Inertial imaging with nanomechanical systems

Abstract

Derivation of Eq. (2) in the main textPrecipitous downward shifts in the modal resonance frequencies of a nanomechanical device occur upon adsorption of individual analytes [1]. These measured frequency shifts can be used to calculate the mass, position, and molecular shape of individual analytes that adsorb upon a NEMS resonator -as described in the main text. Importantly, in the limit where the particle mass is much less than the device mass, the sequential measurement of multiple particles is unaffected by the mass loading due to previous particles.Previous analyses [1,2] have considered the analyte particles to be point masses. In this work, we model the individual particles as finite-sized objects with a spatial mass distribution that is initially unknown. We consider a general device of arbitrary composition that is loaded by an adsorbate with mass, m , which is much less than the device mass, M. We further assume that the particle size is small compared to the device dimensions (and the wavelengths of the vibrational modes) or, if not, that the particle is much more compliant than the device itself.Under such conditions, which are especially relevant for the case of soft biological molecules (of special interest to us), the vibrational mode shapes of the device are unaffected by the adsorbed analyte, and thus the strain energy of the device is also unchanged. It then follows that the maximum kinetic energy of the device, before and after mass loading, is invariant for the same oscillation amplitude, i.e.,

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“…Two applications with particular promise are force microscopy in geometries that transcend the constraints of conventional atomic force microscopy (AFM) [1][2][3] and on-chip mass spectrometry with single molecule sensitivity. [4][5][6] Another burgeoning nanotechnology is quantum nanosensors based upon the electron spin of the NV center in diamond. The NV center has been used to locate single elementary charges, 7 to perform thermometry within living cells 8 and to realize nanoscale MRI in ambient conditions.…”

“…Drawing upon the theory of NEMS inertial detection/ imaging, 6 to first order, a molecular adsorbate changes the frequency and displacement profile ( ) of the ℎ out-of-plane flexural vibrational mode of a nanobeam by…”

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A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields

“…The subsequent emergence of nanomechanical oscillators and evolutions in readout techniques [2][3][4] lead to impressive improvements in force sensitivity [5], enabling detection of collective spin dynamics [6][7][8], single electron spin [9], mass sensing of atoms [10,11] or inertial sensing [12]. Attractive perspectives arise too when nanoresonators are hybridized to single quantum systems, such as molecular magnets [13], spin or solid states qubits [14][15][16][17].…”

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“…The methodology presented in Ref. [15] involves a numerical algorithm to perform the required virtual mode re-engineering and iteratively determine the measurement zone (i.e., the spatial region of the device) over which the moments are to be 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 4 of 16 determined. Since this approach requires some computational analysis, it is desirable to simplify its underlying theoretical framework to enable its general use.…”