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arXiv:1605.03693 · Physical review. B./Physical review. B

Generating spin squeezing states and Greenberger-Horne-Zeilinger entanglement using a hybrid phonon-spin ensemble in diamond

Keyu Xia, Jason Twamley

Published Nov 10, 2016• 36 citations
arXivHTMLPDF

Abstract

Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to a mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9\phantom{\rule{4.pt}{0ex}}\text{dB}$ for 20 spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for 20 spins with a fidelity of $\ensuremath{\sim}0.62$ at cryogenic temperature. The numerical simulations show that the geometric-phase-based scheme is mostly immune to thermal mechanical noise.

DOI
10.1103/physrevb.94.205118

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Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to a mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of 5.9dB5.9\phantom{\rule{4.pt}{0ex}}\text{dB}5.9dB for 20 spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for 20 spins with a fidelity of \ensuremath∼0.62\ensuremath{\sim}0.62\ensuremath∼0.62 at cryogenic temperature. The numerical simulations show that the geometric-phase-based scheme is mostly immune to thermal mechanical noise.
A scheme to achieve spin squeezing using a geometric phase induced by a single mechanical mode is proposed. The analytical and numerical results show that the ultimate degree of spin squeezing depends on the parameter nth+1/2QN\frac{{n}_{th}+1/2}{Q\sqrt{N}}QN​nth​+1/2​, which is the ratio between the thermal excitation, the quality factor, and square root of ensemble size. The undesired coupling between the spin ensemble and the bath can be efficiently suppressed by bang-bang control pulses. With high quality factor, the ultimate limit of the ideal one-axis twisting spin squeezing can be obtained for a nitrogen-vacancy ensemble in diamond.
In this study, we propose a theoretical scheme for achieving long-distance Greenberger-Horne-Zeilinger states in a driven hybrid quantum system. By applying a microwave field to the YIG sphere, we utilize the Kerr effect to induce the squeezing of the magnon, thereby achieving an exponential enhancement of the coupling strength between the magnonic mode and spins, and we also discuss in detail the relationship between the squeezing parameter and the external microwave field. By means of the Schrieffer-Wolff transformation, the magnonic mode can be adiabatically eliminated under the large detuning condition, thereby establishing a robust effective interaction between spins essential for realizing the desired entangled state. Numerical simulations indicate that the squeezing parameter can be effectively increased by adjusting the driving field, and our proposal can generate high-fidelity Greenberger-Horne-Zeilinger states even in dissipative systems. Additionally, we extensively discuss the influence of inhomogeneous broadening on the entangled states, and the experimental feasibility shows that our results provide possibilities in the realms of quantum networking and quantum computing.
As one kind of many body entangled states, spin squeezed states can be used to implement the high precise measurement beyond the standard quantum limit. Inspired by the novel spin squeezing scheme based on phonon-induced spin-spin interactions [S. D. Bennett et al., Phys. Rev. Lett. 110, 156402 (2013)], we reexamine the steady-state behaviors for the spin ensemble in diamond nanostructures by exerting a controllable microwave field. By using the phase-space approach we calculate analytically fluctuations of collective spin operators. We find that there is bistability and spin squeezing for the steady-state spin ensemble, despite the mechanical damping considered. Moreover, our work shows that bistability and spin squeezing can be controlled by microwave field and Zeeman splitting. The present scheme can be used to increase the stability of spin clocks, magnetometers, and other measurements based on spin-spin interaction in diamond nanostructures.
Abstract Spin systems are an attractive candidate for quantum-enhanced metrology. Here we develop a variational method to generate metrological states in small dipolar-interacting spin ensembles with limited qubit control. For both regular and disordered spatial spin configurations the generated states enable sensing beyond the standard quantum limit (SQL) and, for small spin numbers, approach the Heisenberg limit (HL). Depending on the circuit depth and the level of readout noise, the resulting states resemble Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing beyond the SQL holds in the presence of finite spin polarization and a non-Markovian noise environment. The developed black-box optimization techniques for small spin numbers ( N ≤ 10) are directly applicable to diamond-based nanoscale field sensing, where the sensor size limits N and conventional squeezing approaches fail.
Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) with an added quadratic optomechanical coupling is considered, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical coupling is coupled to a squeezed-vacuum reservoir with a phase matching, resulting in that its thermal noise can be suppressed completely. We show that squeezing of the phonon mode triggered by a single photon can be transferred to the spin ensemble totally, and pairwise entanglement of the spin ensemble can be realized if and only if there is spin squeezing. Importantly, when considering the impact of the environment, our system can obtain a squeezing degree better than that of the optimal squeezing that can be achieved in the traditional DM. Meanwhile, the spin squeezing generated in our system is immune to the thermal noise. This work offers an effective way to generate spin squeezing with a single photon and to reduce decoherence in an open system, which will have promising applications in quantum information processing.
Abstract We propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.