ABSTRACT A nitrogen-vacancy (NV−) centre in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic centre-of-mass superpositions and for

testing quantum gravity. Here, we study the behaviour of optically levitated nanodiamonds containing NV− centres at sub-atmospheric pressures and show that while they burn in air, this can

be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below ≈10 mB. Exploiting the Brownian motion of a levitated nanodiamond, we extract its

internal temperature (_T__i_) and find that it would be detrimental to the NV− centre’s spin coherence time. These values of _T__i_ make it clear that the diamond is not melting,

TRANSITION INDUCED BY PHOTOELECTRIC ABSORPTION OF ULTRAVIOLET PHOTONS Article Open access 28 January 2021 INWARD MOTION OF DIAMOND NANOPARTICLES INSIDE AN IRON CRYSTAL Article Open access 31

May 2024 INTRODUCTION Even though diamond is thermodynamically metastable in ambient conditions, it has extremely high thermal conductivity, Young’s modulus, electrical resistivity,

chemical stability and optical transparency1,2,3,4. Nanodiamonds inherit most of these spectacular properties from their bulk counterparts and the inclusion of color centres such the NV−

centre has increased their realm of applications1,5. Proposed and demonstrated applications of diamond, nanodiamonds and nanodiamonds with NV− centres include tribology1,6, nanocomposites7,

UV detection in space applications8, magnetometry9, biological imaging10, quantum information processing11,12 and thermometry13. More recently nanodiamonds with NV− centres have been

suggested for testing quantum gravity14 and for demonstrating centre of mass (CM) superpositions of mesoscopic objects15,16. These superpositions and interferometry also point towards a

broader future application of levitated diamonds in sensing and gravitometry. In the scheme for testing quantum gravity, an NV− centre in a nanodiamond is exploited in a Ramsey-Borde

interferometer14 and, in the non-relativistic limit, the first order correction to the energy dispersion scales with the size of a nanodiamond. In the case of creating CM superpositions, the

NV− centre’s spin is utilized and the spatial separation of the superposed CM states depends on the size of a nanodiamond15,16. To prevent the adverse effects of motional decoherence, these

proposals14,15,16 have been conceptualized in high vacuum (10−6 mB). It is, however, well known that at atmospheric temperature and pressure graphite is the most stable form of carbon both

in the bulk as well as at the nanoscale (>5.2 nm)3,4,17,18,19 while diamond is stable between ≈1.9 nm and ≈5.2 nm17. Since the utility of diamond and diamond with various color centres

depends on its crystalline existence, it is imperative to study the behaviour of diamond in vacuum for scientific as well as for practical purposes. Furthermore, while the determination of

the size of nanoparticles using electron microscopy and dynamic light scattering are well established, their utility in levitated experiments is limited if not completely excluded. As a

result it seems reasonable to devise a way by which one can determine the size of an individual levitated object while performing the experiment. This is particularly useful in experiments

in which the size of a nanoparticle plays important roles. The significance of _in situ_ size determination is further emphasized by the polydisperse nature of nanoparticles. In this

article, we levitate high pressure high temperature (HPHT) synthesized nanodiamonds containing ≈500 NV− centres (ND-NV-100 nm, Adamas Nanotechnology, USA) using an optical tweezer and study

their behaviour under different levels of vacuum. We show that as the pressure of the trapping chamber is reduced, the internal temperature (_T__i_) of a trapped nanodiamond can reach ≈800 

K. Due to this elevated temperature levitated nanodiamonds burn in air. We also demonstrate that the burning of nanodiamond is preventable under a nitrogen environment down to 10 mB, but

beyond that, it graphitizes. The source of heating is believed to be the absorption of 1064 nm trapping laser light by the impurities in diamond and the amorphous carbon on the surface.

Lastly, exploiting the measured damping rate of a levitated object, we present a new way of determining its size _in situ_. EXPERIMENTAL SETUP Figure 1a shows a schematic of our experimental

setup where we use a 0.80 numerical aperture (NA) microscope objective to focus a 1064 nm laser beam into a diffraction limited spot. The force resulting from the electric field gradient

forms the basis of our dipole trap20. The balanced photodiode visible in Fig. 1a provides a voltage signal generated from the interference between the directly transmitted trapping laser

light and the oscillator’s position dependent scattered electromagnetic radiation20. Performing a Fourier transform on this voltage signal provides the measured spectral information as well

as the damping rate of a levitated nanoparticle. We use this spectral information and damping rate to retrieve _T__i_ and the size of a nanodiamond. In the regime where the oscillation

amplitude of a trapped particle is small, the trapping potential of an optical tweezer can be approximated as harmonic20. Under this condition, the motion of a levitated object can be

expressed as where _x_ is the displacement of a trapped particle from the centre of the trap along the _x_-axis. _M_ and γ_CM_, respectively, are the mass and the damping rate of a trapped

particle while is the trap frequency and κ is the spring constant of the trap20. _f_(_t_) is a Gaussian random force exerted by the gas molecules on a trapped particle with and , where

_k__B_ is the Boltzmann constant, _T__CM_ is the CM temperature of a trapped particle, and δ(_t_2 − _t_1) is the Dirac delta function20. Similar analyses for the remaining two axes are also

valid. After performing a Fourier transform and rearrangement, the power spectral density (PSD) of (1) can be written as We fit (2) with the experimental data. Figure 1b shows the PSDs

corresponding to the measured voltage signals from a levitated nanodiamond for different trapping powers along with the respective fits (solid lines) of equation (2) at 20 mB. For the

purpose of comparison, in Fig. 1b we have also included the relevant theoretical PSDs (dashed grey lines). In plotting the theoretical PSDs we have assumed that all parameters are identical

to the measured PSDs except _T__CM_ which has been taken equal to 300 K. Figure 1c demonstrates the measured damping rate as a function of pressure at a constant trapping power of 180 mW.

Later, we use this damping rate to find the size of a nanoparticle. LEVITATED NANODIAMONDS IN VACUUM To study the behaviour of diamond below atmospheric pressure, after levitating a

nanodiamond with the minimum possible trapping power (180 mW), we gradually take it to different levels of vacuum whilst continuously monitoring its scattering intensity (size) using a

camera. Figure 2a shows a typical plot of scattering intensity versus pressure (pink circles) from a levitated nanodiamond (for more data points see supplementary information Fig. S1). It

can be observed that as we evacuate the trapping chamber, the scattering intensity diminishes: a levitated nanodiamond shrinks in size as the pressure is reduced. We attribute this reduction

in size to the removal of physisorbed water and organic substances such as the carboxyl groups (nanodiamonds as obtained from the supplier are in water and are coated with carboxyl groups

for stabilization) present on the surface of nanodiamonds down to 20 mB where the temperature reaches ≈450 K (see Fig. 3). Physisorbed water and organic impurities normally disappear21 at or

below 473 K. This is further confirmed when we keep a levitated nanodiamond in a vacuum of less than 10 mB for an extended period of time (about an hour) and take it to back to atmospheric

pressure (red squares in Fig. 2a) and bring it down to the low pressures again. In the second round of evacuation, the scattering intensity remains constant down to 10 mB. This unaltered

scattering intensity in the second round of evacuation indicates the absence of substances which evaporate/burn at relatively lower temperatures. The reduction in size below 10 mB is

attributed to the burning of amorphous carbon or diamond. Amorphous carbon is generally found as an outer layer on the surface of nanodiamonds21,22,23. The burning temperature of amorphous

carbon21 at atmospheric pressure varies between 573–723 K while the oxidation temperature of nanodiamonds21,22,24 ranges from 723–769 K. Also, the exact oxidation temperature of nanodiamonds

depend on the surface quality, the crystallographic faces and the densities of impurities in nanodiamonds21,22,24. To confirm the presence of amorphous carbon as well as diamond in the

nanoparticles that we have used in our experiments, we performed Raman spectroscopy using a 785 nm laser. At this wavelength amorphous carbon is more sensitive than diamond25. Figure 2b

presents the relevant data. This figure clearly shows the presence of amorphous carbon and diamond peaked at ≈1400 cm−1 and at ≈1335 cm−1, respectively23,25,26,27. Given that amorphous

carbon is a strongly absorbing material28,29,30,31, trapping light (1064 nm) absorption and hence raised _T__i_ and consequent burning in an air environment is highly probable. This burning

of nanodiamond in air can potentially be a major hurdle in applications where vacuum is inevitable. Based on the idea that an oxygen-less environment may be a cure to this problem, we have

studied the behaviour of levitated nanodiamonds in a nitrogen environment. This is shown in Fig. 2a as blue crosses for a constant trapping power of 300 mW. It can be observed that at

pressures >10 mB the scattering intensity hence the size of a nanodiamond remains unchanged; even though temperature is quite high (see Fig. 3). This is due to the fact that for burning

to occur, a nanodiamond requires oxygen which is absent in a nitrogen rich environment. However, if the pressure is reduced below 10 mB, the scattering intensity of the nanodiamond gradually

diminishes. Given that there is almost no oxygen in the chamber and the reduced pressure means less cooling due to gas molecules and hence higher internal temperature, we believe this is

the onset of graphitization of the nanodiamond. At atmospheric pressure graphitization of nanodiamonds starts in the temperature range 943–1073 K and depends on the surface quality of

nanodiamonds24,26. Since we are operating at sub-atmospheric pressures, graphitization at a lower temperature is most likely to happen. Lastly, it is noteworthy that irrespective of an air

or a nitrogen environment, below 5 mB levitated nanodiamonds rapidly shrink in size and by ≈2 mB completely disappear from the trap. INTERNAL TEMPERATURE OF A LEVITATED NANODIAMOND Even

though the nanodiamonds that we use in our experiments contain NV− centres, most of them do not fluoresce upon levitation - consistent with the results of a previous study32 by Neukirch _et

al._ It has been shown that the resonant frequency of optically-detected magnetic resonance from the fluorescing levitated nanodiamonds can reveal the internal temperature32, but in this

article we instead use a Brownian motion based temperature determination technique developed by Millen _et al._ in ref. 33. According to this technique, the interaction between two thermal

baths - one consisting of the impinging gas molecules while the other is composed of the emerging gas molecules, is mediated by a levitated object whose internal temperature is higher than

that of the impinging gas molecules. The temperature of the impinging gas molecules is _T__imp_ while that of the emerging gas molecules is _T__em_. _T__CM_ can be expressed as , where

γ_imp_ and γ_em_ are the damping rates due to the impinging and emerging gas molecules, respectively33. Using this methodology and assuming a full accommodation (_T__i_ = _T__em_), in Fig. 3

we present _T__i_ obtained from the same nanodiamond used in Fig. 2 as a function of trapping power in air (blue circles) at 20 mB. In measuring _T__i_ we have assumed that a levitated

nanodiamond is at room temperature at ≈150 mB (see supplementary info Fig. S2). This assumption is also supported by the optically detected magnetic resonance based temperature measurements

performed on nanodiamonds by Hoang _et al._ using a similar setup to ours34. Also, since fitting uncertainties increase with the increasing pressure, _T__i_ has been plotted as a function of

trapping power at a constant pressure and it was measured during the 2_nd_ round of evacuation at which a levitated nanodiamond maintains its size. Constancy in size/mass is a requirement

of the PSD analysis. From Fig. 3 one can see that the internal temperature reaches ≈750 K at 380 mW of trapping power in air. This is well within the reported burning temperature of

amorphous carbon or diamond21,22,24. In Fig. 3 we have also included _T__i_s obtained from a levitated nanodiamond submerged in a nitrogen environment. In this case _T__i_ reaches

approximately 800 K at the maximum trapping power. At pressures below 20 mB, temperatures are expected to be higher given that the cooling due to gas molecules becomes less effective while

the absorption remains constant. It is noteworthy that the fluorescence from NV− centres in diamond decreases significantly at temperatures beyond 550 K and by 700 K it reduces to 20% of the

room temperature value13. Also, at _T__i_ = 700 K, NV− centre’s fluorescence lifetime and the contrast between electron spin resonances reduce below 20% of the room temperature value13. At

a temperature above 625 K, the spin coherence time of the NV− centre decreases as well13. Furthermore, the highest temperature that we have measured here, using trapping powers higher than

those have been used by Neukirch _et al._32, rules out the possibility of melting diamond as suggested in ref. 32. Diamond usually melts at temperatures ≥4000 K and requires pressure above

atmospheric pressure35. A slight difference between the temperatures at a constant power such as at 300 mW in Fig. 3 between different environments can be attributed to the variation in

surface qualities and the densities of impurities in different nanodiamonds24,36. Additionally, it has been demonstrated that bigger particles heat up rapidly compared to smaller particles

under the same experimental conditions33. As a result, variation in the internal temperatures is expected unless all the attributes of different particles are identical. However, due to the

inherent nature of levitated experiments, it is difficult to levitate particles with the same attributes in different runs of an experiment. This is further worsened by the polydispersity of

nanoparticles. For example, the average size of the nanodiamonds that we have used in our experiment is quoted to be 100 nm by the manufacturer. A representative scanning electron

microscope (SEM) image of this nanodiamond is shown in Fig. 4a. Nanodiamonds from a few tens of nanometers to a few hundred nanometers are visible. Consequently, trapping different sizes of

nanodiamonds in different runs of an experiment is possible. Nevertheless, to be consistent throughout the experiment, we levitate nanodiamonds of similar size by monitoring their scattering

intensities. Also, next we present a way of determining the size of an individual levitated object from the measured damping rate (γ_CM_) that it encounters while oscillating inside the

trap. For the purpose of following calculations, we assume that a levitated nanodiamond is of spherical shape. DETERMINATION OF THE SIZE OF A LEVITATED NANODIAMOND The effective damping rate

as shown in Fig. 1c can be expressed as γ_CM_ = γ_imp_ + γ_em_, where γ_imp_ and γ_em_ are the damping rates due to the impinging and emerging gas molecules, respectively33. γ_imp_ can be

written as while γ_em_ is related to γ_imp_ by , where _R_, _N_, _m_ and are the radius of a trapped particle, the number density of gas molecules at pressure _P_, molecular mass and the

mean thermal velocity of impinging gas molecules, respectively33. _N_ can further be expressed as _N_ = _N_0_P_/_P_0, where _N_0 is the number of gas molecules per cubic meter at atmospheric

conditions and _P_0 is the atmospheric pressure. On substitutions of various terms, one can express _R_ as where _M_ has been expressed as and ρ is the mass density of diamond. Given that

the levitated nanodiamonds burn, equation (3) gives the ultimate size of a nanodiamond for which we previously found temperatures. That is, it is the size of the nanodiamond after the first

round of evacuation. The actual size of a nanodiamond before burning can be found using scattering theory. The scattering intensity of a Rayleigh particle is given by , where and _I_ is the

intensity of the trapping light37. Provided that we know the scattering intensity (see Fig. 2b) at different pressures, we can find the actual size of a nanodiamond using equation (4): where

_R__p_ and are the radius and the scattering intensity of the particle at pressure _P_, respectively. As examples, using the model developed here, we estimate the sizes of the nanodiamonds

for which we have presented internal temperatures in Fig. 3. Using equations (3) and (4) and parameters _N_0 = 2.43 × 1025, _T__imp_ = 300 K, _T__em_ = 450 K, ρ = 3500 kg/_m_3, _m_ = 4.81 × 

10−26 kg, _P_ = 20 mB and γ_cm_ = 2.18 × 105 radian with the minimum trapping power of 180 mW, Fig. 4b shows the radius of the trapped nanodiamond at various pressures in air. It can be

observed that when the nanodiamond was initially trapped at atmospheric pressure, its diameter was ≈41 nm. Similarly, for the nitrogen case using the same parameters except γ_cm_ = 2.22 × 

105 radian and _T__i_ = 650 K, we get the ultimate diameter of the nanodiamond is ≈38 nm. Given the uncertainty in the shape of nanodiamonds as visible in Fig. 4a, the nanodiamonds that we

have used to find _T__i_s in air and nitrogen ambients are of similar size. This is also in good agreement with the technique (initial scattering intensities) that we have utilized to trap

similar size nanodiamonds in different runs of an experiment. Furthermore, even though the actual dimensions of a nanodiamond will be different from _R_ due to its asymmetric shape, the

estimated size provided by our model is well within the distribution visible in the SEM image (Fig. 4a). Lastly, we believe that the method developed here for the determination of size of an

individual particle can be used in any levitated experiment. CONCLUSIONS We have demonstrated that nanodiamonds burn in air while they graphitize in a nitrogen ambient by absorbing trapping

laser (1064 nm) light as the cooling due to gas molecules becomes less effective with decreasing pressure. We believe that amorphous carbon, a strongly absorbing material, present on the

surface of nanodiamonds is a key reason for this. We also think that purer nanodiamonds instead of the currently available HPHT synthesized nanodiamonds can be a cure to this problem. Our

Brownian motion based analysis has shown that the internal temperature of a levitated nanodiamond can reach up to 800 K. This rules out the possibility of melting diamond which requires35 a

temperature ≥4000 K. Lastly, exploiting the damping rate that a particle encounters while in motion, we have developed a new way of determining its size. We consider that this new technique

will be useful in present and future levitated experiments where the traditional electron microscopy and dynamic light scattering based size determinations are not suitable. METHODS

Nanodiamonds containing ≈500 NV− centres (ND-NV-100 nm) were bought from Adamas Nanotechnology Inc, USA. The average size of the nanodiamonds quoted by the manufacturer is 100 nm. To prevent

agglomeration we sonicate as received nanodiamonds for ≈10 minutes in an ultrasonic bath and then put them into a nebulizer and inject them into the trapping chamber. The trapping chamber

is continuously monitored by a CMOS camera (Thorlabs Inc). Once a nanodiamond is trapped, the trapping chamber is evacuated to study the behaviour of nanodiamonds in vacuum. Power spectral

density data were collected using a balanced photodiode (Thorlabs Inc) and a Picoscope oscilloscope (Pico Technology, UK). In the case of nanodiamonds immersed in nitrogen, the trapping

chamber was purged with nitrogen fifteen times. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Rahman, A. T. M. A. _et al._ Burning and graphitization of optically levitated nanodiamonds

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Wavelength 130–157 (Wiley-VCH Verlag GmbH, 2007). Download references ACKNOWLEDGEMENTS This work is supported by the U.K. Engineering and Physical Sciences Research Council through grants

EP/J014664/1 and EP/M003019/1 as well as EP/M013243/1 (the UK Quantum Technology Hub for Networked Quantum Information Technologies). G.W.M. is supported by the Royal Society. AUTHOR

INFORMATION AUTHORS AND AFFILIATIONS * Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT, UK A. T. M. A. Rahman, S. Bose & P. F. Barker * Department

of Physics, University of Warwick, Gibbet Hill Road, CV4 7AL, UK A. T. M. A. Rahman, A. C. Frangeskou & G. W. Morley * QOLS, Blackett Laboratory, Imperial College London, SW7 2BW, UK M.

S. Kim Authors * A. T. M. A. Rahman View author publications You can also search for this author inPubMed Google Scholar * A. C. Frangeskou View author publications You can also search for

this author inPubMed Google Scholar * M. S. Kim View author publications You can also search for this author inPubMed Google Scholar * S. Bose View author publications You can also search

for this author inPubMed Google Scholar * G. W. Morley View author publications You can also search for this author inPubMed Google Scholar * P. F. Barker View author publications You can

also search for this author inPubMed Google Scholar CONTRIBUTIONS P.F.B. and G.W.M. conceived the experiment while A.T.M.A.R. and A.C.F. built the experiment. A.T.M.A.R. collected the data.

P.F.B. and A.T.M.A.R. analysed the data. A.T.M.A.R. and G.W.M. wrote the manuscript. All authors, A.T.M.A.R., A.C.F., M.S.K., S.B., G.W.M. and P.F.B., discussed the results and commented on

the manuscript. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY INFORMATION RIGHTS AND

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Rahman, A., Frangeskou, A., Kim, M. _et al._ Burning and graphitization of optically levitated nanodiamonds in vacuum. _Sci Rep_ 6, 21633 (2016). https://doi.org/10.1038/srep21633 Download

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