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arXiv:1509.00724 · Physical Review A

Tolerance in the Ramsey interference of a trapped nanodiamond

C. Wan, M. Scala, Sougato Bose, Angelo Frangeskou, Anisur Rahman, Gavin W. Morley, P. F. Barker, M. S. Kim

Published Apr 27, 2016• 23 citations
arXivHTMLPDF

Abstract

In the scheme recently proposed by M. Scala et al. [Phys. Rev. Lett. 111, 180403 (2013)], a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle. This provides a way to detect spatial quantum superpositions by means of only spin measurements. Here, the effect of unwanted coupling with other motional degrees of freedom is considered, and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to misalignment between the quantization axis of the NV center spin and the trapping axis are shown not to change the qualitative behavior of the system, so that a proof-of-principle experiment can be neatly performed. Our analysis, which shows that the scheme retains the important features of not requiring ground-state cooling and of being resistant to thermal fluctuations, can be useful for several schemes which have been proposed recently for testing macroscopic superpositions in trapped microsystems.

DOI
10.1103/physreva.93.043852

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In the scheme recently proposed by M. Scala et al. [Phys. Rev. Lett. 111, 180403 (2013)], a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle. This provides a way to detect spatial quantum superpositions by means of only spin measurements. Here, the effect of unwanted coupling with other motional degrees of freedom is considered, and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to misalignment between the quantization axis of the NV center spin and the trapping axis are shown not to change the qualitative behavior of the system, so that a proof-of-principle experiment can be neatly performed. Our analysis, which shows that the scheme retains the important features of not requiring ground-state cooling and of being resistant to thermal fluctuations, can be useful for several schemes which have been proposed recently for testing macroscopic superpositions in trapped microsystems.
The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of 10−6g/Hz10^{-6}g/\sqrt{\text{Hz}}10−6g/Hz​. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.
We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9} amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.
Trapping of a nanodiamond/microdiamond containing Nitrogen-Vacancy centers in the vacuum is an ideal platform to develop a hybrid mechanical system. In such a system, the coupling between the Nitrogen-Vacancy centers and the mechanical motion of a trapped diamond provides pathways for generating a quantum superposition state of the mechanical motion with long coherence time. In this work, I demonstrate our preliminary data in the detection of Nitrogen-Vacancy spin signals from trapped diamonds using optical and magneto-gravitational trapping technologies. I compared the advantages and drawbacks of both techniques and improvements need to be made. I also explored the charge dynamics of Nitrogen-Vacancy centers in diamonds under near-IR laser illumination and first demonstrate low energy (0.95 to 1.18 eV or 1050 to 1300 nm) Multi-photon Photoluminescence Excitation (PLE) spectrum of NV centers in a sub-millimeter diamond crystal.
We propose a scheme to realize the controlled-phase gates between nitrogen-vacancy (NV) centers in an optically trapped nanodiamond, through a uniform magnetic field-induced coupling between the NV centers and the torsional mode of the levitated nanodiamond. The gates are insensitive to the thermal noise of the torsional mode. By combining the scheme with the dynamical decoupling, it is found that the high-fidelity universal quantum gates are possible with present experimental technology. The proposed scheme is useful for an NV-center-based quantum network and distributed quantum computation.
Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers $({\text{NV}}^{\ensuremath{-}})$ have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long ${\text{NV}}^{\ensuremath{-}}$ spin coherence time, which necessitates formulating a dynamical decoupling strategy in which the regular spin flips do not cancel the growth of the superposition through the Stern-Gerlach effect in an inhomogeneous magnetic field. Here, we propose a scheme to place a $250\text{\ensuremath{-}}\mathrm{n}\mathrm{m}$-diameter diamond in a superposition with spatial separation of over 250nm250\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}250nm, while incorporating dynamical decoupling. We achieve this by letting a diamond fall for 2.4m2.4\phantom{\rule{0.16em}{0ex}}\mathrm{m}2.4m through a magnetic structure, including 1.13m1.13\phantom{\rule{0.16em}{0ex}}\mathrm{m}1.13m in an inhomogeneous region generated by magnetic teeth.
There is significant interest in potential experimental tests of macroscopic quantum effects, both to test potential modifications to quantum theory and to probe the quantum nature of gravity. A proposed platform with which to generate the required macroscopic quantum spatial superposition is a nanodiamond containing a negatively charged nitrogen vacancy (NV-) centre. In this review, methods to fabricate nanodiamonds containing NV­suitable for these quantum applications are discussed. The proposed probes of the macroscopic limits of quantum theory are presented along with the spin physics of the NV- centre relevant to those tests.