Atom-interferometric test of the universality of gravitational redshift and free fall
Christian Ufrecht, Fabio Di Pumpo, Alexander Friedrich, Albert Roura, Christian Schubert, Dennis Schlippert, Ernst M. Rasel, Wolfgang P. Schleich, Enno Giese
Light-pulse atom interferometers constitute powerful quantum sensors for inertial forces. They are based on delocalised spatial superpositions and the combination with internal transitions directly links them to atomic clocks. Since classical tests of the gravitational redshift are based on a comparison of two clocks localised at different positions under gravity, it is promising to explore whether the aforementioned interferometers constitute a competitive alternative for tests of general relativity. Here we present a specific geometry which together with state transitions leads to a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity. The proposed interferometer does not rely on a superposition of internal states, but merely on transitions between them, and therefore generalises the concept of physical atomic clocks and quantum-clock interferometry. An experimental realisation seems feasible with already demonstrated techniques in state-of-the-art facilities.
The modification of the effect of interactions of a particle as a function of its pre- and postselected states is analyzed theoretically and experimentally. The universality property of this modification in the case of local interactions of a spatially pre- and postselected particle has been found. It allowed to define an operational approach for characterization of the presence of a quantum particle in a particular place: the way it modifies the effect of local interactions. The experiment demonstrating this universality property provides an efficient interferometric alignment method, in whic…
We report on an improved test of the Universality of Free Fall using a rubidium-potassium dual-species matter wave interferometer. We describe our apparatus and detail challenges and solutions relevant when operating a potassium interferometer, as well as systematic effects affecting our measurement. Our determination of the Eötvös ratio yields $η_{\,\text{Rb,K}}=-1.9\times10^{-7}$ with a combined standard uncertainty of $σ_η=3.2\times10^{-7}$.
Can quantum-mechanical particles propagating on a fixed spacetime background be approximated as test bodies satisfying the weak equivalence principle? We ultimately answer the question in the negative but find that, when universality of free-fall is assessed locally, a nontrivial agreement between quantum mechanics and the weak equivalence principle exists. Implications for mass sensing by quantum probes are discussed in some details.
A major challenge common to all Galilean drop tests of the Universality of Free Fall (UFF) is the required control over the initial kinematics of the two test masses upon release due to coupling to gravity gradients and rotations. In this work, we present a two-fold mitigation strategy to significantly alleviate the source preparation requirements in space-borne quantum tests of the UFF, using a compensation mechanism together with signal demodulation. To this end, we propose a scheme to reduce the gravity-gradient-induced uncertainties in an atom-interferometric experiment in a dedicated sate…
Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary "point" particle (in the particle physics sense) can be described by a localized wave-packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. (So point-like elementary particles, in the particle physics sens…
We demonstrate how simultaneously-operated $^{39}$K -- $^{87}$Rb interferometers exhibiting a high level of correlation can be used to make competitive tests of the university of free fall. This work provides an overview of our experimental apparatus and data analysis procedure, including a detailed study of systematic effects. With a total interrogation time of $2T = 40$ ms in a compact apparatus, we reach a statistical uncertainty on the measurement of the Eötvös parameter of $7.8 \times 10^{-8}$ after $2.4 \times 10^4$ s of integration. The main limitations to our measurement arise from a c…
We have performed a precision atomic interferometry experiment on testing the universality of free fall (UFF) considering atoms' spin degree of freedom. Our experiment employs the Bragg atom interferometer with $^{87}$Rb atoms either in hyperfine state $\left| {F = 1,{m_F} = 0} \right\rangle $ or $\left| {F = 2,{m_F} = 0} \right\rangle $, and the wave packets in these two states are diffracted in one pair of Bragg beams alternatively, which can help suppress the common-mode systematic errors. We have obtained an E$\rm{\ddot{o}}$tv$\rm{\ddot{o}}$s ratio $η= \left( { 0.9 \pm 2.7} \right) \times …
Atomic interference experiments test the universality of the coupling between matter-energy and gravity at different spacetime points, thus being in principle able to probe possible violations of the universality of the gravitational redshift (UGR). In this contribution, we introduce a UGR violation model and then discuss UGR tests performed by atomic clocks and atom interferometers on the same footing. We present a large class of atom-interferometric geometries which are sensitive to violations of UGR.
Does gravity influence local measurements? We use a dual-species atom interferometer with $2\,\text{s}$ of free-fall time to measure the relative acceleration between $^{85}$Rb and $^{87}$Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an Eötvös parameter of $η= [1.6\; \pm\; 1.8\; \text{(stat)}\; \pm \; 3.4 \; \text{(sys)}] \times 10^{-12}$, consistent with zero violation of the equivalence principle. With a resolution of up…
That gravitation can be understood as purely metric phenomenon depends crucially on the validity of a number of hypotheses which are summarised by the Einstein Equivalence Principle, the least well tested part of which being the Universality of Gravitational Redshift. A recent and currently widely debated proposal (Nature 463 (2010) 926-929) to re-interpret some 10-year old experiments in atom interferometry would imply, if tenable, substantial reductions on upper bounds for possible violations of the Universality of Gravitational Redshift by four orders of magnitude. This interpretation, howe…
The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales, is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to challenge collapse models and the quantum superposition principle more and more with a variety of different experiments. Among them, non-interferome…
The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a meas…
Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model's universality class and effective dimension, insights may be gained on their finite temperature dynamics and robustness. Our technique is demonstrated in particular on the 4D Toric Code and Haah's Code -- we find that the former falls into the 4D Ising universality cl…
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. We demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a facto…
Atomic clock interferometers are a valuable tool to test the interface between quantum theory and gravity, in particular via the measurement of gravitational time dilation in the quantum regime. Here, we investigate whether gravitational time dilation may be also used as a resource in quantum information theory. In particular, we show that for a freely falling interferometer and for a Mach-Zehnder interferometer, the gravitational time dilation may enhance the precision in estimating the gravitational acceleration for long interferometric times. To this aim, the interferometric measurements sh…
We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth's gravitational field. This shows that free fall depends on quantum-matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms fr…
We study how single- and double-slit interference patterns fall in the presence of gravity. First, we demonstrate that universality of free fall still holds in this case, i.e., interference patterns fall just like classical objects. Next, we explore lowest order relativistic effects in the Newtonian regime by employing a recent quantum formalism which treats mass as an operator. This leads to interactions between non-degenerate internal degrees of freedom (like spin in an external magnetic field) and external degrees of freedom (like position). Based on these effects, we present an unusual phe…
Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift (or universality of clock rates). Considering the atom as a clock operating at the Compton frequency associated…
Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase shift due to a sample which has an associated optical loss, and compare phase estimation strategies using classical and non-classical probe states. These comparisons are based on the attainable (quantum) Fisher information calculated per number of photons absorbed or scattered by the sample throughout the sensing process. We find that, for a given number of i…
The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle kn…
The compatibility of cavity-generated spin-squeezed atomic states with atom-interferometric sensors that require freely falling atoms is demonstrated. An ensemble of $500,000$ spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to $\sim$10 dB of metrologically-relevant squeezing is retrieved for 700 microsecond free-fall times, and decaying levels of squeezing are realized for up to 3 millisecond free-fall times. The degradation of squeezing results from loss of atom-cavity c…
Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift when considering the atom as a clock operating at the Compton frequency associated with the rest mass. We analy…
Interplays between quantum physics and gravity have long inspired exciting studies, which reveal subtle connections between quantum laws and the general notion of curved spacetime. One important example is the uniqueness of free-falling motions in both quantum and gravitational physics. In this work, we re-investigate the free-falling motions of quantum test wave packets that are distributed over weakly curved spacetime backgrounds. Except for the de Broglie relations, no assumption of priori given Hamiltonians or least actions satisfied by the quantum system is made. We find that the mean mot…
Motivated by the recent surge of transverse-field experiments on quasi-one-dimensional antiferromagnets Sr(Ba)Co$_2$V$_2$O$_8$, we investigate the quantum phase transition in a Heisenberg-Ising chain under a combination of two in-plane inter-perpendicular transverse fields and a four-period longitudinal field, where the in-plane transverse field is either uniform or staggered. We show that the model can be unitary mapped to the one-dimensional transverse-field Ising model (1DTFIM) when the $x$ and $y$ components of the spin interaction and the four-period field are absent. When these two terms…
We stand by our result [H. Mueller et al., Nature 463, 926-929 (2010)]. The comment [P. Wolf et al., Nature 467, E1 (2010)] revisits an interesting issue that has been known for decades, the relationship between test of the universality of free fall and redshift experiments. However, it arrives at its conclusions by applying the laws of physics that are questioned by redshift experiments; this precludes the existence of measurable signals. Since this issue applies to all classical redshift tests as well as atom interferometry redshift tests, these experiments are equivalent in all aspects in q…
Gravity gradient is known as a serious systematic effect in atomic tests of the universality of free fall, where the initial central position and velocity of atoms need to be exactly controlled. In this paper, we study quantum free fall with high-order gravity gradients. It is shown that the cubic terms in the Newtonian potential shall generate a new phase shift in atom interferometers, which depends on the position and velocity uncertainties of the incident atoms. We further investigate the nonclassicality of free fall and show that, due to the cubic potential, the gravitational Wigner equati…
In this paper we discuss in detail an experimental scheme to test the universality of free fall (UFF) with a differential $^{87}$Rb / $^{85}$Rb atom interferometer applicable for extended free fall of several seconds in the frame of the STE-QUEST mission. This analysis focuses on suppression of noise and error sources which would limit the accuracy of a violation measurement. We show that the choice of atomic species and the correctly matched parameters of the interferometer sequence are of utmost importance to suppress leading order phase shifts. In conclusion we will show the expected perfor…
The GBAR experiment will time the free fall of cold antihydrogen atoms dropped onto an annihilation plate to test the universality of free fall on antimatter. In this contribution, we study the quantum reflection of the anti-atom resulting from the Casimir-Polder attraction to the plate. We evaluate the Casimir-Polder potential and the associated quantum reflection amplitudes and find that reflection is enhanced for weaker potentials. A Liouville transformation of the Schrödinger equation is used to map the quantum reflection problem onto an equivalent problem of scattering on a barrier, leadi…
Atom interferometers are powerful tools for both measurements in fundamental physics and inertial sensing applications. Their performance, however, has been limited by the available interrogation time of freely falling atoms in a gravitational field. We realize an unprecedented interrogation time of 20 seconds by suspending the spatially-separated atomic wavepackets in a lattice formed by the mode of an optical cavity. Unlike traditional atom interferometers, this approach allows potentials to be measured by holding, rather than dropping, atoms. After seconds of hold time, gravitational potent…
