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Physical Review A

Rovibrational quantum interferometers and gravitational waves

Andreas Wicht, Cláus Lämmerzahl, Dennis Lorek, Hansjörg Dittus

Published Jul 7, 2008• 9 citations
Publisher

Abstract

We show that the application of atom interferometry techniques to the internal, i.e., rotational-vibrational states of molecules provides a new tool for ultrahigh precision tests of fundamental physics. The measurement principle is based on the fact that the electronic structure of molecules is not spherically symmetric. A diatomic quantum sensor can hence distinguish between the direction along its internuclear axis and the two orthogonal directions and is therefore direction sensitive. As an example we show how a molecular rotational-vibrational quantum interferometer based on the hydrogen deuteride molecular ion $({\text{HD}}^{+})$ may be used to detect gravitational waves. We show that a monochromatic gravitational wave of dimensionless amplitude $h={10}^{\ensuremath{-}19}$ will cause a frequency shift of the order of $30\text{ }\ensuremath{\mu}\text{Hz}$ between appropriately prepared quantum states, a frequency difference likely to be detectable with the next generation atom interferometers in 1 s.

DOI
10.1103/physreva.78.013610

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•Jan 1, 2026•0 citations
We show that the application of atom interferometry techniques to the internal, i.e., rotational-vibrational states of molecules provides a new tool for ultrahigh precision tests of fundamental physics. The measurement principle is based on the fact that the electronic structure of molecules is not spherically symmetric. A diatomic quantum sensor can hence distinguish between the direction along its internuclear axis and the two orthogonal directions and is therefore direction sensitive. As an example we show how a molecular rotational-vibrational quantum interferometer based on the hydrogen deuteride molecular ion (HD+)({\text{HD}}^{+})(HD+) may be used to detect gravitational waves. We show that a monochromatic gravitational wave of dimensionless amplitude h=10\ensuremath−19h={10}^{\ensuremath{-}19}h=10\ensuremath−19 will cause a frequency shift of the order of 30 \ensuremathμHz30\text{ }\ensuremath{\mu}\text{Hz}30 \ensuremathμHz between appropriately prepared quantum states, a frequency difference likely to be detectable with the next generation atom interferometers in 1 s.
We present an atom interferometer that differs from common atom interferometers as it is not based on the spatial splitting of electronic wave functions, but on orienting atoms in space. As an example we present how an orientational atom interferometer based on highly charged hydrogen--like atoms is affected by gravitational waves. We show that a monochromatic gravitational wave will cause a frequency shift that scales with the binding energy of the system rather than with its physical dimension. For a gravitational wave amplitude of $h={10}^{\ensuremath{-}23}$ the frequency shift is of the order of $110 \ensuremath{\mu}\mathrm{Hz}$ for an atom interferometer based on a 919191-fold charged uranium ion. A frequency difference of this size can be resolved by current atom interferometers in 1s1 \mathrm{s}1s.
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.
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.
Atomic quantum sensors are a major breakthrough in the technology of time and frequency standards as well as ultra-precise sensing and monitoring of accelerations and rotations. They apply a new kind of optics based on matter waves. Today, atomic clocks are the standard for time and frequency measurement at the highest precisions. Inertial and rotational sensors using atom interferometers have already shown similar potential for replacing state-of-the-art sensors in other fields. With Bose-Einstein condensates, also refered as atom lasers, the traditional experiments with atom interferometers can be greatly improved. Testing of fundamental principles, studies of atomic properties, applications as inertial sensors, and measurements of fundamental constants can benefit from the brightness (intensity and small momentum spread) of these coherent sources. In addition, the coherence properties of condensates may also allow BEC based atom interferometers to approach the Heisenberg detection limit. This corresponds to a measurement precision which scales like 1/N for N atoms and not like 1 / N as for independent measurements on N atoms.
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.
Quantum sensing using atom interferometry possesses immense potential for application in gravimetry, inertial navigation and for gravitational wave detection, apart from carrying out tests of fundamental physics. Atom interferometry can be used to perform absolute inertial measurements with unprecedented long term stability, unlike classical sensors which are prone to drift and incur calibration errors. However, atom interferometers seldom achieve their fundamental sensitivity due to the coupling of ambient vibrations. It is the dominant noise source that not only impairs performance but also affects its operability. Ideal compensation of the effects due to vibration noise using a versatile accelerometer, while concurrently enabling miniaturized atom interferometer setups has not been pioneered. Such a compact hybrid quantum sensor will enable reliable operation with an enhanced performance in field applications, paving the way for robust atom interferometry beyond laboratory conditions. A novel optomechanical resonator has been designed, developed and successfully hybridized with an atom interferometer to suppress the effects of vibration noise, and the results are presented in this thesis. The optomechanical resonator’s inertial test mass is simultaneously used to create a continuous intracavity optical lattice to sense its displacement, and a pulsed optical lattice to manipulate the atoms. For the first time, a broadband accelerometer is seamlessly hybridized with an atom interferometer via mechanical resonator mediated coupling of the optical lattices to measure acceleration. This enables elimination of vibration induced measurement ambiguity in our atom interferometer with a well defined mechanical transfer function. Vibration noise correlation is demonstrated up to our prototype atom interferometer’s most sensitive operating mode of T = 6 ms using double Bragg diffraction, ultimately limited by its technical noise. The optomechanical resonator measures acceleration with a sensitivity down to 1.1×10−6 ms−2/ √Hz corresponding to a displacement sensitivity of 8.6 × 10−15 m/ √Hz. Substantial 1/f noise suppression due to the developed optical readout scheme enables a measurement bandwidth spanning from sub-hertz frequencies up to several kilohertz. Multiple versions of the optomechanical resonator with different characteristics were developed and hybridized with our atom interferometer. This paves the way for developing tailored optomechanical resonators for specific inertial sensing applications.