Despite growing interest, there is a scarcity of known predictions in the regime where both quantum and general relativistic effects become observable. Here, we investigate a combined atom-field system in a curved spacetime, with a specific focus on gravitational-wave backgrounds. We demonstrate that a plane gravitational wave alters spontaneous emission from a single atom, manifesting itself as a direction-dependent change in the emission spectrum. Although the total decay rate remains unchanged, implying that no information about the gravitational wave is stored in the atomic internal state alone, the wave leaves imprints on the evolution of the composite atom-field system. To quantify how well this effect can be measured, we analyze both the classical Fisher information associated with photon number measurements and the quantum Fisher information. Our analysis indicates that the effect could be measured in state-of-the-art cold-atom experiments and points to spontaneous emission as a potential probe of low-frequency gravitational waves.

The traditional view from particle physics is that quantum-gravity effects should become detectable only at extremely high energies and small length scales. Owing to the significant technological challenges involved, there has been limited progress in identifying experimentally detectable effects that can be accessed in the foreseeable future. However, in recent decades the size and mass of quantum systems that can be controlled in the laboratory have reached unprecedented scales, enabled by advances in ground-state cooling and quantum-control techniques. Preparations of massive systems in quantum states pave the way for the explorations of a low-energy regime in which gravity can be both sourced and probed by quantum systems. Such approaches constitute an increasingly viable alternative to accelerator-based, laser-interferometric, torsion-balance, and cosmological tests of gravity. In this review an overview of proposals where massive quantum systems act as interfaces between quantum mechanics and gravity is provided. Conceptual difficulties in the theoretical description of quantum systems in the presence of gravity are discussed, tools for modeling massive quantum systems in the laboratory are reviewed, and an overview of the current state-of-the-art experimental landscape is provided. Proposals covered in this review include precision tests of gravity, tests of gravitationally induced wave-function collapse and decoherence, and gravity-mediated entanglement. The review concludes with an outlook and summary of the key questions raised.

Quantum technologies rely on the control of quantum systems at the level of individual quanta. Mathematically, this control is described by Hamiltonian or Liouvillian evolution, requiring the application of various techniques to solve the resulting dynamic equations. Here, we present a tutorial for how the quantum dynamics of systems can be solved using a Lie-algebra decoupling method. The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. As background, we include an overview of Lie groups and Lie algebras aimed at a general-physicist audience. We then prove the Lie-algebra decoupling theorem and apply it to both closed and open dynamics. The results represent a broad methodology to find the dynamics of quantum systems with applications across many fields of modern quantum research.

We study force-gradient sensing with a coherently driven mechanical resonator and phase-sensitive detection of motion through the two-Tone backaction evading measurement of cavity optomechanics. The response of the optomechanical system, solved by numerical integration of the classical equations of motion, shows an extended region which is monotonic to changes in force gradient. We use Floquet theory to model the fluctuations, which rise only slightly above that of the usual backaction evading measurement in the presence of the mechanical drive. The monotonic response and minimal backaction are advantageous for applications such as atomic force microscopy.

In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.

The photon blockade effect is commonly exploited in the development of single-photon sources. While the photon blockade effect could be used to prepare high-fidelity single-photon states in idealized regimes, practical implementations in optomechanical systems suffer from an interplay of competing processes. Here we derive a control scheme that exploits destructive interference of Fock state amplitudes of more than one photon. The resulting preparation time for photon-blockaded quantum states is limited only by the optomechanical interaction strength and can thus be orders of magnitude shorter than in existing schemes that achieve photon blockade in the steady state.

We propose an optimal protocol using phase-preserving quantum measurements and phase-dependent modulations of the trapping potential at parametric resonance to cool a quantum oscillator to an occupation number of less than one quantum. We derive the optimal phase relationship and duration for the parametric modulations and compute the lowest-possible occupation number in the steady state. The protocol is robust against moderateamounts of dissipation and phase errors in the feedback loop. Our work has implications for the cooling oflevitated mechanical resonators in the quantum regime.

We derive the best possible bounds that can be placed on Yukawa- and chameleon-like modifications to the Newtonian gravitational potential with a cavity optomechanical quantum sensor. By modelling the effects on an oscillating source-sphere on the optomechanical system from first-principles, we derive the fundamental sensitivity with which these modifications can be detected in the absence of environmental noise. In particular, we take into account the large size of the optomechanical probe compared with the range of the fifth forces that we wish to probe and quantify the resulting screening effect when both the source and probe are spherical. Our results show that optomechanical systems in high vacuum could, in principle, further constrain the parameters of chameleon-like modifications to Newtonian gravity.

Cavity quantum optomechanics has emerged as a new platform for quantum science and technology with applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrödinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a pulsed approach that utilizes the nonlinearity of the radiation–pressure interaction combined with photon-counting measurements to generate this entangled non-Gaussian mechanical state, and, importantly, describe a protocol using subsequent pulsed interactions to verify the non-Gaussian entanglement generated. Our pulsed verification protocol allows quadrature moments of the two mechanical oscillators to be measured up to any finite order providing a toolset for experimental characterisation of bipartite mechanical quantum states and allowing a broad range of inseparability criteria to be evaluated. Key experimental factors, such as optical loss and open-system dynamics, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.