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Physical Review A

Orientational atom interferometers sensitive to gravitational waves

Dennis Lorek, Cláus Lämmerzahl, Andreas Wicht

Published Feb 24, 2010• 7 citations
Publisher

Abstract

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 $91$-fold charged uranium ion. A frequency difference of this size can be resolved by current atom interferometers in $1 \mathrm{s}$.

DOI
10.1103/physreva.81.023621

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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−23h={10}^{\ensuremath{-}23}h=10\ensuremath−23 the frequency shift is of the order of 110\ensuremathμHz110 \ensuremath{\mu}\mathrm{Hz}110\ensuremathμHz 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.
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 $h={10}^{\ensuremath{-}19}$ 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.
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.
We propose a terrestrial detector for gravitational waves with frequencies between 0.3 and 5 Hz based on atom interferometry. As key elements, we discuss two symmetric matter-wave interferometers, the first one with a single loop and the second one featuring a folded triple-loop geometry. The latter eliminates the need for atomic ensembles at femtokelvin energies imposed by the Sagnac effect in other atom interferometric detectors. The folded triple-loop geometry also combines several advantages of current vertical and horizontal matter wave antennas and enhances the scalability in order to achieve a peak strain sensitivity of 2×10−21/Hz.
Relativistic models for two concepts for detecting gravitational waves with atom interferometers are presented and their features discussed. We calculate the phase difference due to a gravitational wave of an atom interferometer in a Ramsey–Bordé configuration. A general expression for the phase is presented including the case that the center of mass of the device and the center of symmetry of the matter wave trajectories do not coincide. The sensitivity of atom interferometers and laser interferometers are then compared for the detection in the low and high frequency regimes. Finally, we calculate the phase difference due to a gravitational wave of an atom gravimeter, and discuss possible strategies to solve the problem of the phase noise and of the measurement frequency.
Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all atomic degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii) Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests. However, modified configurations, for example by relaunching the atoms, can mimic such tests under certain conditions and may constitute a competitive alternative. (iii) Guided atom interferometers are comparable to atomic clocks. (iv) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.
Atom interferometers have been used to measure acceleration with at best a T2T^2T2 scaling in sensitivity as the interferometer time TTT is increased. This limits the sensitivity to acceleration which is theoretically achievable by these configurations for a given frequency of acceleration. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will scale as T3T^3T3. This enhanced scaling will allow an increase in achievable sensitivity for any given frequency of an oscillatory acceleration signal, which will be of particular use for inertial and navigational sensors, and proposed gravitational wave detectors. A straight forward extension should allow a T4T^4T4 scaling in acceleration sensitivity.