For the past four years I have worked on research in Quantum Optics. Most of this time I have spent at NIST working with Dr. Alan Migdall. More recently I have begun working with Prof. Alexander Sergienko in Boston University's Quantum Imaging Laboratory .My research involves entangled photons whose special properties allow for a number of useful techniques and applications to be developed. The two applications I have been involved in developing are absolute radiance measurements of high temperature IR sources and measurements of polarization mode dispersion in anisotropic materials.
A laser incident on a birefringent crystal is intense enough so that non-linear effects lead to the spontaneous emission of pairs of photons. The conditions this process must obey are the conservation of energy and momentum, which is also known as phase-matching. The conservation of energy constraint requires the frequency (which is proportional to the energy) of the two output photons to equal that of the laser's input photon. The constraint from the conservation of momentum is more complicated because the velocity of the photons depends on the index of refraction within the crystal. Since the crystal is birefringent (it has a direction or multiple directions in which the indices of refraction are different), the angle at which the output photons exit the crystal will affect their velocity and in certain cases allow momentum to be conserved. It is these cases, in which the angles of the output photons allow their total momentum to equal the original momentum, that phase-matching occurs.
In fact, the two paired photons form a two-particle entangled state in which an observation of a property in one photon (energy, direction, polarization) determines the corresponding value in the paired photon. The polarization of the paired photon is either parallel (Type I) or perpendicular (Type II) to that of the detected photon. A video (Type II) shows how changing the indices of refraction by tilting a crystal affect the angles of output light (the output angles relationship to wavelength produce cones of light at a specific wavelength).
One application of entangled photons is measuring the absolute spectral radiance of a high temperature infrared source. Radiance is a measure of the power of emitted light divided by both the area and angular spread being measured. Conventionally, power is actually measured and the area and angular spread of the device are determined by separate measurements of the detector. However an absolute measurement of radiance itself (without reference to the detector) can be made using entangled photons.
The pairs of photons are produced because of a one-photon per mode background radiance that exists throughout space, including in a vacuum. An additional source of radiance can be added to stimulate further production of photons (also called down-conversion). By measuring the ratio of down-coverted photons with and without the additional source, the radiance of the source, rather than just its power, can be determined. The only setup-dependent part of this measurement is the percentage of the sources intial radiance that is eventually detected. Since the detector is the same for the measurements both with and without the source, its efficiency is not important because it affects both parts of the ratio and thus does not change the final result. It is only attenuation before the stimulation of down-covension that must be accounted for when computing the source's orginal radiance.
Another advantage this method has, particularly for long wavelengths, is that the photons detected do not even have to be at the wavelength being measured. If an IR source is being measured, the production of down-converted photons would be stimulated at both that wavelength and direction and at its pair's, which could be in the visible. This allows the radiance of an IR source to be detected using a more accurate visible detector. Experiments testing this method have shown that it is in good agreement with conventional methods and can achieve uncertainties comparable and even better than conventional methods, especially for long wavelengths (See publications).
Another application of entangled photons is measuring the relative delay of two photons of different polarization within a material. This delay is too small in many materials to measure electronically, so instead the quantum interference of two entagled photons can be measured. The experiment can be set up to produce two co-linear photons of opposite polarization that can then be sent through the sample and another birefringent material with known delay. The two photons can then be split through a beam splitter and recombined where the rate of coincidences can be measured. If the thickness of the material with known delay is changed, a scan of the rate of coincidences vs. delay can be made.
Depending on the experimental setup, different interference patterns are produced. The accuracy with which the position of this pattern can be found is dependent on the length of the crystal, spectral filters and laser wavelength used for downconversion as well as the strength of the signal (See publications). Experimentally it can be found with subfemtosecond precision. The method's accuracy with several materials is now be tested.