Quantum Limited Particle Sensing in Optical Tweezers

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The application of the radiation pressure force for the trapping of atoms and neutral particles was pioneered by Arthur Ashkin cite{ashkin70s}. This was followed by a plethora of seminal experiments utilizing the radiation pressure force cite{ashkin80}, for example in the displacement and levitation in air and water of micron-sized particles cite{ashkin-levitate}, and together with Steve Chu, for the development of a stable three-dimensional atom cooling and trapping experiment using frequency-detuned counter-propagating laser beams cite{chu-MOT}. In particular, the demonstration of {it optical tweezers} cite{ashkin-tweezer}, based largely on the transverse gradient force of a single focused Gaussian optical beam was a significant contribution to optical trapping in biology cite{ashkin-tweezera}.

In biological systems, optical tweezers were first used to trap and manipulate viruses and bacteria cite{bacteria}. This was followed by a burgeoning number of experiments using optical tweezers for measurements of DNA/RNA stretching and unfolding cite{gore, bustamante, bustamantea, bryant-dna, smith}, intracellular probing, manipulation of gamete cells, trapping of vesicles, membranes and colloids cite{langblock, neuman} and DNA sequencing using RNA polymerase cite{greenleaf}. In particular, for the first time, quantitative biophysical studies of the kinetics of molecular motors cite{bustamante-motor} (e.g. myosin cite{myosin} and kinesin cite{kinesin}) at the single molecule level was made possible with the use of optical tweezers. Coupled with conventional position sensitive detectors (i.e. using quadrant photodetectors cite{langblock, gittes, pralle}), the position of, and force on, a bead tethered to a molecular mot...

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...s of a single-base pair scale (e.g. 3.4~AA~on dsDNA) cite{moffitt} and the bacterial DNA translocase FtsK moves at speeds of 5 kilobases per second cite{pease}. Therefore, enhanced particle sensing could elucidate these finer features with greater sensitivity than conventional particle sensing techniques in optical tweezers systems.

This paper begins by formalizing an optimal parameter estimation procedure for particle sensing based on the analysis of the spatial properties of the field scattered by a particle in an optical tweezers. We show that split detection is non-optimal and consequently propose an optimal measurement scheme based on spatial homodyne detection. The efficacy of particle sensing is evaluated using the signal-to-noise ratio (SNR) and sensitivity measures; and the efficacy of spatial homodyne detection and split detection systems are compared.