6.1 Controlled force experiments in optical tweezers

The control of force in optical tweezers is usually achieved by two different methods. The first one consists in setting up a feedback that corrects the position of the optical trap so that the position of the bead with respect to the center of the optical trap (and so the force) is always constant in average (see Fig. 3.14b). This method requires the use of analog or digital electronic feedbacks that always have a limited bandwidth. The bandwidth of a feedback is measured in Hertz and it indicates the maximum number of times the position of the trap can be corrected per unit of time. For instance, a force feedback of 100 Hz indicates that the position of the optical trap can be corrected 100 times per second. Ideally, the CF experiments should be done at infinite bandwidth.

The second method is called force-clamp and it was developed by Block and coworkers [149]. It consists in locating the bead in the region of the optical trap where it is about to escape. The bead undergoes a constant force in a local region with zero stiffness, which is an effective infinite bandwidth force feedback. The main disadvantage of this method is that the force is constant only on short ranges of extensions (about 100 nm). So the method is useful to exert forces on short DNA hairpins ($ < 100$ bp) but it is not possible to perform unzipping experiments of long DNA molecules because the opening of base pairs moves the bead away from the region of zero stiffness.

There is a third technique not developed yet that consists in forming a uniform gradient of laser light in a confined region where the bead would always undergo the same force. Apart from the TEM$ _{00}$, other laser modes such as Laguerre-Gaussian [72] or Bessel [150] have been used to trap particles. However, a practical laser beam with a uniform gradient of light intensity has never been produced.

The experiments described in the present chapter are performed with the first method, i.e., with a finite bandwidth force feedback.

JM Huguet 2014-02-12