SU(1,1) interferometry
SU(1,1) interferometry is a technique that uses parametric amplification for splitting and mixing of electromagnetic waves for precise estimation of phase change and achieves the Heisenberg limit of sensitivity with fewer optical elements than conventional interferometric techniques.
Interferometry is an important technique in the field of optics that have been utilised for fundamental proof of principles experiments and in the development of new technologies.
This technique, primarily based on the interference of electromagnetic waves, has been widely explored in the field of quantum metrology and precision measurements for achieving sensitivity in measurements beyond what is possible with classical methods and resources.
Interferometry is a desired platform for precise estimation of physical quantities because of its ability to sense small phase changes.
One of the most prominent examples of the application of this property is the detection of gravitational waves (LIGO).
The estimation of the phase difference is done through the detection of the intensity change at the output after the interference at the second beam splitter.
These standard interferometric techniques, based on beam-splitters for the splitting of the beams and linear optical transformations, can be classified as SU(2) interferometers as these interferometric techniques can be naturally characterized by SU(2) (Special Unitary(2)) group.
is the mean number of particles (photons for electromagnetic waves) entering the input port of the interferometer.
The shot noise limit can be overcome by using light that utilizes quantum properties such as quantum entanglement (e.g. squeezed states, NOON states), at the unused input port.
with the change in the mean number of photons entering the input port.
The advantage that comes with the parametric amplifiers is that the input fields can be coherently split and interfere that would be fundamentally quantum in nature.
This is attributed to the nonlinear processes in parametric amplifiers such as four-wave mixing.
[2] To briefly understand the benefit of using a parametric amplifier, a balanced SU(1,1) interferometer can be considered.
The first feature indicates a high correlation of the output photon numbers (intensities) and the second feature shows that there is an enhancement of the signal strength for a small phase change as compared to SU(2) interferometers.
[5] that with no coherent state injection, the SU(1,1) interferometer approaches the Heisenberg limit of sensitivity.
Similar amplification could also be implemented in a SU(2) interferometer where both the signal and the noise (vacuum quantum fluctuations) gets amplified.
Overall, there is an amplification in the signal with no change in the noise (as compared to SU(2) interferometer).
The reduced sensitivity of an interferometer can be mainly due to two types of losses.
Theoretical studies by Marino et al.[5] inferred that an SU(1,1) interferometer is robust against losses due to inefficient detectors because of the disentanglement of states at the second parametric amplifier before the measurements.
The original scheme for an SU(1,1) interferometer proposed by Yurke et al.[2] did not take into account the internal losses and for a moderate gain of the parametric amplifier produced a low number of photons which made it difficult for its experimental realization.
Marino et al.[5] showed that in the presence of any internal losses, an SU(1,1) interferometer could not achieve the Heisenberg limit for configurations with no input fields at both the ports or a coherent state input in one of the ports (this configuration was considered for the Theory section above).
The originally proposed configuration of an SU(1,1) interferometer by Yurke et al. was challenging to realize experimentally due to very low photon numbers expected at the output (for ideal sensitivity) and also the theory did not take into account the internal losses that could affect the phase change sensitivity of the interferometer.
Subsequently, modifications to the scheme were studied taking into account the losses and other experimental imperfections.
The boost in the photon numbers from a coherent state injection was proposed and studied by Plick et al..[7] Such a scheme was experimentally implemented by Jing et al.[8] with Rb-85 vapor cells for parametric amplification.
The experiment verified the increase in the fringe size due to the amplification of the signal.
Later, experiments performed by Hudelist et al.[9] showed that there is an enhancement in the signal by a factor of
SU(1,1) interferometry with one parametric amplifier and a beam splitter replacing the second amplifier:[1] The signal to noise ratio improvement in this configuration was found to be essentially the same as that of the original SU(1,1) interferometry sensitivity improvement over conventional interferometers.
This study showed that the improvement is mainly due to the entangled fields generated at the first parametric amplifier.
“Truncated” SU(1,1) interferometer with no second parametric amplifier and rather using a photocurrent mixer to realize the superposition of the fields.
[10] Such a configuration opens the possibility to implement SU(1,1) interferometry in experiments where fewer optical elements help minimize the error due to experimental imperfections.
