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Recently, multilevel collectively coupled quantum machines like heat engines and refrigerators have been shown to admit performance enhancements in analogy to superradiance. Thus far, investigations of the performance of collective quantum machines have largely restricted the dynamics to particles with bosonic exchange symmetry, especially for large numbers of particles. However, collections of indistiguishable but not fundamentally identical particles may assume quantum states of more general exchange symmetry or combinations thereof, raising the question of whether collective advantages can be observed for dynamics that allow the full Hilbert space to be explored. Here, we compare a collection of single-particle three-level masers with their collectively coupled counterpart, while admitting more general forms of exchange symmetry. We study ergotropy and emitted power as the figures of merit and show which of the known results applicable to a single three-level engine carry over to an engine made up of a collectively coupled ensemble. We do this using results from representation theory to characterise the full basis of the Hilbert space and provide general tools for the description of the dynamics of such systems. We find that collective work extraction can extend beyond the temperature window of three-level lasing, whereas in the lasing regime, individual may outperform collective operation. In addition, the optimal parameter regime for work-like energy output varies for different symmetry types. Our results show a rich picture in which bosonic symmetry is not always optimal and sometimes individual particles may even perform best.

We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regards to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. Here, we prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle., Comment: 9 pages, 9 figures

Coherent spin resonance methods, such as nuclear magnetic resonance and electron spin resonance spectroscopy, have led to spectrally highly sensitive, non-invasive quantum imaging techniques. Here, we propose a pump-probe spin resonance spectroscopy approach, designed for electron microscopy, based on microwave pump fields and electron probes. We investigate how quantum spin systems couple to electron matter waves through their magnetic moments and how the resulting phase shifts can be utilized to gain information about the states and dynamics of these systems. Notably, state-of-the-art transmission electron microscopy provides the means to detect phase shifts almost as small as that due to a single electron spin. This could enable state-selective observation of spin dynamics on the nanoscale and indirect measurement of the environment of the examined spin systems, providing information, for example, on the atomic structure, local chemical composition and neighboring spins., Comment: 12 pages, 3 figures

Quantum entanglement is the essential resource for quantum communication and distributed information processing in a quantum network. However, the remote generation over a network suffers from inevitable transmission loss and other technical difficulties. This paper introduces the concept of entanglement buffers as a potential primitive for preparing long-distance entanglement. We investigate the filling of entanglement buffers with either one Bell state or a stream of Bell states. We illustrate their resilience to non-ideal interactions and transmission loss, making them sometimes more advantageous than other entanglement generation approaches in the quantum network scenario. Additionally, larger entanglement buffers can always enhance these benefits., Comment: 6+7 pages, 6+6 figures; comments and suggestions are welcome!

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study non-invasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the non-Markovian dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behaviour of finite many-body systems beyond the validity of mean-field models., Comment: 11 pages, 8 figures

Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper we harness the versatility of Tsirelson inequalities to address two distinct problems: detecting cheating in classic shell games and probing quantumness in spatially separated systems and harmonic oscillators. By adopting a black-box approach and a geometric characterization of the space of conditional probabilities, we demonstrate that Tsirelson inequalities can be used in both scenarios, enabling us to uncover quantum signatures and identify cheaters in a single unified framework. This connection provides an intuitive different perspective on quantumness of mechanical systems.

Temperature estimation plays a vital role across natural sciences. A standard approach is provided by probe thermometry, where a probe is brought into contact with the sample and examined after a certain amount of time has passed. In many situations however, continuously monitoring the probe may be preferred. Here, we consider a minimal model, where the probe is provided by a two-level system coupled to a thermal reservoir. Monitoring thermally activated transitions enables real-time estimation of temperature with increasing accuracy over time. Within this framework we comprehensively investigate thermometry in both bosonic and fermionic environments employing a Bayesian approach. Furthermore, we explore adaptive strategies and find a significant improvement on the precision. Additionally, we examine the impact of noise and find that adaptive strategies may suffer more than non-adaptive ones for short observation times. While our main focus is on thermometry, our results are easily extended to the estimation of other environmental parameters, such as chemical potentials and transition rates.

Optical near fields are at the heart of various applications in sensing and imaging. We investigate dipole scattering as a parameter estimation problem and show that optical near-fields carry more information about the location and the polarizability of the scatterer than the respective far fields. This increase in information originates from and occurs simultaneously with the scattering process itself. Our calculations also yield the far-field localization limit for dipoles in free space., Comment: v2: 32 pages, 11 figures, amended main text, modified plots, extended appendix, added Figs. S1, S2, S3, S6

We present and discuss a master equation blueprint for a generic class of quantum measurement feedback based models of friction. A desired velocity-dependent friction force is realized on average by random repeated applications of unsharp momentum measurements followed by immediate outcome-dependent momentum displacements. The master equations can describe arbitrarily strong measurement-feedback processes as well as the weak continuous limit resembling diffusion master equations of Caldeira-Leggett type. We show that the special case of linear friction can be equivalently represented by an average over random position measurements with squeezing and position displacements as feedback. In fact, the dissipative continuous spontaneous localization model of objective wavefunction collapse realizes this representation for a single quantum particle. We reformulate a consistent many-particle generalization of this model and highlight the possibility of feedback-induced correlations between otherwise non-interacting particles., Comment: 10+6 pages, 2 figures

The quantum battery capacity is introduced in this letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement., Comment: 5+7 pages, 2+3 figure. To be published

We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest neighbour interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions., Comment: 11 pages, 8 figures

Recently, solid-state mechanical resonators have become a platform for demonstrating non-classical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of $\mu= 11.3$ is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could confirm the quantum superposition principle at unprecedented scales., Comment: 5+9 pages, 2+6 figures, comments are welcome

The study of molecular physics using ultracold gases has provided a unique probe into the fundamental properties of nature and offers new tools for quantum technologies. In this article we outline how the use of a space environment to study ultracold molecular physics opens opportunities for 1) exploring ultra-low energy regimes of molecular physics with high efficiency, 2) providing a toolbox of capabilities for fundamental physics, and 3) enabling new classes of matter-wave interferometers with applications in precision measurement for fundamental and many-body physics., Comment: 6 pages

We consider quantum batteries given by composite interacting quantum systems in terms of the thermodynamic work cost of local random unitary processes. We characterize quantum correlations by monitoring the average energy change and its fluctuations in the high-dimensional bipartite systems. We derive a hierarchy of bounds on high-dimensional entanglement (the so-called Schmidt number) from the work fluctuations and thereby show that larger work fluctuations can verify the presence of stronger entanglement in the system. Finally, we develop two-point measurement protocols with noisy detectors that can estimate work fluctuations, showing that the dimensionality of entanglement can be probed in this manner., Comment: 16 pages, 3 figures

Recently, an unconditional advantage has been demonstrated for the process of charging of a quantum battery in a collisional model. Motivated by the question of whether such an advantage could be observed experimentally, we consider a model where the battery is modeled by a quantum harmonic oscillator or a large spin, charged via repeated interactions with a stream of non-equilibrium qubit units. For both setups, we show that a quantum protocol can significantly outperform the most general adaptive classical schemes, leading to 90\% and 38\% higher charging power for the cavity and large spin batteries respectively. Towards an experimental realization, we also characterise the robustness of this quantum advantage to imperfections (noise and decoherence) considering implementations with state-of-the-art micromasers and hybrid superconducting devices., Comment: 10+4 pages, 6 figures Related to: arXiv:2105.01863 and arXiv:2204.09995

Interfacing electrons and light enables ultrafast electron microscopy, quantum control of electrons, as well as new optical elements for high sensitivity imaging. Here we demonstrate for the first time programmable transverse electron beam shaping in free space based on ponderomotive potentials from short intense laser pulses. We can realize both convex and concave electron lenses with a focal length of a few millimeters, comparable to those in state-of-the-art electron microscopes. We further show that we can realize almost arbitrary deflection patterns by shaping the ponderomotive potentials using a spatial light modulator. Our modulator is lossless, programmable, has unity fill factor, and could pave the way to electron wavefront shaping with hundreds of individually addressable pixels., Comment: 13 pages, 9 figures

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments. This will result in the development of novel quantum sensors and a means to probe the foundations of quantum physics at the interface with gravity. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. These new technologies will open up the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade., Comment: 9 pages, 2 figures, submitted as a Research Campaign Whitepaper for the BPS2023 Decadal Survey

We study the Bayesian approach to thermometry with no prior knowledge about the expected temperature scale, through the example of energy measurements on fully or partially thermalized qubit probes. We show that the most common Bayesian estimators, namely the mean and the median, lead to high-temperature divergences when used for uninformed thermometry. To circumvent this and achieve better overall accuracy, we propose two new estimators based on an optimization of relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements the Cram\'er-Rao bound for smaller probe numbers and unrestricted temperature ranges. Furthermore, we show that, using partially thermalized probes, one can increase the range of temperatures to which the thermometer is sensitive at the cost of the local accuracy., Comment: 12 pages, 8 figures, v2: corrected conversion of the logarithmic error, v3: citations added

We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy., Comment: 4 pages, 5 figures

Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise., Comment: 10 pages, 10 figures

The model of continuous spontaneous localization (CSL) is the most prominent consistent modification of quantum mechanics predicting an objective quantum-to-classical transition. Here we show that precision interferometry with Bose-Einstein condensed atoms can serve to lower the current empirical bound on the localization rate parameter by several orders of magnitude. This works by focusing on the atom count distributions rather than just mean population imbalances in the interferometric signal of squeezed BECs, without the need for highly entangled GHZ-like states. In fact, the interplay between CSL-induced diffusion and dispersive atom-atom interactions results in an amplified sensitivity of the condensate to CSL. We discuss experimentally realistic measurement schemes utilizing state-of-the-art experimental techniques to test new regions of parameter space and, pushed to the limit, to probe and potentially rule out large relevant parameter regimes of CSL., Comment: 13 pages, 5 figures, 1 table

We assess the most macroscopic matter-wave experiments to date as to the extent to which they probe the quantum-classical boundary by demonstrating interference of heavy molecules and cold atomic ensembles. To this end, we consider a rigorous Bayesian test protocol for a parametrized set of hypothetical modifications of quantum theory, including well-studied spontaneous collapse models, that destroy superpositions and reinstate macrorealism. The range of modification parameters ruled out by the measurement events quantifies the macroscopicity of a quantum experiment, while the shape of the posterior distribution resulting from the Bayesian update reveals how conclusive the data are at testing macrorealism. This protocol may serve as a guide for the design of future matter-wave experiments ever closer to truly macroscopic scales., Comment: 13 pages, 9 figures

We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer's erasure strokes for optimal performance, we restrict this demon's action to pointer measurements, i.e. random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and operate in temperature regimes where quantum Otto engines would fail., Comment: 7 pages, 4 figures; accepted version

We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially independent. Using tools from parameter estimation theory, we show through a minimal qubit model that individual ancillas can already outperform the thermal Cramer-Rao bound. In addition, due to the steady-state nature of our model, when measured collectively the ancillas always exhibit superlinear scalings of the Fisher information. This means that even collective measurements on pairs of ancillas will already lead to an advantage. As we find in our qubit model, such a feature may be particularly valuable for weak system-ancilla interactions. Our approach sets forth the notion of metrology in a sequential interactions setting, and may inspire further advances in quantum thermometry.

The resource theory of thermal operations explains the state transformations that are possible in a very specific thermodynamic setting: there is only one thermal bath, auxiliary systems can only be in corresponding thermal state (free states), and the interaction must commute with the free Hamiltonian (free operation). In this paper we study the mildest deviation: the reservoir particles are subject to inhomogeneities, either in the local temperature (introducing resource states) or in the local Hamiltonian (generating a resource operation). For small inhomogeneities, the two models generate the same channel and thus the same state transformations. However, their thermodynamics is significantly different when it comes to work generation or to the interpretation of the "second laws of thermal operations"., Comment: 9 pages, 5 figures. Supersedes submission arXiv:1806.08108

We establish an objective scheme to determine the macroscopicity of quantum mechanical superposition tests, which is based on the Bayesian hypothesis falsification of macrorealistic modifications of quantum theory. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation and read-out of nanomechanical oscillators., Comment: 20 pages, 7 figures

We present a minimal model for the quantum evolution of matter under the influence of classical gravity in the Newtonian limit. Based on a continuous measurement-feedback channel that acts simultaneously on all constituent masses of a given quantum system, the model scales and applies consistently to arbitrary mass densities, and it recovers the classical Newton force between macroscopic masses. The concomitant loss of coherence is set by a model parameter, does not depend on mass, and can thus be confined to unobservable time scales for micro- and macroscopic systems alike. The model can be probed in high-precision matter-wave interferometry, and ultimately tested in recently proposed optomechanical quantum gravity experiments., Comment: 10 pages

We investigate the dynamics of interacting quantum planar rotors as the building blocks of gear trains and nano-machinery operating in the quantum regime. Contrary to a classical hard-gear scenario of rigidly interlocked teeth, we consider the coherent contact-less coupling through a finite interlocking potential and study the transmission of motion from one externally driven gear to the next as a function of the coupling parameters and gear profile. The transmission is assessed in terms of transferred angular momentum and transferred mechanical work. We highlight the quantum features of the model such as quantum state revivals in the interlocked rotation and interference-enhanced transmission, which could be observed in prospective rotational optomechanics experiments., Comment: 9 pages, 7 figures

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions with different probes do not overlap, but is otherwise valid for arbitrary values of the interaction strength and mean interaction time. We then apply it to some specific examples. For probes prepared in Gibbs states, such channels have been used to describe thermalisation: while this is the case for many choices of parameters, for others one finds out-of-equilibrium states including inverted Gibbs and maximally mixed states. Gapless probes can be interpreted as performing an indirect measurement, and we study the energy transfer associated with this measurement., Comment: 7+6 pages, 9 figures

In the resource theory of thermodynamics, the decrease of the free energy based on von Neumann entropy is not a sufficient condition to determine free evolution. Rather, a whole family of generalised free energies $F_{\alpha}$ must be monotonically decreasing. We study the resilience of this result to relaxations of the framework. We use a toy collisional model, in which the deviations from the ideal situation can be described as arising from inhomogeneities of local fields or temperatures. For any small amount of perturbation, we find that there exist initial states such that both single-shot and averaged values of $F_{\alpha}$ do not decrease monotonically for all $\alpha>0$. A geometric representation accounts for the observed behavior in a graphic way., Comment: 7 pages, 4 figures

This chapter presents autonomous quantum engines that generate work in the form of directed motion for a rotor. We first formulate a prototypical clock-driven model in a time-dependent framework and demonstrate how it can be translated into an autonomous engine with the introduction of a planar rotor degree of freedom. The rotor plays both the roles of internal engine clock and of work repository. Using the example of a single-qubit piston engine, the thermodynamic performance is then reviewed. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation; and we compare them with the actual energy output to an external dissipative load. The chapter closes with a quantum-classical comparison of the engine's dynamics. For the single-qubit piston example, we propose two alternative representations of the qubit in an entirely classical framework: (i) a coin flip model and (ii) a classical magnet moment, showing subtle differences between the quantum and classical descriptions., Comment: Chapter of the upcoming book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook"

We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all inter-spin coupling strengths. It describes the transition between previous approximate models for the weak and the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the inter-spin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime., Comment: 8 pages, 5 figures, several amendments; accepted in Phys. Rev. E

Pistons are elementary components of a wide variety of thermal engines, allowing to convert input fuel into rotational motion. Here, we propose a single-piston engine where the rotational degree of freedom is effectively realized by the flux of a Josephson loop -- a quantum rotor -- while the working volume corresponds to the effective length of a superconducting resonator. Our autonomous design implements a Carnot cycle, relies solely on standard thermal baths and can be implemented with circuit quantum electrodynamics. We demonstrate how the engine is able to extract a net positive work via its built-in synchronicity using a filter cavity as an effective valve, eliminating the need for external control., Comment: 7 pages, 3 figures

We study the mechanical performance of quantum rotor heat engines in terms of common notions of work using two prototypical models: a mill driven by the heat flow from a hot to a cold mode, and a piston driven by the alternate heating and cooling of a single working mode. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation, and we compare them to the energy output for the case of an external dissipative load and for externally driven engine cycles. Our results connect work definitions from both physical and information-theoretical perspectives. In particular, we find that apart from signatures of angular momentum quantization, the ergotropy is consistent with the intuitive notion of work in the form of net directed motion. It also agrees with the energy output to an external load or agent under optimal conditions. This sets forth a consistent thermodynamical description of rotating quantum motors, flywheels, and clocks., Comment: 22 pages, 9 figures, accepted version, added reference to L\"orch et al, 1802.10572

We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework., Comment: 11 pages, 8 figures; additions and corrections; accepted in Quantum on 2017-12-06

Quantum enhanced microscopy allows for measurements at high sensitivities and low damage. Recently, multi-pass microscopy was introduced as such a scheme, exploiting the sensitivity enhancement offered by multiple photon-sample interactions. Here we theoretically and numerically compare three different contrast enhancing techniques that are all based on self-imaging cavities: CW cavity enhanced microscopy, cavity ring-down microscopy and multi-pass microscopy. We show that all three schemes can lead to sensitivities beyond the standard quantum limit., Comment: 13 pages, 7 figures

We study how matter-wave interferometry with Bose-Einstein condensates is affected by hypothetical collapse models and by environmental decoherence processes. Motivated by recent atom fountain experiments with macroscopic arm separations, we focus on the observable signatures of first-order and higher-order coherence for different two-mode superposition states, and on their scaling with particle number. This can be used not only to assess the impact of environmental decoherence on many-body coherence, but also to quantify the extent to which macrorealistic collapse models are ruled out by such experiments. We find that interference fringes of phase-coherently split condensates are most strongly affected by decoherence, whereas the quantum signatures of independent interfering condensates are more immune against macrorealistic collapse. A many-body enhanced decoherence effect beyond the level of a single atom can be probed if higher-order correlations are resolved in the interferogram., Comment: 29 pages, 5 figures; minor clarifications

Thermodynamics is one of the oldest and well-established branches of physics that sets boundaries to what can possibly be achieved in macroscopic systems. While it started as a purely classical theory, it was realized in the early days of quantum mechanics that large quantum devices, such as masers or lasers, can be treated with the thermodynamic formalism. Remarkable progress has been made recently in the miniaturization of heat engines all the way to the single Brownian particle as well as to a single atom. However, despite several theoretical proposals, the implementation of heat machines in the fully quantum regime remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime, and demonstrate cooling below both the steady-state energy and the benchmark predicted by the classical thermodynamics treatment., Comment: 11 pages, 7 figures, 2 tables

The triumph of heat engines is their ability to convert the disordered energy of thermal sources into useful mechanical motion. In recent years, much effort has been devoted to generalizing thermodynamic notions to the quantum regime, partly motivated by the promise of surpassing classical heat engines. Here, we instead adopt a bottom-up approach: we propose a realistic autonomous heat engine that can serve as a testbed for quantum effects in the context of thermodynamics. Our model draws inspiration from actual piston engines and is built from closed-system Hamiltonians and weak bath coupling terms. We analytically derive the performance of the engine in the classical regime via a set of nonlinear Langevin equations. In the quantum case, we perform numerical simulations of the master equation. Finally, we perform a dynamic and thermodynamic analysis of the engine's behaviour for several parameter regimes in both the classical and quantum case, and find that the latter exhibits a consistently lower efficiency due to additional noise., Comment: 13 pages, 8 figures; added a thermodynamic analysis of the engine's performance

We present a theory for the diffraction of large molecules or nanoparticles at a standing light wave. Such particles can act as a genuine photon absorbers due to their numerous internal degrees of freedom effecting fast internal energy conversion. Our theory incorporates the interplay of three light-induced properties: the coherent phase modulation due to the dipole interaction, a non-unitary absorption-induced amplitude modulation described as a generalized measurement, and a coherent recoil splitting that resembles a quantum random walk in steps of the photon momentum. We discuss how these effects show up in near-field and far-field interference schemes, and we confirm our effective description by a dynamic evaluation of the grating interaction, which accounts for the internal states., Comment: 13 pages, 7 figures

Diffraction of matter-waves is an important demonstration of the fact that objects in nature possess a mixture of particle-like and wave-like properties. Unlike in the case of light diffraction, matter-waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of indium atoms is diffracted around a silicon dioxide sphere. The result is an amplification of the on-axis bright feature which is the matter-wave analogue of the well-known `Poisson spot' from optics. Our treatment confirms that the diffraction patterns resulting from our complete account of the sphere Casimir-Polder potential are indistinguishable from those found via a large-sphere non-retarded approximation in the discussed experiments, establishing the latter as an adequate model., Comment: 13 pages, 10 figures

We study the interaction of dielectric rods and disks with the laser field of a high finesse cavity. The quantum master equation for the coupled particle-cavity dynamics, including Rayleigh scattering, is derived for particle sizes comparable to the laser wavelength. We demonstrate that such anisotropic nanoparticles can be captured from free flight at velocities higher than those required to capture dielectric spheres of the same volume, and that efficient ro-translational cavity cooling into the deep quantum regime is achievable.

Optical control of nanoscale objects has recently developed into a thriving field of research with far-reaching promises for precision measurements, fundamental quantum physics and studies on single-particle thermodynamics. Here, we demonstrate the optical manipulation of silicon nanorods in high vacuum. Initially, we sculpture these particles into a silicon substrate with a tailored geometry to facilitate their launch into high vacuum by laser-induced mechanical cleavage. We manipulate and trace their center-of-mass and rotational motion through the interaction with an intense intra-cavity field. Our experiments show optical forces on nanorotors three times stronger than on silicon nanospheres of the same mass. The optical torque experienced by the spinning rods will enable cooling of the rotational motion and torsional opto-mechanics in a dissipation-free environment., Comment: 8 pages

We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and dispersive interaction with complex materials. We present Talbot-Lau interferometry (TLI), the Kapitza-Dirac-Talbot-Lau interferometer (KDTLI) and interferometry with pulsed optical gratings (OTIMA) as the most advanced devices to study the quantum wave nature of composite matter. These experiments define the current mass and complexity record in interferometric explorations of quantum macroscopicity and they open new avenues to quantum assisted metrology with applications in physical chemistry and biomolecular physics.

We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential equation. In the deterministic form of the equation, as studied so far, the nonlinearity would lead to diverging energy corrections for localized wave packets and would create observable correlations admitting faster-than-light communication. By regularizing the divergencies and adding specific random jumps or a specific Brownian noise process, the effect of the nonlinearity vanishes in the stochastic average and gives rise to a linear and Galilean invariant evolution of the density operator., Comment: 12 pages, minor corrections, equivalent to published version

We investigate the influence of thermally activated internal molecular dynamics on the phase shifts of matter waves inside a molecule interferometer. While de Broglie physics generally describes only the center-of-mass motion of a quantum object, our experiment demonstrates that the translational quantum phase is sensitive to dynamic conformational state changes inside the diffracted molecules. The structural flexibility of tailor-made hot organic particles is sufficient to admit a mixture of strongly fluctuating dipole moments. These modify the electric susceptibility and through this the quantum interference pattern in the presence of an external electric field. Detailed molecular dynamics simulations combined with density functional theory allow us to quantify the time-dependent structural reconfigurations and to predict the ensemble-averaged square of the dipole moment which is found to be in good agreement with the interferometric result. The experiment thus opens a new perspective on matter wave interferometry as it demonstrates for the first time that it is possible to collect structural information about molecules even if they are delocalized over more than hundred times their own diameter., Comment: 5 pages, 3 figures

Quantum experiments with nanomechanical oscillators are regarded as a testbed for hypothetical modifications of the Schr\"{o}dinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macro-scale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements., Comment: 3 figures, revised version with extended supplemental material