Ramsey interferometry, also known as the separated oscillating fields method, is a form of particle interferometry that uses the phenomenon of magnetic resonance to measure transition frequencies of particles. It was developed in 1949 by Norman Ramsey, who built upon the ideas of his mentor, Isidor Isaac Rabi, who initially developed a technique for measuring particle transition frequencies. Ramsey's method is used today in atomic clocks and in the S.I. definition of the second. Most precision atomic measurements, such as modern atom interferometers and quantum logic gates, have a Ramsey-type configuration. A more modern method, known as Ramsey–Bordé interferometry uses a Ramsey configuration and was developed by French physicist Christian Bordé and is known as the Ramsey–Bordé interferometer. Bordé's main idea was to use atomic recoil to create a beam splitter of different geometries for an atom-wave. The Ramsey–Bordé interferometer specifically uses two pairs of counter-propagating interaction waves, and another method named the "photon-echo" uses two co-propagating pairs of interaction waves.
Introduction
A main goal of precision spectroscopy of a two-level atom is to measure the absorption frequency between the ground state and excited state of the atom. One way to accomplish this measurement is to apply an external oscillating electromagnetic field at frequency and then find the difference (also known as the detuning) between and by measuring the probability to transfer to . This probability can be maximized when , when the driving field is on resonance with the transition frequency of the atom. Looking at this probability of transition as a function of the detuning , the narrower the peak around the more precision there is. If the peak were very broad about then it would be difficult to distinguish precisely where is located due to many values of having close to the same probability.
Physical principles
The Rabi method
A simplified version of the Rabi method consists of a beam of atoms, all having the same speed and the same direction, sent through one interaction zone of length . The atoms are two-level atoms with a transition energy of (this is defined by applying a field in an excitation direction , and thus , the Larmor frequency), and with an interaction time of in the interaction zone. In the interaction zone, a monochromatic oscillating magnetic field labeled is applied perpendicular to the excitation direction, and this will lead to Rabi oscillations between and at a frequency of .
The Hamiltonian in the rotating frame (including the rotating wave approximation) is:
The probability of transition from and can be found from this Hamiltonian and is
This probability will be at its maximum when . The line width of this vs. determines the precision of the measurement. Because , by increasing , or , and correspondingly decreasing so that their product is , the precision of the measurement increases; i.e. the peak of the graph becomes narrower.
In reality, however, inhomogeneities such as the atoms having a distribution of velocities or there being an inhomogeneous will cause the line shape to broaden and lead to decreased precision. Having a distribution of velocities means having a distribution of interaction times, and therefore there would be many angles through which state vectors would flip on the Bloch sphere. There would be an optimal length in the Rabi setup that would give the greatest precision, but it would not be possible to increase the length ad infinitum and expect ever increasing precision, as was the case in the perfect, simple Rabi model.
The Ramsey method
Ramsey improved upon Rabi's method by splitting the one interaction zone into two very short interaction zones, each applying a pulse. The two interaction zones are separated by a much longer non-interaction zone. By making the two interaction zones very short, the atoms spend a much shorter time in the presence of the external electromagnetic fields than they would in the Rabi model. This is advantageous because the longer the atoms are in the interaction zone, the more inhomogeneities (such as an inhomogeneous field) lead to reduced precision in determining . The non-interaction zone in Ramsey's model can be made much longer than the one interaction zone in Rabi's method because there is no perpendicular field being applied in the non-interaction zone (although there is still