Detecting continuous gravitational waves with superfluid⁴He

Abstract

Direct detection of gravitational waves is opening a new window onto our universe. Here, we study the sensitivity to continuous-wave strain fields of a kg-scale optomechanical system formed by the acoustic motion of superfluid helium-4 parametrically coupled to a superconducting microwave cavity. This narrowband detection scheme can operate at very high Q-factors, while the resonant frequency is tunable through pressurization of the helium in the 0.1-1.5 kHz range. The detector can therefore be tuned to a variety of astrophysical sources and can remain sensitive to a particular source over a long period of time. For thermal noise limited sensitivity, we find that strain fields on the order of~h 10 Hz 23 are detectable. Measuring such strains is possible by implementing state of the art microwave transducer technology. We show that the proposed system can compete with interferometric detectors and potentially surpass the gravitational strain limits set by them for certain pulsar sources within a few months of integration time.He 8 for superfluid 4 He, which appears to be limited by a combination of 3 He impurities, sample temperature, and radiation loss. All of these dissipation mechanisms can be reduced and we assume quality factors of 10 11 are possible in future experiments with isotropically pure samples at lower temperatures of around 10 mK.The power spectrum of GWs is expected to be extremely broad and is estimated to range from 10 −16 to 10 3 Hz [7-9] for known sources. Ground-based optical interferometers (such as LIGO, Virgo, GEO, TAMA) allow OPEN ACCESS RECEIVED for broad-band search for GWs in the frequency range 10 Hz-5 kHz. These detectors are expected to be predominantly sensitive to the chirped, transient, GW impulse resulting from the last moments of coalescing binaries involving compact objects (BHs and/or NSs) [10]. Space-based interferometric detectors can be sensitive to lower frequency GWs, as they are not limited by seismic noise [11].Unlike broadband impulse sources, rapidly rotating compact objects such as pulsars are expected to generate highly coherent, continuous GW signals due to the off-axis rotating mass, with frequencies spanning from ∼1 kHz for millisecond pulsars (MSPs) in binaries, to 1 Hz for very old pulsars [7,[12][13][14][15]. Given the unknown mass distribution of the pulsar, one can only estimate the strain field here at earth. Several mechanisms give upper bounds to the strength of GWs on earth. One such limit is the 'spin down limit', which is given by the observed spin-down rate of the pulsar, and the assumption that all of the rotational kinetic energy which is lost is in the form of GWs [16]. Another limit is given by the yield strength of the material which makes up the NS, and how much strain the crust can sustain before breaking apart due to centripetal forces [17,18]. The presence of strong magnetic fields indicate a potential mechanism for producing and sustaining such strains due to deformation of the NS [19,20]. However, without knowing the strength and direction...

Frequency spectrum of an optical resonator in a curved spacetime

“…For example, the frequency spectrum of a resonator depends on its dimensions and hence knowledge of the precise values of these dimensions is of utmost importance. Cases in which the effects of gravitational fields and acceleration must be considered include those in which the gravitational field is to be measured, such as in proposals for the measurement of gravitational waves with electromagnetic cavity resonators [1][2][3][4][5][6][7] or other extended matter systems [8][9][10][11][12][13][14], tests of GR [15,16] or the expansion of the universe [17,18]. Other situations are those in which the metrological system is significantly accelerated [19][20][21].…”

Testing small scale gravitational wave detectors with dynamical mass distributions

“…We found that the effect of a gravitational wave on a small scale gravitational wave detector of any type mentioned in the introduction can be mimicked by a system of 10 oscillating spheres or a system of 8 oscillating cylinders. In principle, strains can be mimicked that are several orders larger than the sensitivities claimed by some of the proposals [8,10]. Additionally, the orientation of the polarization plane of the mimicked gravitational waves is known and the local detectors can be oriented so that their signal is maximized.…”

“…The dimensions of this detector would be about 50 cm. Therefore, L can be of the order of meters and strains could be mimicked that are up to 3 orders of magnitude larger than the expected sensitivity of the Gen1 detector in [10]. Therefore, the mimicked strains could be used as a tool to experimentally test the proposed detector designs.…”

“…Among such proposals are some that consider detectors on scales between meters and micrometers, we shall refer to these as small scale detectors. Proposed systems range from electromagnetic cavity resonators [2][3][4][5] and resonant mass detectors [6,7] over Bose-Einstein condensates [8,9] to a microwave cavity resonator coupled to a superfluid helium container [10,11]. Some proposals for small scale detectors are based on quantum technologies, for example the one presented in [8,9].…”

Cavity optomechanics in a levitated helium drop

“…In this case only the mechanical degree of freedom is provided by the fluid, for example, as a density wave or surface wave that detunes the cavity by modulating the overlap between the liquid and the cavity mode. This approach has been used at cryogenic temperatures with superfluid 4 He serving as the liquid [22][23][24][25][26].…”