Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based setups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be encoded in the joint probability distribution of two or more interferometers, provided that these are initialized in suitable states. We develop a general framework that makes use of $N+1$ interferometers, which may differ in their masses, to correct for environmental potential fields up to order $N$ in their multipole expansion. Remarkably, our approach works for fields that fluctuate stochastically in any timescale and does not require the presence of quantum correlations among the different interferometers. Finally, we also show that the same ideas can be extended to the protection of entanglement between pairs of interferometers.
Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based setups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be encoded in the joint probability distribution of two or more interferometers, provided that these are initialized in suitable states. We develop a general framework that makes use of N+1 interferometers, which may differ in their masses, to correct for environmental potential fields up to order N in their multipole expansion. Remarkably, our approach works for fields that fluctuate stochastically in any timescale and does not require the presence of quantum correlations among the different interferometers. Finally, we also show that the same ideas can be extended to the protection of entanglement between pairs of interferometers.
Matter-wave interferometry is a striking quantum phenomenon that differs fundamentally from classical mechanics. In the quantum regime, matter behaves like a wave and can exist in spatial superpositions, allowing a single quantum object to move along multiple trajectories simultaneously. Similar to optical interferometers, such quantum matter systems act as interferometers themselves, with the differential phase that encodes information about external forces experienced during their evolution. This makes matter-wave interferometry a powerful platform for quantum sensing across various applications: (i) One of the most direct applications is precision measurement. Atomic interferometers can measure local acceleration and have already been implemented in devices such as accelerometers, seismometers, gravimeters, and gradiometers. (ii) Atomic interferometers are proposed as complementary tools for future gravitational-wave observatories, including ongoing projects MIGA, MAGIS-100, AION and ZAIGA. (iii) Matter-wave interferometry also offers a promising platform for probing quantum aspects of gravity. Numerous tabletop proposals aim to test quantum gravity models, investigate collapse mechanisms, study gravity-induced decoherence, and search for gravity-mediated quantum entanglement. The Stern-Gerlach interferometer (SGI) is a type of matter-wave interferometer that manipulates spatial superpositions using magnetic-field gradients. The witness of an SGI can be designed via its spin, enabling more precise measurements of the differential phase. Recent developments in atomic chip technology have enabled the generation of highly controlled magnetic fields on compact platforms, allowing for precise manipulation of spin states and making SGIs experimentally realizable. Robustness is a critical challenge for matter-wave interferometers. In real experiments, various sources of classical noises arise from mechanical vibrations, seismic motions, inertial forces, tidal forces, magnetic field fluctuations and so on. These noises can disturb the spin and spatial degrees of freedom of the test mass, resulting in witness loss of the interferometer. While spin decoherence is relatively well understood and can be formulated by the Bloch-Redfield master equation, the impact on spatial degrees of freedom still requires systematic investigation. This thesis therefore aims to explore witness loss in an SGI induced by stochastic noises acting on spatial degrees of freedom. As investigated by this thesis, the witness gets lost via several mechanisms: (i) Dephasing. The spatial phase is fluctuated by stochastic noise, resulting in a random phase factor eiδϕ, whose ensemble average contributes a decay factor e−Γ to the spin density matrix and leads to a loss of witness. As is demonstrated by the thesis, this decay factor is a linear response to the external noise, with a transfer function as the Fourier transform of the unperturbed classical trajectories. (ii) Humpty-Dumpty problem. The classical trajectories are also disturbed by stochastic noise, resulting in a non-closure problem of the interferometer, known as the Humpty-Dumpty problem. The resulting witness loss is usually characterized by the contrast of the final states ⟨ψ1|ψ2⟩, which equals the phase-space distance |α1 − α2|2 when the test mass is in coherent states. (iii) Position localization decoherence. Due to the randomness of the noise, the spatial wavefunction of the test mass is thus also stochastic, of which the ensemble average experiences decoherence characterized by the power spectrum density of external noise. However, as illustrated by this thesis, this type of decoherence does not affect spin-based witnesses in most practical scenarios. The general theoretical framework is mainly constructed in chapter 3 of this thesis. The subsequent chapters analyze several representative noise sources: (i) Gravitational and electrostatic noise. Molecules in the surrounding gas move randomly due to thermal motion, generating stochastic gravitational accelerations and electrostatic forces that can be expanded in multipole series. Since the random motion follows Maxwell’s distribution and approximately has a cylindrical symmetry, the resulting noise power spectrum density takes the form of Bessel functions. (ii) Inertial acceleration noise. The mechanical support of the experimental apparatus is always fluctuated by vibrational noise, resulting in random inertial force on the test mass. In practice, dephasing can be mitigated through destructive interference by introducing appropriate coupling between different directional components. (iii) Inertial torsion noise. In suspended experiments, the experimental apparatus is fluctuated by torsional noise, leading to another inertial noise on the test mass. The power spectrum density of the inertial torsion noise is formulated by the selfconvolution of the original noise, resulting in the peak frequencies that are doubled. Taken together, these analyses build a comprehensive picture of how stochastic noise affects the spatial dynamics of an SGI and leads to the loss of spin-based witnesses. Future work may include more realistic noise sources such as magnetic noise and trap-potential noise. These insights will be valuable for future experimental implementations, particularly in precision sensing for quantum gravity, where preserving coherence and maintaining reliable witness signals are essential.
Matter-wave interferometry is highly susceptible to inertial acceleration noises arising from the vibration of the experimental apparatus. There are various methods for noise suppression. In this paper, we propose leveraging the cross-correlation of multidirectional vibration noises to mitigate their dephasing effect in matter-wave interferometers. Specifically, we analyze an interferometer driven by its internal state under an external field and examine the dephasing caused by a two-dimensional random inertial force. As we will demonstrate, the coupling between the two-dimensional inertial force noise components will shift the resonance peak but not change the shape of the power spectral density. Moreover, when the noise approximately resonates with the intrinsic frequency of the test mass, we find that the standard deviation of the phase can be suppressed by a factor roughly equal to the Q factor of the noise. This technique holds significant potential for future gravity experiments utilizing quantum sensors, such as measuring gravitational acceleration and exploring quantum entanglement induced by gravity.
Matter-wave interferometry is highly susceptible to inertial acceleration noises arising from the vibration of the experimental apparatus. There are various methods for noise suppression. In this paper, we propose leveraging the cross-correlation of multi-directional vibration noises to mitigate their dephasing effect in matter-wave interferometers. Specifically, we analyse an interferometer driven by its internal state under an external field and examine the dephasing caused by a two-dimensional random inertial force. As we will demonstrate, the coupling between the two-dimensional inertial force noise components will shift the resonance peak but not change the shape of the power spectral density. Moreover, when the noise approximately resonates with the intrinsic frequency of the test mass, we find that the standard deviation of the phase can be suppressed by a factor roughly equal to the Q-factor of the noise. This technique holds significant potential for future gravity experiments utilising quantum sensors, such as measuring gravitational acceleration and exploring quantum entanglement induced by gravity.
High-contrast matter-wave interferometry is essential in various fundamental quantum mechanical experiments as well as for technical applications. Thereby, contrast and sensitivity are typically reduced by decoherence and dephasing effects. While decoherence accounts for a general loss of quantum information in a system due to entanglement with the environment, dephasing is due to collective time-dependent external phase shifts, which can be related to temperature drifts, mechanical vibrations, and electromagnetic oscillations. In contrast to decoherence, dephasing can, in principle, be reversed. Here, we demonstrate in experiment and theory a method for the analysis and reduction of the influence of dephasing noise and perturbations consisting of several external frequencies in an electron interferometer. This technique uses the high spatial and temporal resolution of a delay-line detector to reveal and remove dephasing perturbations by second-order correlation analysis. It allows matter-wave experiments under perturbing laboratory conditions and can be applied, in principle, to electron, atom, ion, neutron, and molecule interferometers.
Interferometers with single particles are susceptible for dephasing perturbations from the environment, such as electromagnetic oscillations or mechanical vibrations.On the one hand, this limits sensitive quantum phase measurements as it reduces the interference contrast in the signal.On the other hand, it enables single-particle interferometers to be used as sensitive sensors for electromagnetic and mechanical perturbations.Recently, it was demonstrated experimentally, that a secondorder correlation analysis of the spatial and temporal detection signal can decrease the electromagnetic shielding and vibrational damping requirements significantly.Thereby, the relevant matter-wave characteristics and the perturbation parameters could be extracted from the correlation analysis of a spatially 'washed-out' interference pattern and the original undisturbed interferogram could be reconstructed.This method can be applied to all interferometers that produce a spatial fringe pattern on a detector with high spatial and temporal single-particle resolution.In this article, we present and discuss in detail the used two-dimensional second-order correlation theory for multifrequency perturbations.The derivations of an explicit and approximate solution of the correlation function and corresponding amplitude spectra are provided.It is explained, how the numerical correlation function is extracted from the measurement data.Thereby, the influence of the temporal and spatial discretization step size on the extracted parameters, as contrast and perturbation amplitude, is analyzed.The influence of noise on the correlation function and corresponding amplitude spectrum is calculated and numerically cross-checked by a comparison of our theory with numerical singleparticle simulations of a perturbed interference pattern.Thereby, an optimum spatial discretization step size is determined to achieve a maximum signal-to-noise ratio, which was used in former experiments to identify the perturbation caused by the electrical network.Our method can also be applied for the analysis of broad-band frequency noise, dephasing the interference pattern.Using Gaussian distributed noise in the simulations, we demonstrate that the relevant matter-wave parameters and the applied perturbation spectrum can be revealed by our correlation analysis.
Current models of quantum interference experiments in external gravitational fields lack a common framework: while matter-wave interferometers are commonly described using the Schrödinger equation with a Newtonian potential, gravitational effects in quantum optics are modeled using either post-Newtonian metrics or highly symmetric exact solutions to Einstein's field equations such as those of Schwarzschild and Kerr. To coherently describe both kinds of experiments, this paper develops a unified framework for modeling quantum interferometers in general stationary space-times. This model provides a rigorous description and coherent interpretation of the effects of classical gravity on quantum probes.