Tolerance in the Ramsey interference of a trapped nanodiamond

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

doi:10.1103/physreva.93.043852

Cited by 25 publications

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References 37 publications

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“…Optically levitated nanodiamonds containing nitrogen vacancy (NV − ) centre spin defects have been proposed as probes of quantum gravity [1,2], mesoscopic wavefunction collapse [3][4][5][6], phonon mediated spin coupling [7], and the direct detection of dark matter [8,9]. The NV − centre is a point defect in diamond that has a single electron spin which has long coherence times at room temperature and can be both polarized and read out optically [10,11].…”

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confidence: 99%

Pure nanodiamonds for levitated optomechanics in vacuum

et al. 2018

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Optical trapping at high vacuum of a nanodiamond containing a nitrogen vacancy centre would provide a test bed for several new phenomena in fundamental physics. However, the nanodiamonds used so far have absorbed too much of the trapping light, heating them to destruction (above 800 K) except at pressures above ∼10 mbar where air molecules dissipate the excess heat. Here we show that milling diamond of 1000 times greater purity creates nanodiamonds that do not heat up even when the optical intensity is raised above 700 GW m −2 below 5 mbar of pressure.

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Pure nanodiamonds for levitated optomechanics in vacuum

et al. 2018

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“…Subsequently, these frequencies are used for parametric feedback cooling to actively control the motion of a levitated particle. [1][2][3]5,[8][9][10][11][12][13][14] As with other interferometric schemes, this system is well known for its high precision and resilience to noise. In optomechanical setups, this is further enhanced by a balanced detection system.…”

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An analytical model for the detection of levitated nanoparticles in optomechanics

Rahman

Frangeskou

Barker

et al. 2018

Review of Scientific Instruments

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Interferometric position detection of levitated particles is crucial for the centre-of-mass (CM) motion cooling and manipulation of levitated particles. In combination with balanced detection and feedback cooling, this system has provided picometer scale position sensitivity, zeptonewton force detection, and sub-millikelvin CM temperatures. In this article, we develop an analytical model of this detection system and compare its performance with experimental results allowing us to explain the presence of spurious frequencies in the spectra.

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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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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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Tolerance in the Ramsey interference of a trapped nanodiamond

Cited by 25 publications

References 37 publications

Pure nanodiamonds for levitated optomechanics in vacuum

Pure nanodiamonds for levitated optomechanics in vacuum

An analytical model for the detection of levitated nanoparticles in optomechanics

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