Single-molecule force spectroscopy has emerged as a powerful tool to investigate the forces and motions associated with biological molecules and enzymatic activity. The most common force spectroscopy techniques are optical tweezers, magnetic tweezers and atomic force microscopy. Here we describe these techniques and illustrate them with examples highlighting current capabilities and limitations.

Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy

The fact that light carries both linear and angular momentum is well-known to physicists. One application of the linear momentum of light is for optical tweezers, in which the refraction of a laser beam through a particle provides a reaction force that draws the particle towards the centre of the beam. The angular momentum of light can also be transfered to particles, causing them to spin. In fact, the angular momentum of light has two components that act through different mechanisms on various types of particle. This Review covers the creation of such beams and how their unusual intensity, polarization and phase structure has been put to use in the field of optical manipulation.

Tweezers with a twist

Theoretical analysis suggests that there exists an optical attractive force capable of “pulling” microparticles towards a light source. This backwards force is generated by using interference to optimize the scattering of light in the forwards direction.

Optical pulling force

Microscale resonators cooled so that their vibrational motion approaches the quantum limit enable the study of quantum effects in macroscopic systems. An approach that could probe the interface between quantum mechanics and general relativity is now demonstrated by using lasers to suspend a glass microsphere in a vacuum. Cooling of micromechanical resonators towards the quantum mechanical ground state in their centre-of-mass motion has advanced rapidly in recent years1,2,3,4,5,6,7,8. This work is an important step towards the creation of ‘Schrodinger cats’, quantum superpositions of macroscopic observables, and the study of their destruction by decoherence. Here we report optical trapping of glass microspheres in vacuum with high oscillation frequencies, and cooling of the centre-of-mass motion from room temperature to a minimum temperature of about 1.5 mK. This new system eliminates the physical contact inherent to clamped cantilevers, and can allow ground-state cooling from room temperature9,10,11,12,13,14,15. More importantly, the optical trap can be switched off, allowing a microsphere to undergo free-fall in vacuum after cooling15. This is ideal for studying the gravitational state reduction16,17,18,19, a manifestation of the apparent conflict between general relativity and quantum mechanics16,20. A cooled optically trapped object in vacuum can also be used to search for non-Newtonian gravity forces at small scales21, measure the impact of a single air molecule14 and even produce Schrodinger cats of living organisms9.

/pdf/millikelvin-cooling-of-an-optically-trapped-microsphere-in-2zlaiibcdb.pdf

Millikelvin cooling of an optically trapped microsphere in vacuum

Holograms for sound waves, encoded in a 3D printed plate, are used to shape sound fields that can be used for the contactless manipulation of objects. Sound, especially ultrasound, can be used for contactless manipulation of objects in liquid and air, a phenomenon with applications in medical imaging, non-destructive testing and metrology. Usually, the desired sound field is shaped with arrays of transducers that must be carefully connected and controlled. Here Peer Fischer and colleagues describe a relatively simple technique for creating acoustic holograms and demonstrate their potential for use in matter manipulation. The acoustic holograms are encoded in a polymer plate by 3D printing and then used to shape a sound field that can be used for contactless manipulation of objects. The method can produce complex fields with reconstruction degrees of freedom two orders of magnitude greater than existing approaches. Because the holograms are inexpensive and fast to make, the method could be widely adopted to enable new applications with ultrasound manipulation. Holographic techniques are fundamental to applications such as volumetric displays1, high-density data storage and optical tweezers that require spatial control of intricate optical2 or acoustic fields3,4 within a three-dimensional volume. The basis of holography is spatial storage of the phase and/or amplitude profile of the desired wavefront5,6 in a manner that allows that wavefront to be reconstructed by interference when the hologram is illuminated with a suitable coherent source. Modern computer-generated holography7 skips the process of recording a hologram from a physical scene, and instead calculates the required phase profile before rendering it for reconstruction. In ultrasound applications, the phase profile is typically generated by discrete and independently driven ultrasound sources3,4,8,9,10,11,12; however, these can only be used in small numbers, which limits the complexity or degrees of freedom that can be attained in the wavefront. Here we introduce monolithic acoustic holograms, which can reconstruct diffraction-limited acoustic pressure fields and thus arbitrary ultrasound beams. We use rapid fabrication to craft the holograms and achieve reconstruction degrees of freedom two orders of magnitude higher than commercial phased array sources. The technique is inexpensive, appropriate for both transmission and reflection elements, and scales well to higher information content, larger aperture size and higher power. The complex three-dimensional pressure and phase distributions produced by these acoustic holograms allow us to demonstrate new approaches to controlled ultrasonic manipulation of solids in water, and of liquids and solids in air. We expect that acoustic holograms will enable new capabilities in beam-steering and the contactless transfer of power, improve medical imaging, and drive new applications of ultrasound.

Holograms for acoustics.

We use digital holographic microscopy and Mie scattering theory to simultaneously characterize and track individual colloidal particles. Each holographic snapshot provides enough information to measure a colloidal sphere's radius and refractive index to within 1%, and simultaneously to measure its three-dimensional position with nanometer in-plane precision and 10 nanometer axial resolution.

http://physics.nyu.edu/grierlab/index12c/index12c.pdf

Characterizing and tracking single colloidal particles with video holographic microscopy

We demonstrate both theoretically and experimentally that phase gradients in a light field can be used to create a new category of optical traps complementary to the more familiar intensity-gradient traps known as optical tweezers. We further show that the work done by phase-gradient forces is path dependent and briefly discuss some ramifications of this nonconservativity.

http://physics.nyu.edu/grierlab/phaseforce8b/phaseforce8b.pdf

Optical forces arising from phase gradients.

Optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction -limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. The solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light's propagation. Optical solenoid beams therefore act as true tractor beams that are capable of transporting material back toward their source.

http://physics.nyu.edu/grierlab/solenoid5c/solenoid5c.pdf

Optical solenoid beams

We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This nonequilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by nonconservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.

http://physics.nyu.edu/grierlab/fountain6c/fountain6c.pdf

Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-004816.pdf

Yohai Roichman

Papers

Characterizing and tracking single colloidal particles with video holographic microscopy

Optical forces arising from phase gradients.

Optical solenoid beams

Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability.

Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability