Determining electromagnetic wave control for matter-wave interferometry

An apparatus comprising:

• a housing configured to provide a low-pressure environment;
• a gaseous cloud of ions, atoms, or molecules (IAMs) located in the housing and characterized by a first distribution of momentum states;
• a laser configured to emit one or more optical waves;
• a memory storing information associated with a set of control signals for controlling at least one of an intensity, frequency, phase, start time, or duration of the one or more optical waves emitted by the laser;
• one or more control modules configured to control at least one of the intensity, frequency, phase, start time, or duration of the one or more optical waves emitted by the laser based at least in part on the set of control signals;
• at least one photodetector configured to measure a measurement signal associated with a final distribution of momentum states of the IAMs;
• and
• a computing device comprising one or more processors in communication with the photodetector and configured to estimate an estimation parameter associated with the IAMs;
• where, during one or more active periods of time over which at least one of an amplitude, frequency, or phase of the one or more optical waves emitted by the laser are modified, the one or more optical waves overlap with and interact with the IAMs and
• transfer a first portion of the IAMs from the first distribution of momentum states to a second distribution of momentum states, and
• transfer a second portion of the IAMs from the second distribution of momentum states to a third distribution of momentum states;
• where the set of control signals are determined based at least in part on at least one of
• a constraint determined based at least in part on a set of optical wave parameters associated with the one or more optical waves, and a set of quantum state parameters that are associated with one or more quantum states of the IAMs, where two or more of the quantum state parameters do not satisfy the constraint, or
• a partial derivative of one or more quantum states associated with the IAMs, where the partial derivative is with respect to an optimization parameter determined based at least in part on the one or more optical waves or the estimation parameter.