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arXiv:2103.02618 · AVS Quantum Science

Quantum frequency interferometry: With applications ranging from gravitational wave detection to dark matter searches

Richard Howl, Ivette Fuentes

Published Jan 23, 2023• 6 citations
arXivHTMLPDF

Abstract

We introduce a quantum interferometric scheme that uses states that are sharp in frequency and delocalized in position. The states are frequency modes of a quantum field that is trapped at all times in a finite volume potential, such as a small box potential. This allows for significant miniaturization of interferometric devices. Since the modes are in contact at all times, it is possible to estimate physical parameters of global multimode channels. As an example, we introduce a three-mode scheme and calculate precision bounds in the estimation of parameters of two-mode Gaussian channels. This scheme can be implemented in several systems, including superconducting circuits, cavity-QED, and cold atoms. We consider a concrete implementation using the ground state and two phononic modes of a trapped Bose–Einstein condensate. We apply this to show that frequency interferometry can improve the sensitivity of phononic gravitational waves detectors by several orders of magnitude, even in the case that squeezing is much smaller than assumed previously, and that the system suffers from short phononic lifetimes. Other applications range from magnetometry, gravimetry, and gradiometry to dark matter/energy searches.

DOI
10.1116/5.0084821

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We introduce a quantum interferometric scheme that uses states that are sharp in frequency and delocalized in position. The states are frequency modes of a quantum field that is trapped at all times in a finite volume potential, such as a small box potential. This allows for significant miniaturization of interferometric devices. Since the modes are in contact at all times, it is possible to estimate physical parameters of global multimode channels. As an example, we introduce a three-mode scheme and calculate precision bounds in the estimation of parameters of two-mode Gaussian channels. This scheme can be implemented in several systems, including superconducting circuits, cavity-QED, and cold atoms. We consider a concrete implementation using the ground state and two phononic modes of a trapped Bose–Einstein condensate. We apply this to show that frequency interferometry can improve the sensitivity of phononic gravitational waves detectors by several orders of magnitude, even in the case that squeezing is much smaller than assumed previously, and that the system suffers from short phononic lifetimes. Other applications range from magnetometry, gravimetry, and gradiometry to dark matter/energy searches.
Matter–wave interferometry is a powerful tool for high-precision measurements of the quantum properties of atoms, many-body phenomena and gravity. The most precise matter–wave interferometers exploit the excellent localization in momentum space and coherence of the degenerate gases. Further enhancement of the sensitivity and reduction of complexity are crucial conditions for the success and widening of their applications. Here we introduce a multi-state interferometric scheme that offers advances in both these aspects. The coherent coupling between Bose–Einstein condensates in different Zeeman states is used to generate high-harmonic output signals with an enhanced resolution and the maximum possible interferometric visibility. We demonstrate the realization of such an interferometer as a compact, easy to use, atom-chip device. This provides an alternative method for the measurement of the light–atom and surface–atom interactions and enables the application of multi-parameter sensing schemes in cold-atom interferometry.
Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard technique, the production of squeezed states of the collective excitations in gases of ultracold atoms, the phonons of a Bose-Einstein condensate (BEC), is a comparably recent problem. This task is continuously gaining relevance with a growing number of proposals for BEC-based quantum metrological devices and the possibility to apply them in the detection of gravitational waves. The objective of this thesis is to find whether the recently described effect of an oscillating external potential on a uniform BEC can be exploited to generate two-mode squeezed phonon states, given present day technology. This question brings together elements of a range of fields beyond cold atoms, such as general relativity and Efimov physics. To answer it, the full transformation caused by the oscillating potential on an initially thermal phononic state is considered, allowing to find an upper bound for the magnitude of this perturbation as well as to quantify the quality of the final state with respect to its use in metrology. These findings are then applied to existing experiments to judge the feasibility of the squeezing scheme and while the results indicate that they are not well suited for it, a setup is proposed that allows for its efficient implementation and seems within experimental reach. In view of the vast parameter space leaving room for optimization, the considered mechanism could find applications not only in the gravitational wave detector that originally motivated this work, but more generally in the field of quantum metrology based on ultracold atoms.
Interferometry is a powerful method for studying many fundamental phenomena ranging from gravitational waves to anyon excitations. Besides loss of coherence in the interferometer paths, quantum mechanics sets an incompressible bound for linear interferometry arising from the quantum noise of the light beam, called the shot noise limit. Here, we implement a non-linear quantum interferometer that uses a microwave cavity and a magnetic field resilient anharmonic superconducting quantum circuit made of granular aluminum. The circuit enables interferometry beyond the shot noise limit. A direct application of our findings is the detection of dark matter (axions or dark photons), high-frequency gravitational waves or astronomical masers.
Gravitational-wave astronomy promises a radically new method of investigating the universe, one that does not detect elementary particles, but rather ripples in space-time itself. One might expect that with this radically new method, our understanding of the universe will make an equally giant leap. One of the most promising methods for the eventual detection of gravitational-waves is that of interferometric gravitational-wave detection. The sensitivity of these devices is nothing short of amazing, and their sensitivity continues to improve. The next generation of detectors are expected reach a point where increasing the laser power, previously used to increase the sensitivity, is no longer expected to provide any benefit. One of the most promising options for further increasing the sensitivity, through reduction of the quantum noise, is via the application of "squeezed states of light". Squeezed states of light are light fields for which the noise of some observable has been reduced below the quantum noise limit. These states have been shown for many years to offer increased sensitivity in interferometers and recently in interferometric gravitational-wave detectors. One of the most challenging tasks to make suitable squeezed light sources for these detectors is to produce low-frequency squeezing, corresponding to the detection band of these interferometers. This thesis details the doubly resonant travelling wave bow-tie squeezer as a source of squeezing for interferometric gravitational-wave detection. This squeezer achieves record results of squeezing in the gravitational-wave detection band. For the first time, 10 dB of shot noise suppression at 10Hz is directly observed and above 200Hz, 11.6 dB is observed. The work presented in this thesis provides evidence that further substantiates previous progress indicating that squeezed states of light are now ready for full-time integration into interferometric gravitational-wave detectors. The new cavity design, described in detail throughout this thesis, is shown to outperform previous designs and provide benefits when integrating squeezing into these detectors, in particular, isolation to backscattered light from the interferometer. The noise sources that typically lead to degradation in squeezing measurements are investigated and discussed. Additionally, a modification to the standard locking technique used to control these vacuum squeezed states, coherent locking, is presented and discussed. The modified technique reduces the required number of locking loops and provides a larger beat note from which to derive an error signal for one of the remaining loops. A squeezer using these design philosophies is then constructed and used to inject squeezing into the LIGO gravitational-wave detector. Injection of the squeezed state provides enhancement of the sensitivity of the detector at frequencies around 200Hz and above. The sensitivity seen was equivalent to approximately 2 dB of shot noise reduction. The enhancement is limited by the loss within the interferometer. Injection of the squeezed state did not show any degradation in the sensitivity of the device below 200Hz, indicating for the first time that noise couplings between the interferometer and the squeezer could be sufficiently suppressed at these frequencies even for the most sensitive detectors.
Atom interferometry is a quantum sensor technology that uses ultra-cold atoms placed in entangled quantum states to detect minute changes in local fields arising from gravitational waves and ultra-light dark matter. Their extreme sensitivity to accelerations has been demonstrated for measurements of Newton’s gravitation constant, tests of the Equivalence Principle, and measurement of local gravity gradients. The search for ultra-light dark matter and measurements of gravitational waves requires interferometer baselines greater than approximately 100 m. In understanding the fundamental systematics and backgrounds of these detectors, we have discovered that atmospheric and seismic effects, even though physically decoupled from the atoms which are in vacuum and free-fall, are still detectable by the quantum phase of the atoms. From a different perspective these “noise” sources are also interesting signals that we may be able to understand better with these sensor platforms leading to cross-disciplinary studies in Earth sciences.