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Interferometry using injection-locked pump-noise-suppressed semiconductor lasers

Gunnar G. Bjork, Shuichiro Inoue, Y. Yamamoto

Published May 8, 1994• 0 citations
OpenAlex

Abstract

In a conventional interferometer one shines light only into one interferometer input port while the second input port is unexcited. This allows vacuum states to enter the unexcited port, leading to imperfect correlation between both the amplitude and the phase fluctuations of the light in the upper and lower interferometer arms. This, in turn, limits the interferometer sensitivity regardless of its operating panel (its arm-length difference, which we in the following will translate into a phase shift θ). The sensitivity of an ideal conventional interferometer is 1 / N. That is, a phase shift of 1 / N radians can be detected with a signal-to-noise ratio of unity by using N photons. Since N typically is a large number, it is tempting to try to find some scheme approaching the fundamental (Heisenberg) limit of phase-shift detection, 1/N. One way of doing that is to inject squeezed vacuum into the unexcited input port of the interferometer.1

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In a conventional interferometer one shines light only into one interferometer input port while the second input port is unexcited. This allows vacuum states to enter the unexcited port, leading to imperfect correlation between both the amplitude and the phase fluctuations of the light in the upper and lower interferometer arms. This, in turn, limits the interferometer sensitivity regardless of its operating panel (its arm-length difference, which we in the following will translate into a phase shift θ). The sensitivity of an ideal conventional interferometer is 1 / N. That is, a phase shift of 1 / N radians can be detected with a signal-to-noise ratio of unity by using N photons. Since N typically is a large number, it is tempting to try to find some scheme approaching the fundamental (Heisenberg) limit of phase-shift detection, 1/N. One way of doing that is to inject squeezed vacuum into the unexcited input port of the interferometer.1
Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).
We consider an interferometer powered by laser light (a coherent state) into one input port and ask the following question: what is the best state to inject into the second input port, given a constraint on the mean number of photons this state can carry, in order to optimize the interferometer's phase sensitivity? This question is the practical question for high-sensitivity interferometry. We answer the question by considering the quantum Cramér-Rao bound for such a setup. The answer is squeezed vacuum.
A potential application of squeezed-state light is to improve the sensitivity of high-precision interferometers whose performance is generally limited by photon shot noise or photon-counting statistics. Such interferometers include passive laser gyroscopes and the very sensitive interferometers being developed to detect cosmic gravitational waves. One usually operates a high-precision interferometer in a differential mode, so that noise from the (laser) light source is in principle irrelevant. Operation in a differential mode means that there is a second, normally unused input port. Vacuum noise entering this second port is responsible for the irreducible photon shot noise at the interferometer’s output. Injecting squeezed-state light into the normally unused input port can improve the sensitivity. I discuss the use of squeezed-state light in ring interferometers, delayline Michelson interferometers, and Fabry-Perot interferometers. Included in the discussion are real degrading effects, such as losses, inefficient photodetectors, and laser noise in the presence of nonideal fringe contrast. I explore the compatibility of the squeezed-state technique with other exotic techniques for improving sensitivity, such as Drever's idea for power recycling. Sensitivity estimates for various configurations and techniques are presented.
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25 , 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.
The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.