Figure 1

We use the Bloch sphere to represent the action of three pulses and the interspersed relative free evolution of the mixed states, as rotations around a horizontal and vertical axis. The coordinates $\{x,y,z\}$ identify the two-level system. The ground and the excited state correspond to $z=-1$ and $z=1$ on the sphere. Other points correspond to mixed states. Here and in the following illustrations we consider three equally spaced pulses.Reuse & Permissions

Figure 2

The internal evolution of a two state superposition is represented by a continuous rotation around the axis $z$ of the Bloch vector. Perfect splits make the system maximally sensitive to the strength of the rotation, thus enabling an accurate determination of it.Reuse & Permissions

Figure 3

This figure illustrates the importance of the central pulse and why the encoded phase is affected.Reuse & Permissions

Figure 4

Because of how they work, Mach-Zehnder interferometers are not sensitive to gravitational waves, whose period is much longer than the transit time of the matter or laser wave $(\mathrm{a})+(\mathrm{b})-({\mathrm{a}}^{\prime })-({\mathrm{b}}^{\prime })$ is measured by. The inherent cancellation does not affect Michelson interferometers that observe $(\mathrm{a})-({\mathrm{a}}^{\prime })$ in this picture. These two pictures represent the first and second part of the flight time of an atom or photon through the interferometer: an effect is only observable if there is a change of the gravitational-wave amplitude before the matter or light wave has completed its path.Reuse & Permissions

Figure 5

The phase difference between the two arms produces a phase that depends on the different trajectories of the split beams, both via geometry and relative velocity. The implications of the role of the origin of the reference system are discussed in the text.Reuse & Permissions

Figure 6

The elements of a rigid interferometer are bound to move along the same geodesic and interact with the propagating matter waves, at the times determined by their finite velocity.Reuse & Permissions