Steady motional entanglement between two distant levitated nanoparticles.

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Experimental Test of the Jarzynski Equality in a Single Spin-1 System Using High-Fidelity Single-Shot Readouts.

The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.

Highly sensitive gyroscope based on a levitated nanodiamond.

A gyroscope is one of the core components of an inertial navigation system. Both the high sensitivity and miniaturization are important for the applications of the gyroscope. We consider a nitrogen-vacancy (NV) center in a nanodiamond, which is levitated either by an optical tweezer or an ion trap. Based on the Sagnac effect, we propose a scheme to measure the angular velocity with ultra-high sensitivity through the matter-wave interferometry of the nanodiamond. Both the decay of the motion of the center of mass of the nanodiamond and the dephasing of the NV centers are included when we estimate the sensitivity of the proposed gyroscope. We also calculate the visibility of the Ramsey fringes, which can be used for estimating the limitation of gyroscope sensitivity. It is found that the sensitivity ∼6.86×10-7 r a d/s/H z can be achieved in an ion trap. As the working area of the gyroscope is extremely small (∼0.01~µm2), it could be made on-chip in the future.

Ultralow-threshold green fluorescent protein laser based on high Q microbubble resonators.

Biological lasers have attracted vast attention because of their potential medical application prospects, especially the low threshold biological laser that can be used for ultrasensitive biological detection while leaving the luminous gain medium undamaged by the pump light. By coupling the low concentration green fluorescent protein (GFP) solution with a high Q whispering gallery mode microbubble resonator, we managed to fabricate a miniature GFP laser with the lowest threshold and highest Q value compared to any known type of the GFP laser. The threshold energy is as low as 380 fJ, two orders of magnitude lower than any type of GFP laser at present. The Q value of the optical cavity in this biological laser is 5.3 × 107, two orders higher than the highest Q value of GFP lasers. We further confirmed the long-term stability of the working characteristics of GFP laser. It can work well nearly a month in temperature 3-4°C. Finally, we measured the effects of different concentrations of fluorescent protein on laser threshold. The data show that this biological laser can be used for highly sensitive detection of GFP concentration, which is particularly useful when the GFP is used as tracers.

Testing a quantum error-correcting code on various platforms.

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

Observation of Topological Magnon Insulator States in a Superconducting Circuit.

Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progress on observing topological phenomena has been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.

Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin.

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels appears when the rotating frequency is comparable to the spin frequency at zero magnetic field. Then we use Floquet theory to numerically solve the spin energy spectrum, study the spin dynamics and calculate the geometric phase under a finite magnetic field, where the rotating frequency to induce resonant transition could be greatly reduced.

Sensitivity of displacement detection for a particle levitated in the doughnut beam.

Displacement detection of a spherical particle in focused laser beams with a quadrant photodetector provides a fast and high precision way to determine the particle location. In contrast to the traditional Gaussian beams, the sensitivity of displacement detection using various doughnut beams is investigated. The sensitivity improvement for large spherical particles along the longitudinal direction is reported. With appropriate vortex charge l of the doughnut beams, they can outperform the Gaussian beam to get more than one order of magnitude higher sensitivity and, thus, have potential applications in various high-precision measurements. By using the levitating doughnut beam to detect the particle displacement, the result will also facilitate the recent proposal of levitating a particle in doughnut beams to suppress the light absorption.

Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit.

Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.

Single phonon source based on a giant polariton nonlinear effect.

We propose a single phonon source based on nitrogen-vacancy (NV) centers, which are located in a diamond phononic crystal resonator. The strain in the lattice would induce the coupling between the NV centers and the phonon mode. The strong coupling between the excited state of the NV centers and the phonon is realized by adding an optical laser driving. This four-level NV center system exhibits coherent population trapping and yields giant resonantly enhanced acoustic nonlinearities, with zero linear susceptibility. Based on this nonlinearity, the single phonon source can be realized. We numerically calculate g(2)(0) of the single phonon source. We discuss the effects of the thermal noise and the external driving strength.

NMRCloudQ: a quantum cloud experience on a nuclear magnetic resonance quantum computer.

Cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms has followed up yet. Here, we report our new cloud quantum computing service - NMRCloudQ (http://nmrcloudq.com/zh-hans/), where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. In our current version, four qubits are already usable with in average 99.10% single-qubit gate fidelity and 97.15% two-qubit fidelity via randomized benchmaking tests. Improved control precisions as well as a new seven-qubit processor are also in preparation and will be available later.

High-precision gravimeter based on a nano-mechanical resonator hybrid with an electron spin.

We show that the gravitational acceleration can be measured with the matter-wave Ramsey interferometry, by using a nitrogen-vacancy center coupled to a nano-mechanical resonator. We propose two experimental methods to realize the similar Hamiltonian, by using either a cantilever resonator or a trapped nanoparticle. The scheme is robust against the thermal noise, and could be realized at the temperature much higher than the quantum regime. The effects of decoherence on the interferometry fringe visibility is calculated, considering both the mechanical motional decay and dephasing of the nitrogen-vacancy center. In addition, we demonstrate that under the various sources of random and systematic noises, our gravimeter can be made on-chip and achieve a high measurement of precision. Under experimental feasible parameters, the proposed gravimeter could achieve 10-10 relative precision.

Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble.

In a diamond, the mechanical vibration-induced strain can lead to interaction between the mechanical mode and the nitrogen-vacancy (NV) centers. In this work, we propose to utilize the strain-induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in a diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach 98.57%.

Generation of macroscopic Schrödinger cat state in diamond mechanical resonator.

We propose a scheme to generate macroscopic Schrödinger cat state (SCS) in diamond mechanical resonator (DMR) via the dynamical strain-mediated coupling mechanism. In our model, the direct coupling between the nitrogen-vacancy (NV) center and lattice strain field enables coherent spin-phonon interactions in the quantum regime. Based on a cyclic Δ-type transition structure of the NV center constructed by combining the quantized mechanical strain field and a pair of external microwave fields, the populations of the different energy levels can be selectively transferred by controlling microwave fields, and the SCS can be created by adjusting the controllable parameters of the system. Furthermore, we demonstrate the nonclassicality of the mechanical SCS both in non-dissipative case and dissipative case. The experimental feasibility and challenge are justified using currently available technology.

Torsional Optomechanics of a Levitated Nonspherical Nanoparticle.

An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be 1 order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10^{-29} N m/sqrt[Hz] under realistic conditions.

Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators.

We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.

Quantum Zeno and Zeno-like effects in nitrogen vacancy centers.

We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal (13)C nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a (13)C nuclear spin in the vicinity of an NV center.

One-step generation of multipartite entanglement among nitrogen-vacancy center ensembles.

We describe a one-step, deterministic and scalable scheme for creating macroscopic arbitrary entangled coherent states (ECSs) of separate nitrogen-vacancy center ensembles (NVEs) that couple to a superconducting flux qubit. We discuss how to generate the entangled states between the flux qubit and two NVEs by the resonant driving. Then the ECSs of the NVEs can be obtained by projecting the flux qubit, and the entanglement detection can be realized by transferring the quantum state from the NVEs to the flux qubit. Our numerical simulation shows that even under current experimental parameters the concurrence of the ECSs can approach unity. We emphasize that this method is straightforwardly extendable to the case of many NVEs.