Abstract Recent advances in quantum sensing—optical clocks at 5.5 × 10 − 19 systematic uncertainty, frequency-dependent squeezing below the standard quantum limit, quantum magnetometers approaching fundamental sensitivity limits—raise a natural question: can these technologies detect gravitational waves directly, or enhance existing detectors beyond current capabilities? We show that the answer is primarily determined by the coupling mechanism between the gravitational wave and the sensor. Starting from the tidal Hamiltonian in Fermi normal coordinates, we identify three physically distinct mechanisms by which a gravitational wave couples directly to a quantum system, and derive their transducer gains within linearized general relativity and non-relativistic quantum mechanics. Internal atomic coupling (tidal distortion of electronic wavefunctions) yields a transducer gain G A = 2.4 × 10 − 20 , with vanishing first-order energy shifts for all J = 0 clock states—a ∼ 10 35 deficit relative to laser interferometry that exceeds any projected quantum enhancement. Center-of-mass coupling (Doppler shifts from geodesic motion) reaches strain sensitivities of ∼ 10 − 18 , still 10 4 above LISA requirements. Light propagation coupling (phase accumulation over macroscopic baselines) provides the enormous transducer gain that makes laser interferometry—and atom interferometry—viable. For detectors exploiting this third mechanism, we quantify how much improvement quantum sensors can provide through the detector’s noise architecture: LISA’s noise budget is predominantly classical, limiting combined quantum enhancement to E ≈ 1.04 , while ground-based detectors in the shot-noise-dominated regime achieve E = 1.6 – 2.1 . Atom interferometers exploit the same light-propagation mechanism to target the 0.01–10 Hz band between the LISA and LIGO ranges.
Abstract Recent advances in quantum sensing—optical clocks at 5.5 × 10 − 19 systematic uncertainty, frequency-dependent squeezing below the standard quantum limit, quantum magnetometers approaching fundamental sensitivity limits—raise a natural question: can these technologies detect gravitational waves directly, or enhance existing detectors beyond current capabilities? We show that the answer is primarily determined by the coupling mechanism between the gravitational wave and the sensor. Starting from the tidal Hamiltonian in Fermi normal coordinates, we identify three physically distinct mechanisms by which a gravitational wave couples directly to a quantum system, and derive their transducer gains within linearized general relativity and non-relativistic quantum mechanics. Internal atomic coupling (tidal distortion of electronic wavefunctions) yields a transducer gain G A = 2.4 × 10 − 20 , with vanishing first-order energy shifts for all J = 0 clock states—a ∼ 10 35 deficit relative to laser interferometry that exceeds any projected quantum enhancement. Center-of-mass coupling (Doppler shifts from geodesic motion) reaches strain sensitivities of ∼ 10 − 18 , still 10 4 above LISA requirements. Light propagation coupling (phase accumulation over macroscopic baselines) provides the enormous transducer gain that makes laser interferometry—and atom interferometry—viable. For detectors exploiting this third mechanism, we quantify how much improvement quantum sensors can provide through the detector’s noise architecture: LISA’s noise budget is predominantly classical, limiting combined quantum enhancement to E ≈ 1.04 , while ground-based detectors in the shot-noise-dominated regime achieve E = 1.6 – 2.1 . Atom interferometers exploit the same light-propagation mechanism to target the 0.01–10 Hz band between the LISA and LIGO ranges.
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.
The first detections of gravitational waves have opened an exciting new field of astronomy. One of the most fundamental limitations for the sensitivity of current and future interferometric gravitational-wave detectors is imposed by the quantum nature of light: Quantum vacuum fluctuations entering the interferometer through the readout port will contribute to the detection noise, at high frequencies in the form of shot noise and at low frequencies by radiation pressure noise. A promising way to reduce this quantum noise is the injection of squeezed states of light that have a lower uncertainty in one quadrature than the vacuum state. The GEO 600 gravitational-wave detector demonstrated the use of squeezed light in 2010 and it is now the first detector to routinely apply squeezing to improve its sensitivity beyond the limits set by classical quantum shot noise. This thesis details the practical aspects of long-term stable and efficient squeezed-light integration in a large-scale gravitational-wave detector. Imperfections that can limit the amount of observable non-classical noise improvement, such as optical losses and phase fluctuations, were studied in detail and methods for their mitigation were developed. Novel control schemes for the active stabilisation of the squeezed light field's phase and alignment were one main focus of the investigations. At the same time, important experience was gathered in the operation of the squeezed light source over long timescales. Over the course of the thesis work, improvements were implemented that significantly increased the performance of the squeezed-light application. Squeezing was injected with an overall duty cycle of 88%, reaching a noise reduction of up to 4.4 dB, corresponding to a 40% lowered shot-noise level. This work has firmly established the practical application of squeezing as a mature technology. The gained knowledge will directly inform the implementation of squeezed light for all future gravitational-wave detectors.
A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.
The present cumulative thesis (Publications (I)–(III) [1– 3]) explores three complementary directions: (i) tunneling-based gravimetry, (ii) phase contributions of tunneled Ramsey clocks, and (iii) resource optimization for very-long-baseline atom interferometers designed for the detection of gravitational waves and dark matter. The development of atom interferometers and atomic clocks seeks to steadily increase the measurement sensitivity, with the ultimate bound set by the Heisenberg limit. Enhancements can be achieved by exploiting quantum phenomena such as entanglement and squeezing, which allow sensitivities below the shot-noise limit. Another fundamental quantum effect, tunneling, remains less explored in the context of metrology, despite its inherent quantum nature. While entanglement and squeezing have already been demonstrated in atom interferometers, tunneling has not yet been widely investigated for gravimetric sensing applications. Publication (I) explores two configurations of tunneling-based gravimeters using a matter-wave Fabry–Pérot interferometer. (i) In the transmission setup, the wave packet is prepared in front of the cavity generated by optical potentials and transmitted. (ii) In the tunneling setup, the wave packet is prepared inside the cavity, representing a configuration without a classical analogue. Through our numerical simulations of the wave packet dynamics, including gravitational effects, we find that gravity primarily alters the motion of the packet by accelerating, decelerating, and deforming it, which modifies in particular its width at impact. While a single Gaussian barrier shows no resonances, the Fabry–Pérot configuration supports multiple resonances, defining tunable working points and acting as a velocity filter. In Publication (II), we turn to the phase accumulated during tunneling, investigated via a Ramsey clock. The Ramsey clock consists of a superposition of two internal states, accumulating a phase that is read out via a Ramsey sequence. Adopting an operational definition where time is what you read off a clock, we identify a tunneling time associated with the tunneling phase, alongside relativistic contributions accumulated by the tunneled clock. This approach naturally unifies several conventional definitions of tunneling time. Furthermore, the tunneling phase can be amplified experimentally by introducing state-dependent barrier heights through differential light shifts. In Publication (III), we study differential geometries of terrestrial very-long baseline atom interferometers, currently in development for gravitational-wave and dark-matter detection. We analyze three strategies for signal enhancement: (i) large-momentum-transfer pulses to increase atom–light interaction points, (ii) resonant-mode enhancement by matching the interrogation time to the target frequency, and (iii) extending baseline lengths. The achievable number of pulses is limited by atomic losses, distributed between large-momentum-transfer sequences and number of diamonds. Additionally, more diamonds require taller atomic fountains, constrained by the finite baseline. Thus, a trade-off emerges between the number of large-momentum-transfer pulses, the number of diamonds, and the baseline length. Considering this interplay, we derive an analytical relation for the optimal number of pulses under given loss rates. We explicitly optimize the allocation of the available resources and account for the finite spatial extent of individual interferometers, baseline constraints, and atom loss from imperfect pulses.
Quantum computers allow for direct simulation of the quantum interference and entanglement used in modern interferometry experiments with applications ranging from biological sensing to gravitational wave detection. Inspired by recent developments in quantum sensing at the Laser Interferometer Gravitational-wave Observatory (LIGO), here we present two quantum circuit models that demonstrate the role of quantum mechanics and entanglement in modern precision sensors. We implemented these quantum circuits on IBM quantum processors, using a single qubit to represent independent photons traveling through the LIGO interferometer and two entangled qubits to illustrate the improved sensitivity that LIGO has achieved by using non-classical states of light. The one-qubit interferometer illustrates how projection noise in the measurement of independent photons corresponds to phase sensitivity at the standard quantum limit. In the presence of technical noise on a real quantum computer, this interferometer achieves the sensitivity of 11\% above the standard quantum limit. The two-qubit interferometer demonstrates how entanglement circumvents the limits imposed by the quantum shot noise, achieving the phase sensitivity 17\% below the standard quantum limit. These experiments illustrate the role that quantum mechanics plays in setting new records for precision measurements on platforms like LIGO. The experiments are broadly accessible, remotely executable activities that are well suited for introducing undergraduate students to quantum computation, error propagation, and quantum sensing on real quantum hardware.
Atom interferometers measure quantum interference patterns in the wave functions of cold atoms that follow superpositions of different space-time trajectories. These can be sensitive to phase shifts induced by fundamental physics processes such as interactions with ultralight dark matter or the passage of gravitational waves. The capabilities of large-scale atom interferometers are illustrated by their estimated sensitivities to the possible interactions of ultralight dark matter with electrons and photons, and to gravitational waves in the frequency range around 1 Hz, intermediate between the peak sensitivities of the LIGO and LISA experiments. Atom interferometers can probe ultralight scalar couplings with much greater sensitivity than is currently available from probes of the Equivalence Principle. Their sensitivity to mid-frequency gravitational waves may open a window on mergers of masses intermediate between those discovered by the LIGO and Virgo experiments and the supermassive black holes present in the cores of galaxies, as well as fundamental physics processes in the early Universe such as first-order phase transitions and the evolution of networks of cosmic strings.