (DD) protocols at room temperature, we study the sensitivities achieved by utilizing various DD protocols, for measuring magnetic AC fields at frequencies in the 10-250 kHz range, at room temperature and 77 K. By performing measurements on an isotopically pure $^{12}$C sample, we find that the Carr-Purcell-Meiboom-Gill (CPMG) protocol, which is not robust against pulse imperfections, is less efficient for magnetometry …
Long-lived optical quantum memories are of great importance for scalable distribution of entanglement over remote networks (e.g. quantum repeaters). Long-lived storage generally relies on storing the optical states as spin excitations since these often exhibit long coherence times. To extend the storage time beyond the intrinsic spin dephasing time one can use dynamical decoupling techniques. However, it has been shown that dynamical decoupling introduces noise in optical quantum memories based on ensembles of atoms. In this article a simple model is proposed to calculate the resulting signal-…
We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $π$ pulses can reduce dipolar interactions between spins of the same species in solids. Our simulations of pulsed electron spin resonance (ESR) experiments show that $π$ rotations with small ($<$~10\%) imperfections refocus instantaneous diffusion. Here, the intractable N-body problem of interacting dipoles is approximated by the average evolution of a single spin in a changing mean field. These calculations agree well with experiments and do not require powerful hardware. Our results add to past attempts to explain similar …
We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of $d$-level systems (qudits), allowing one to protect the action of an arbitrary multi-qudit gate from general noise. We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit. This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of $^{87}\mathrm{Rb}$ and laser beams whose intensities and phases are modulated according to our prescription. We s…
We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is two-fold: first, it decouples individual spins from magnetic noise; second and more important, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can enhance the decay of the tails of the inhomogeneous broadening distribution considerably. This fact enables a spin ensemble based quantum memory to exp…
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins magnetically coupled to a superconducting resonator. We report on a cavity QED experiment with magnetically anisotropic Er3+:Y2SiO5 crystals and demonstrate strong coupling of rare-earth spins to a lumped element resonator. In addition, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without a…
It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability…
We propose the use of non-equally spaced decoupling pulses for high-resolution selective addressing of nuclear spins by a quantum sensor. The analytical model of the basic operating principle is supplemented by detailed numerical studies that demonstrate the high degree of selectivity and the robustness against static and dynamic control field errors of this scheme. We exemplify our protocol with an NV center-based sensor to demonstrate that it enables the identification of individual nuclear spins that form part of a large spin ensemble.
We propose a new pulse sequence for dynamical averaging of the dipole-dipole interactions and inhomogeneities of the magnetic fields in the nuclear spin system. The sequence contains a short cycle of the periodic resonant pulse excitation that offers new possibilities for implementing the long-lived multi-qubit quantum memory on the condensed spin ensembles that are so important for construction of universal quantum computer and long-distance quantum communications.
An optimal dynamical decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a new formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultra-cold Rubidium atoms, and use quantum process tomography to identify the effe…
Stroboscopic spin flips have already been shown to prolong the coherence times of quantum systems under noisy environments. Uhrig's dynamical decoupling scheme provides an optimal sequence for a quantum system interacting with a dephasing bath. Several experimental demonstrations have already verified the efficiency of such dynamical decoupling schemes in preserving single qubit coherences. In this work we describe the experimental study of Uhrig's dynamical decoupling in preserving two-qubit entangled states using an ensemble of spin-1/2 nuclear pairs in solution state. We find that the perfo…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon "spectral de…
The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogen-vacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength, and demonstrate an improvement of an order of magnitude in the spin-preservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exh…
The ongoing rapid progress towards quantum technologies relies on new hybrid platforms optimized for specific quantum computation and communication tasks, and researchers are striving to achieve such platforms. We study theoretically a spin qubit exchange-coupled to an anisotropic ferromagnet that hosts magnons with a controllable degree of intrinsic squeezing. We find this system to physically realize the quantum Rabi model from the isotropic to the Jaynes-Cummings limit with coupling strengths that can reach the deep-strong regime. We demonstrate that the composite nature of the squeezed mag…
We have studied the role of thermalization in lifetime reduction of quantum memory based on multi-atomic ensembles. Herein, it is shown to be impossible to remove the thermaization-caused decoherence in such systems using the methods of dynamical decoupling. We have analyzed the existing models of the thermalization and have proposed a new understanding of the thermalization as a result of the internal processes which are not described in the unitary quantum dynamics formalism. The possible ways for reducing the negative influence of thermalization on the quantum memory lifetime are also discu…
Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen-vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nu…
Direct Observation of Dipolar-Driven Anisotropic Quantum Projection Noise in a Solid-State Spin Ensemble
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；California Institute of Technology（加州理工学院）；Boston University（波士顿大学）
Coherence time is an essential parameter for quantum sensing, quantum information, and quantum computation. In this work, we demonstrate electron spin coherence times as long as 0.1 s for an ensemble of rubidium atoms trapped in a solid parahydrogen matrix. We explore the underlying physics limiting the coherence time. The properties of these matrix isolated atoms are very promising for future applications, including quantum sensing of nuclear spins. If combined with efficient single-atom readout, this would enable NMR and magnetic resonance imaging of single molecules cotrapped with alkali-me…
Quantum decoherence of nitrogen-vacancy spin ensembles in a nitrogen spin bath in diamond under dynamical decoupling
SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University（成均馆大学 SKKU 纳米技术高级研究所）；Department of Physics and Department of Energy Systems Research, Ajou University（亚洲大学物理系与能源系统研究部）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Center for Quantum Information, Korea Institute of Science and Technology（韩国科学技术院量子信息中心）；Division of Nano and Information Technology, KIST School, Korea University of Science and Technology（韩国科学技术院 KIST 学院纳米与信息技术分部）；Department of Chemistry, University of Chicago（芝加哥大学化学系）；Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory（阿贡国家实验室分子工程与材料科学中心）；Department of Quantum Information Engineering, Sungkyunkwan University（成均馆大学量子信息工程系）
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will with high probability be decoupled from the channel's environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modificat…
Dynamical decoupling (DD) is a powerful method for controlling arbitrary open quantum systems. In quantum spin control, DD generally involves a sequence of timed spin flips ($π$ rotations) arranged to average out or selectively enhance coupling to the environment. Experimentally, errors in the spin flips are inevitably introduced, motivating efforts to optimise error-robust DD. Here we invert this paradigm: by introducing particular control "errors" in standard DD, namely a small constant deviation from perfect $π$ rotations (pulse adjustments), we show we obtain protocols that retain the adva…
Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically, and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indisti…
Quantum memories with long storage times are key elements in long-distance quantum networks. The atomic frequency comb (AFC) memory in particular has shown great promise to fulfill this role, having demonstrated multimode capacity and spin-photon quantum correlations. However, the memory storage times have so-far been limited to about one millisecond, realized in a Eu${}^{3+}$ doped Y${}_2$SiO${}_5$ crystal at zero applied magnetic field. Motivated by studies showing increased spin coherence times under applied magnetic field, we developed a AFC spin-wave memory utilizing a weak 15 mT magnetic…
We report the implementation of a 3-qubit quantum error correction code (QECC) on a quantum information processor realized by the magnetic resonance of Carbon nuclei in a single crystal of Malonic Acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuc…
The demonstration of strong and ultrastrong coupling regimes of cavity QED with polyatomic molecules has opened new routes to control chemical dynamics at the nanoscale. We show that strong resonant coupling of a cavity field with an electronic transition can effectively decouple collective electronic and nuclear degrees of freedom in a disordered molecular ensemble, even for molecules with high-frequency quantum vibrational modes having strong electron-vibration interactions. This type of polaron decoupling can be used to control chemical reactions. We show that the rate of electron transfer …
The ability to initialise nuclear spins, which are typically in a mixed state even at low temperature, is a key requirement of many protocols used in quantum computing and simulations as well as in magnetic resonance spectroscopy and imaging. Yet, it remains a challenging task that typically involves complex and inefficient protocols, limiting the fidelity of ensuing operations or the measurement sensitivity. We introduce here a class of dynamical nuclear spin state selective (DNSS) protocols which, when applied to a polarised electron spin such as the nitrogen-vacancy (NV) centre in diamond, …
Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling --- the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath coupling spectrum in an ensemble of optically trapped ultracold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low…
Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University（台湾大学电机工程学系暨通信工程学研究所）；Department of Mathematics, National Taiwan University（台湾大学数学系）；Center for Quantum Science and Engineering, National Taiwan University（台湾大学量子科学与工程中心）；Physics/Mathematics Division, National Center for Theoretical Sciences（国家理论科学中心物理/数学组）；Hon Hai (Foxconn) Quantum Computing Center（鸿海（富士康）量子计算中心）
We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve a factor of 30 improvement in signal-to-noise ratio, translating to a sensitivity enhancement exceeding an order of magnitude. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous bias and control fields, ensuring that all of the ${\sim}10^9$ two-qubit sensors are sufficiently identical to permit global control of the NV en…
Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-two dimensional magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane an…
