We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise, a squeezed vacuum is injected into the usually unused input port. It is investigated under which conditions the gravitational wave signal may be amplified without increasing counting noise concurrently. Such a possibility was suggested as a consequence of the entanglement of the two output ports of a beam splitter. We find that amplification without concurrent increase of noise is not possible for reasonable squeezing parameters. Photon distributions for various beam splitter angles and squeezing parameters are calculated.
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise, a squeezed vacuum is injected into the usually unused input port. It is investigated under which conditions the gravitational wave signal may be amplified without increasing counting noise concurrently. Such a possibility was suggested as a consequence of the entanglement of the two output ports of a beam splitter. We find that amplification without concurrent increase of noise is not possible for reasonable squeezing parameters. Photon distributions for various beam splitter angles and squeezing parameters are calculated.
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.
The sensitivity of future gravitational wave interferometers is expected to be limited throughout the detection band by quantum vacuum fluctuations, which can be reduced by applying quantum optics techniques such as squeezed vacuum injection. However, decoherence caused by optical losses in the readout chain will severely limit the effectiveness of such schemes. It was proposed that effect of losses in the final stage of detection can be mitigated by a phase-sensitive amplifier placed in between the output port of the interferometer and the photodetector. In this paper we propose to implement such amplification using an optomechanical device, study some of its practical limitations, and discuss its applicability to next-generation gravitational-wave detectors.
Current gravitational wave detectors, such as LIGO, Virgo and KAGRA, are laser interferometers. This technique consists of injecting a laser beam through an input port, which is then separated into two arms several kilometers long by a semi-reflecting mirror. At the end of each arm, a mirror reflects the beam back to the semi-reflecting mirror. The two beams then interfere and the power of the resulting beam, measured at the detection port, contains information about the relative length of the two arms. When a gravitational wave passes through the detector, this relative length varies in time. Several noise sources degrade the quality of the recorded signal, which affects the number of gravitational waves that can be observed. Currently, this sensitivity is limited at high-frequency by the quantum noise.An electromagnetic wave described by quantum mechanics has a classical amplitude and quantum fluctuations in amplitude and phase. A state with a null classical amplitude is called a vacuum state, but still has these quantum fluctuations. Thus, in the detector, although no light beam is introduced through the detection port, the vacuum state is present. It is then the quantum fluctuations of this vacuum state that are responsible for the quantum noise of the interferometer. In particular, the phase and amplitude fluctuations are respectively responsible for the quantum noise at high and low frequencies; the separation between these two regions occurs at about 100 Hz.The work presented in this thesis focuses on the injection of squeezed vacuum states into the Virgo detector via the detection port in order to lower the quantum noise. These states are characterized by the fact that their phase (amplitude) fluctuations are reduced, which allows reducing the quantum noise at high (low) frequency. As the Virgo detector is currently limited only by high-frequency quantum noise, only phase squeezed vacuum states were used during the last observation period O3. It was first necessary to ensure that these squeezed vacuum states had the proper geometric and phase parameters with respect to the interferometer beam such that they were not degraded. Control loops allowed these parameters to be maintained at their nominal values during O3, a year long period. The decrease in high-frequency quantum noise, but also the increase in low-frequency quantum noise, have been measured for the first time with the Virgo detector. These observations were in agreement with the measurements of the losses that affect the squeezed vacuum states.From O4 , quantum noise will also be limiting at low frequency. It will then be possible to use squeezed vacuum states having their amplitude fluctuations reduced at low frequency and their phase fluctuations reduced at high frequency. Thus, the total quantum noise can be reduced. Such states can be generated using an optical cavity called a filter cavity. The second part of the work presented in this thesis consisted in defining the optical parameters of the filter cavity that will be installed on Virgo for O4. To do this, it was first necessary to study the sources of degradation of the squeezed states of the vacuum. This then allowed defining the length of the filtering cavity and the set of parameters of the mirrors that compose it. Finally, the implementation of this filter cavity within the Virgo infrastructure was studied. This has shown that the use of compressed states will effectively reduce quantum noise over the entire sensitivity spectrum of Virgo.
Current gravitational wave detectors, such as LIGO, Virgo and KAGRA, are laser interferometers. This technique consists of injecting a laser beam through an input port, which is then separated into two arms several kilometers long by a semi-reflecting mirror. At the end of each arm, a mirror reflects thebeam back to the semi-reflecting mirror. The two beams then interfere and the power of the resulting beam, measured at the detection port, contains information about the relative length of the two arms. When a gravitational wave passes through the detector, this relative length varies in time. Several noise sources degrade the quality of the recorded signal, which affects the number of gravitational waves that can be observed. Currently, this sensitivity is limited at high-frequency by the quantum noise.An electromagnetic wave described by quantum mechanics has a classical amplitude and quantum fluctuations in amplitude and phase. A state with a null classical amplitude is called a vacuum state, but still has these quantum fluctuations. Thus, in the detector, although no light beam is introduced through the detection port, the vacuum state is present. It is then the quantum fluctuations of this vacuum state that are responsible for the quantum noise of the interferometer. In particular, the phase and amplitude fluctuations are respectively responsible for the quantum noise at high and low frequencies; the separation between these two regions occurs at about 100 Hz.The work presented in this thesis focuses on the injection of squeezed vacuum states into the Virgo detector via the detection port in order to lower the quantum noise. These states are characterized by the fact that their phase (amplitude) fluctuations are reduced, which allows reducing the quantum noise at high (low) frequency. As the Virgo detector is currently limited only by high-frequency quantum noise, only phase squeezed vacuum states were used during the last observation period O3. It was first necessary to ensure that these squeezed vacuum states had the proper geometric and phase parameters with respect to the interferometer beam such that they were not degraded. Control loops allowed these parameters to be maintained at their nominal values during O3, a year long period. The decrease in high-frequency quantum noise, but also the increase in low-frequency quantum noise, have been measured for the first time with the Virgo detector. These observations were in agreement with the measurements of the losses that affect the squeezed vacuum states.From O4 , quantum noise will also be limiting at low frequency. It will then be possible to use squeezed vacuum states having their amplitude fluctuations reduced at low frequency and their phase fluctuations reduced at high frequency. Thus, the total quantum noise can be reduced. Such states can be generated using an optical cavity called a filter cavity. The second part of the work presented in this thesis consisted in defining the optical parameters of the filter cavity that will be installed on Virgo for O4. To do this, it was first necessary to study the sources of degradation of the squeezed states of the vacuum. This then allowed defining the length of the filtering cavity and the set of parameters of the mirrors that compose it. Finally, the implementation of this filter cavity within the Virgo infrastructure was studied. This has shown that the use of compressed states will effectively reduce quantum noise over the entire sensitivity spectrum of Virgo.
It is shown in the present Letter that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer. The experimental details of such physical system have been described in a recent article by Barak and Ben-Aryeh (JOSA-B, 25, 361(2008)). In another very recent article by Voronov and Weyrauch (Phys. Rev.A 81, 053816 (2010)) they have followed our methods for treating the same physical system, and have pointed out an error in the sign of one of our expressions thus claiming for the elimination of our physical results. I show here a method by which the expectation value for the photon number operator is increased and at the same time the standard deviation is reduced. Although due to the mistake in sign in our expression the physical method for obtaining such result is different from our original study [1], the main physical effect can remain .
We analyze in detail a system of two interferometers aimed at the detection of extremely faint phase fluctuations. The idea behind is that a correlated phase-signal like the one predicted by some phenomenological theory of Quantum Gravity (QG) could emerge by correlating the output ports of the interferometers, even when in the single interferometer it confounds with the background. We demonstrated that injecting quantum light in the free ports of the interferometers can reduce the photon noise of the system beyond the shot-noise, enhancing the resolution in the phase-correlation estimation. Our results confirm the benefit of using squeezed beams together with strong coherent beams in interferometry, even in this correlated case. On the other hand, our results concerning the possible use of photon number entanglement in twin beam state pave the way to interesting and probably unexplored areas of application of bipartite entanglement and, in particular, the possibility of reaching surprising uncertainty reduction exploiting new interferometric configurations, as in the case of the system described here.