A recurrence tracking microscope (RTM) is a

microscope A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...

that is based on the quantum recurrence phenomenon of an atomic wave packet. It is used to investigate the nano-structure on a surface.

History

In 2006, Farhan Saif used quantum recurrence phenomena of wave packet as a probe to study nano-structures on a surface, naming it Recurrence Tracking Microscope (RTM).

Background

The tunneling phenomenon is used as a probe to study nano-structure on a surface with the help of

scanning tunneling microscope A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. ...

(STM). The STM is a powerful device for viewing surfaces at the atomic level. The STM can be used not only in an ultra-high vacuum, but also in air and a variety of other media and at temperatures ranging from nearly zero to hundreds of

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...

. This idea was enhanced to create the

atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the diffr ...

(AFM),V. J. Morris, A. R. Kirby, A. P. Gunning, Atomic Force Microscopy for Biologists(Imperial College Press, 1999). which is a very high-resolution type of

scanning probe microscope Scan may refer to: Acronyms * Schedules for Clinical Assessment in Neuropsychiatry (SCAN), a psychiatric diagnostic tool developed by WHO * Shared Check Authorization Network (SCAN), a database of bad check writers and collection agency for bad ...

with resolution of fractions of a nanometer. The AFM is one of the foremost tools for imaging, measuring and manipulating matter at the nanoscale. The application of RTM includes the visualization and measurement of surface features having sizes and dimensions as small as one nanometer in research and development laboratories as well as a process to control environment.

Design

The RTM consist of a magneto-optic trap (MOT) where super cold atoms are trapped inside; b) a

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...

surface above which the evanescent wave mirror is obtained by the

total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...

of a monochromatic laser from the dielectric film; and c) a

cantilever A cantilever is a rigid structural element that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a canti ...

attached to the dielectric film with its other end above the surface under investigation. The experimental setup of RTM contains trapped atoms that move towards the atomic mirror under the influence of gravitational force. The mirror is made up of an evanescent wave field, which varies exponentially as a function of distance from the surface. Hence, the atoms experience a bounded motion in the presence of the optical potential and the gravitational potential together. The dynamics of an atom above the atomic mirror is controlled by the effective Hamiltonian,

H=+mgz+V_0 e^\quad (1)

where

p

represents the center of mass momentum,

m

is mass of the atom and

g

is the constant gravitational acceleration. The atomic wave packet evolves classically for a short period of time and reappears after a classical period. However, after a few classical periods it spreads all over the available space following

wave mechanics Wave mechanics may refer to: * the mechanics of waves * the ''wave equation'' in quantum physics, see Schrödinger equation See also * Quantum mechanics * Wave equation The (two-way) wave equation is a second-order linear partial different ...

and collapses. Due to quantum dynamics it rebuilds itself after a certain period of time. This process is called the quantum revival of the atomic wave packet and the time at which it reappears after its collapse is called quantum revival time. The quantum revival time for the atom in RTM is calculated by finding the wave function for the Hamiltonian, given in Equation 1.

Static mode

In order to investigate a surface having arbitrary structure, the RTM is used in static mode. That is, the atom falls on the static atomic mirror without moving the surface under investigation. Its evolution over the atomic mirror requires a certain position of the cantilever. The atom displays quantum revivals at multiple revival times. As the surface under study slightly moves, the position of the cantilever changes in the presence of the surface structure. Hence the initial distance between the atomic mirror and the bouncing atom over it changes. This change leads to a creation of initial energy for the atom and thus a different revival time. For each new revival time, the corresponding energy is calculated. This process leads to the knowledge of the structure on the surface and the surface height varies up to one nanometer.

Comparison

RTM advantages over STM and AFM include: a) the surfaces of all kinds of materials ranging from conductors to insulators can be probed; b) surfaces made of impurities can be studied without observing them, as happened in STM; and c) in dynamical operational mode, RTM provide information about a surface with periodic structures in the simplest manner.

References

{{reflist Microscopes Scientific techniques