Matter-Wave Interferometry of a Levitated Thermal Nano-Oscillator Induced and Probed by a Spin

Our papers [1,2] propose an experiment in which the observation of Ramsey fringes would be evidence for a spatial superposition. We analyzed this as a magnetic effect creating a Stern-Gerlach like spin dependent separation of the centre of mass (COM) states in conjunction with a gravitational effect imparting a relative phase between the states. The comment points out that this could be interpreted in a different way. It contends that the interference manifested in the spin states is not due to the spatial separation as the gravity effects can also be interpreted as a Zeeman effect. To support its contention, the comment splits the Hamitonian into parts H 1 and H 2 where only H 1 couples the COM with the spin states, while H 2 imparts the phase factor. However, the periodic factorizability of the COM and the spin states requires the action of H 1 as well. It is this factorizability which makes the phase detectable by a measurement on the spin alone. For instance, if the COM and spin states are not entangled at T /2, the evolution by H 1 alone for an additional time T /2 will not be able to factorise them. This will lead to the Ramsey interference pattern being supressed. Thus the very visibility of the phase due to H 2 hinges on the interference brought about by H 1 . Both treatments (our's and the comment's) are valid and equivalent as they use the same Hamiltonian. In both cases there is a spatial superposition except for certain periodic moments in time (at integer multiples of the oscillator time period T ). In both cases, the absence of coherence in the COM motion (which could be due to decoherence from air molecules for example) would remove these fringes.In the absence of decoherence, an arbitrary initial coherent state |β of the COM and an initial spin statewhere |β(t, ±1) are COM coherent states with the timevarying separation of ∆z(t) = 8λδz ωz (1 − cos ω z t) with δ z = 2mωz being the ground state position spread of the oscillator. Despite the fact that |β(t, ±1) oscillate about centresωz where there are finite magnetic fields, in our approach, the entire inhomogeneous magnetic field term of the Hamitonian is "used up" to accompish the Stern-Gerlach like separation ∆z(t), and is thereby, not available any more to impart a Zeeman phase between the separated states. The integrated gravitational phase shift T 0 mg cos θ∆z(t)dt gives exactly theLet us now clarify that even if the comment's interpretation that the measured signal results from "the common displacement of the COM position of both ±1 states" is adopted, the visibility of this signal is affected by the coherence between the superposed COM states. Consider a case where only the COM motion is decohered: the off diagonal terms |β(t, +1) β(t, −1)| are damped by a factor of e −γ(t) . Then the evolved state at t = N T isThus we see that the spin density matrix has also decohered (thereby lowering the visibility of φ as a relevant parameter, say θ, is varied) despite the fact that the decoherence was exclusively for the COM state [3,4]. In particular...

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“…The integrated gravitational phase shift T 0 mg cos θ∆z(t)dt gives exactly the phase shift φ = φ + (T ) − φ − (T ) = φ grav of Refs. [1,2].…”

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“…The ability to create unambiguous superpositions on a mesoscopic scale would allow tests of quantum collapse theories and gravitational decoherence [3][4][5][6][7], ultimately addressing experimentally the question of why we fail to see superpositions in everyday life [8]. This has inspired numerous challenging proposals to detect interference of larger particles [9][10][11] via optomechanical coupling [12], or by using levitated nanodiamonds [13,14].…”

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Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

et al. 2018

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We introduce the "displacemon" electromechanical architecture that comprises a vibrating nanobeam, e.g., a carbon nanotube, flux coupled to a superconducting qubit. This platform can achieve strong and even ultrastrong coupling, enabling a variety of quantum protocols. We use this system to describe a protocol for generating and measuring quantum interference between trajectories of a nanomechanical resonator. The scheme uses a sequence of qubit manipulations and measurements to cool the resonator, to apply two effective diffraction gratings, and then to measure the resulting interference pattern. We demonstrate the feasibility of generating a spatially distinct quantum superposition state of motion containing more than 10 6 nucleons using a vibrating nanotube acting as a junction in this new superconducting qubit configuration.

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“…Because of the wide applicability and high tunablity of the optically levitated systems, several schemes [16] were proposed to realize the ground-state cooling [17], to search for non-Newtonian gravity [18] and to detect gravitational wave [19]. Particularly, it brings about more interesting phenomena and novel applications [20,21] when the trapped particles have internal degrees of freedom (such as spins or electric dipoles) and enter the quantum regime.Optically levitated nanodiamonds with nitrogen-vacancy (NV) centers [22][23][24][25][26] are one of the most promising candidates for implementing a spin-optomechanical hybrid system. In principle, this system can have both long spin coherence time and high quality factor of mechanical oscillation in vacuum.…”

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Optical levitation of nanodiamonds by doughnut beams in vacuum

Zhou

Xiao

Chen

et al. 2017

Laser & Photonics Reviews

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Optically levitated nanodiamonds with nitrogen-vacancy centers promise a high-quality hybrid spinoptomechanical system. However, the trapped nanodiamond absorbs energy form laser beams and causes thermal damage in vacuum. It is proposed here to solve the problem by trapping a composite particle (a nanodiamond core coated with a less absorptive silica shell) at the center of strongly focused doughnut-shaped laser beams. Systematical study on the trapping stability, heat absorption, and oscillation frequency concludes that the azimuthally polarized Gaussian beam and the linearly polarized Laguerre-Gaussian beam LG 03 are the optimal choices. With our proposal, particles with strong absorption coefficients can be trapped without obvious heating and, thus, the spin-optomechanical system based on levitated nanodiamonds are made possible in high vacuum with the present experimental techniques.Introduction-. By trapping, detecting and manipulating nano-and micro-particles [1], optical tweezers are widely used in biophysics [2-4], colloidal sciences [5], chemistry, microfluidic dynamics [6], and fundamental physics [7][8][9][10][11][12][13][14][15]. Because of the wide applicability and high tunablity of the optically levitated systems, several schemes [16] were proposed to realize the ground-state cooling [17], to search for non-Newtonian gravity [18] and to detect gravitational wave [19]. Particularly, it brings about more interesting phenomena and novel applications [20,21] when the trapped particles have internal degrees of freedom (such as spins or electric dipoles) and enter the quantum regime.Optically levitated nanodiamonds with nitrogen-vacancy (NV) centers [22][23][24][25][26] are one of the most promising candidates for implementing a spin-optomechanical hybrid system. In principle, this system can have both long spin coherence time and high quality factor of mechanical oscillation in vacuum. The electron spins of NV centers were shown to have long spin coherence time (in the order of 10 2 µs) even in nanodiamonds of diameter about 20 nm [27]. When trapped in high-vacuum, the dielectric particles are predicted to have ultra-high quality factor Q larger than 10 10 [16,18,28]. Researchers have trapped diamond particles and observed the signal from NV centers in liquid [29,30], in air [31] and very recently in vacuum with pressure down to ∼ kPa [24,25] and ∼ 100 Pa [26].Realizing high quality mechanical oscillation requires trapping the particles in high vacuum (e.g, 10 −6 Pa) to get Q ∼ 10 10 . However, the high-vacuum condition usually causes the thermal damage problem, and experimentally trapping a nanodiamond in high vacuum is still very challenging. Nanodiamonds will absorb energy from the trapping laser beams due to the intrinsic defects [26] and the inevitable imperfections or graphitization [32] on diamond surface. The absorbed energy can hardly be dissipated in a high-vacuum environment, and the nanodiamonds will be quickly heated up significantly [24][25][26], which is unfavorable to the defect centers...

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Matter-Wave Interferometry of a Levitated Thermal Nano-Oscillator Induced and Probed by a Spin

Cited by 180 publications

References 47 publications

Bose et al. Reply:

Bose et al. Reply:

Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

Optical levitation of nanodiamonds by doughnut beams in vacuum

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