Ramsey interferometry

[3] 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.

[4][5] A main goal of precision spectroscopy of a two-level atom is to measure the absorption frequency

One way to accomplish this measurement is to apply an external oscillating electromagnetic field at frequency

This probability can be maximized when Δ = 0, when the driving field is in resonance with the transition frequency of the atom.

[3] A simplified version of the Rabi method consists of a beam of atoms, all having the same speed

is applied perpendicular to the excitation direction, and this will lead to Rabi oscillations between |↓⟩ and |↑⟩ at a frequency of

infinitely and expect ever increasing precision, as was the case in the perfect, simple Rabi model.

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.

[2] The primary improvement from the Ramsey method is because the main peak resonance frequency represents an average over the frequencies (and inhomogeneities) in the non-interaction region between the cavities, whereas with the Rabi method the inhomogeneities in the interaction region lead to line broadening.

on the Bloch sphere regardless of whether or not they all were excited to exactly the same resonance frequency, the Ramsey fringes will look very similar to those discussed above.

What results are Ramsey fringes in an envelope in the shape of the Rabi method probability for atoms of one velocity.

of the non-interaction zone, the line width can be substantially improved, by a factor of 10 or more, over that of other methods.

The oscillator is the parallel external electromagnetic field in the non-interaction zone of the Ramsey–Bordé interferometer.

By measuring the transition rate from the excited to the ground state, one can tune the oscillator so that

[2] Serge Haroche won the 2012 Nobel Prize in physics (with David J. Wineland[7]) for work involving cavity quantum electrodynamics (QED) in which the research group used microwave-frequency photons to verify the quantum description of electromagnetic fields.

, then there is a single mode of the electromagnetic field within the cavity that will subsequently affect the measurement outcome of the second atom.

[4] The problem that Bordé et al.[5] were trying to solve in 1984 was the averaging-out of Ramsey fringes of atoms whose transition frequencies were in the optical range.

When this was the case, first-order Doppler shifts caused the Ramsey fringes to vanish because of the introduced spread in frequencies.

The first population consists of atoms whose Doppler-induced de-phasing has cancelled, resulting in the familiar Ramsey fringes.

The second consists of atoms whose Doppler-induced de-phasing has doubled and whose Ramsey fringes have completely disappeared (this is known as the "backward-stimulated photon echo", and its signal goes to zero after integrating over all velocities).

The interaction geometry of two pairs of counter-propagating waves that Bordé et al. introduced allows improved resolution of spectroscopy of frequencies in the optical range, such as those of Ca and I2.

This superposition is due to the energy and momentum exchanged between the laser and the atom in the interaction zones during the absorption/emission processes.

Looking at the probability to transition to |b⟩ after the atom has passed through the fourth interaction zone, one would find dependence on the detuning in the form of Ramsey fringes, but due to the difference in two quantum mechanical paths.

The atom-wave interferometer formed by either of these two paths leads to a phase difference that is dependent on both internal and external parameters, i.e. it is dependent on the physical distances by which the interaction zones are separated and on the internal state of the atom, as well as external applied fields.

Another way to think about these interferometers in the traditional sense is that for each path there are two arms, each of which is denoted by the atomic state.

If an external field is applied to either rotate or accelerate the atoms, there will be a phase shift due to the induced de Broglie phase in each arm of the interferometer, and this will translate to a shift in the Ramsey fringes.

In other words, the external field will change the momentum states, which will lead to a shift in the fringe pattern, which can be detected.

A similar effect can be calculated for the shift in the Ramsey fringes caused by the acceleration of gravity.

The Ramsey–Bordé interferometer provides the potential for improved frequency measurements in the presence of external fields or rotations.