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# Stefan Nimmrichter

Junior Professor

Room: B-004

Phone: +49 271 740 3873

## Preprints

Namrata Shukla, Stefan Nimmrichter and Barry C. Sanders
Squeezed comb states
arXiv:2009.12888

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, 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.

Björn Schrinski, Klaus Hornberger and Stefan Nimmrichter
How to rule out collapse models with BEC interferometry
arXiv:2008.13580

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 six 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 preparing highly entangled states. We discuss experimentally realistic measurement schemes which could probe and potentially rule out the entire relevant parameter space of CSL, including the historic values proposed by Ghirardi, Rimini, and Weber, below which CSL is no longer deemed a viable solution to the measurement problem of quantum mechanics.

Kiran E. Khosla and Stefan Nimmrichter
Classical Channel Gravity in the Newtonian Limit
arXiv:1812.03118

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.

Angeline Shu, Yu Cai, Stella Seah, Stefan Nimmrichter and Valerio Scarani
Violation of all the second laws of thermal operations by inhomogeneous reservoirs
arXiv:1806.08108

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.

Stella Seah, Stefan Nimmrichter, Alexandre Roulet and Valerio Scarani
Quantum Rotor Engines
arXiv:1804.11023

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.

Stefan Nimmrichter, Chi-Fang Chen, Brannon B. Klopfer, Mark A. Kasevich and Thomas Juffmann
Full-field cavity enhanced microscopy techniques
arXiv:1704.05217

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.

## Publications

Stella Seah, Stefan Nimmrichter and Valerio Scarani
Maxwell's lesser demon: a quantum engine driven by pointer measurements
Phys. Rev. Lett. 124, 100603 (2020), arXiv:1908.10102

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.

Stella Seah, Stefan Nimmrichter, Daniel Grimmer, Jader P. Santos, Valerio Scarani and Gabriel T. Landi
Collisional quantum thermometry
Phys. Rev. Lett. 123, 180602 (2019), arXiv:1904.12551

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.

Angeline Shu, Yu Cai, Stella Seah, Stefan Nimmrichter and Valerio Scarani
Almost thermal operations: inhomogeneous reservoirs
Phys. Rev. A 10, , 042107 (2019), arXiv:1904.08736

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".

Björn Schrinski, Stefan Nimmrichter, Benjamin A. Stickler and Klaus Hornberger
Macroscopicity of quantum mechanical superposition tests via hypothesis falsification
Phys. Rev. A 10, , 032111 (2019), arXiv:1902.11092

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.

Zheng Liu, Joshua Leong, Stefan Nimmrichter and Valerio Scarani
Quantum gears from planar rotors
Phys. Rev. E 99, 042202 (2019), arXiv:1810.13121

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.

Stella Seah, Stefan Nimmrichter and Valerio Scarani
Nonequilibrium Dynamics with Finite-Time Repeated Interactions
Phys. Rev. E 99, 042103 (2019), arXiv:1809.04781

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.

Gleb Maslennikov, Shiqian Ding, Roland Hablutzel, Jaren Gan, Alexandre Roulet, Stefan Nimmrichter, Jibo Dai, Valerio Scarani and Dzmitry Matsukevich
Quantum absorption refrigerator with trapped ions
Nature Com, nications 10, 202 (2019), arXiv:1702.08672

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.

Stella Seah, Stefan Nimmrichter and Valerio Scarani
Refrigeration beyond weak internal coupling
Phys. Rev. E 98, 012131 (2018), arXiv:1803.02002

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.

Alexandre Roulet, Stefan Nimmrichter and Jacob M. Taylor
An autonomous single-piston engine with a quantum rotor
Quantum S, . Technol. 3, 035008 (2018), arXiv:1802.05486

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.

Stella Seah, Stefan Nimmrichter and Valerio Scarani
Work production of quantum rotor engines
New J. Phys. 20, 043045 (2018), arXiv:1801.02820

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.

Stefan Nimmrichter, Jibo Dai, Alexandre Roulet and Valerio Scarani
Quantum and classical dynamics of a three-mode absorption refrigerator
Quantum 1, 37 (2017), arXiv:1709.08353

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.

Björn Schrinski, Klaus Hornberger and Stefan Nimmrichter
Sensing spontaneous collapse and decoherence with interfering Bose-Einstein condensates
Quantum S, . Technol. 2, 044010 (2017), arXiv:1704.03608

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.

Giulio Gasbarri, Marko Toroš and Angelo Bassi
General Galilei Covariant Gaussian Maps
Phys. Rev. Lett. 119, 100403 (2017), arXiv:1703.05790

We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we characterize translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined in Nimmrichter and Hornbergerl. [Phys. Rev. Lett. 110, 16 (2013)].

Alexandre Roulet, Stefan Nimmrichter, Juan Miguel Arrazola, Stella Seah and Valerio Scarani
Autonomous Rotor Heat Engine
Phys. Rev. E 95, 062131 (2017), arXiv:1609.06011

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.

Kai Walter, Stefan Nimmrichter and Klaus Hornberger
Multi-photon absorption in optical gratings for matter waves
Phys. Rev. A 94, 043637 (2016), arXiv:1608.07135

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.

Joshua Leo Hemmerich, Robert Bennett, Thomas Reisinger, Stefan Nimmrichter, Johannes Fiedler, Horst Hahn, Herbert Gleiter and Stefan Yoshi Buhmann
Impact of Casimir-Polder interaction on Poisson-spot diffraction at a dielectric sphere
Phys. Rev. A 94, 023621 (2016), arXiv:1606.09472

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.

Benjamin A. Stickler, Stefan Nimmrichter, Lukas Martinetz, Stefan Kuhn, Markus Arndt and Klaus Hornberger
Ro-Translational Cavity Cooling of Dielectric Rods and Disks
Phys. Rev. A 94, 033818 (2016), arXiv:1605.05674

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.

Stefan Kuhn, Peter Asenbaum, Alon Kosloff, Michele Sclafani, Benjamin A. Stickler, Stefan Nimmrichter, Klaus Hornberger, Ori Cheshnovsky, Fernando Patolsky and Markus Arndt
Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum
Nano Letters ,, 604 (2015), arXiv:1506.04881

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.

Stefan Nimmrichter and Klaus Hornberger
Stochastic extensions of the regularized Schrödinger-Newton equation
Phys. Rev. D 91, 024016 (2015), arXiv:1410.4702

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.

Stefan Nimmrichter, Klaus Hornberger and Klemens Hammerer
Optomechanical sensing of spontaneous wave-function collapse
Phys. Rev. Lett. 113, 020405 (2014), arXiv:1405.2868

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.

James Bateman, Stefan Nimmrichter, Klaus Hornberger and Hendrik Ulbricht
Near-field interferometry of a free-falling nanoparticle from a point-like source
Nature Com, nications 5:4788 (2014), arXiv:1312.0500

Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories---conceived to explain the apparent quantum to classical transition---forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled, and then free-falling silicon nanoparticle in the mass range of one million atomic mass units, delocalized over more than 150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.

Philipp Haslinger, Nadine Dörre, Philipp Geyer, Jonas Rodewald, Stefan Nimmrichter and Markus Arndt
A universal matter-wave interferometer with optical ionization gratings in the time domain
Nature Phy, cs 9, 144 148 (2013), arXiv:1402.1364

Matter-wave interferometry with atoms and molecules has attracted a rapidly growing interest over the past two decades, both in demonstrations of fundamental quantum phenomena and in quantum-enhanced precision measurements. Such experiments exploit the non-classical superposition of two or more position and momentum states which are coherently split and rejoined to interfere. Here, we present the experimental realization of a universal near-field interferometer built from three short-pulse single-photon ionization gratings. We observe quantum interference of fast molecular clusters, with a composite de Broglie wavelength as small as 275 fm. Optical ionization gratings are largely independent of the specific internal level structure and are therefore universally applicable to different kinds of nanoparticles, ranging from atoms to clusters, molecules and nanospheres. The interferometer is sensitive to fringe shifts as small as a few nanometers and yet robust against velocity-dependent phase shifts, since the gratings exist only for nanoseconds and form an interferometer in the time domain.

Peter Asenbaum, Stefan Kuhn, Stefan Nimmrichter, Ugur Sezer and Markus Arndt
Cavity cooling of free silicon nanoparticles in high-vacuum
Nat. Commun. 4:, 743 (2013), arXiv:1306.4617

Laser cooling has given a boost to atomic physics throughout the last thirty years since it allows one to prepare atoms in motional states which can only be described by quantum mechanics. Most methods, such as Doppler cooling, polarization gradient cooling or sub-recoil laser cooling rely, however, on a near-resonant and cyclic coupling between laser light and well-defined internal states. Although this feat has recently even been achieved for diatomic molecules, it is very hard for mesoscopic particles. It has been proposed that an external cavity may compensate for the lack of internal cycling transitions in dielectric objects and it may thus provide assistance in the cooling of their centre of mass state. Here, we demonstrate cavity cooling of the transverse kinetic energy of silicon nanoparticles propagating in genuine high-vacuum (< 10^8 mbar). We create and launch them with longitudinal velocities even down to v < 1 m/s using laser induced thermomechanical stress on a pristine silicon wafer. The interaction with the light of a high-finesse infrared cavity reduces their transverse kinetic energy by more than a factor of 30. This is an important step towards new tests of recent proposals to explore the still speculative non-linearities of quantum mechanics with objects in the mass range between 10^7 and 10^10 amu.

Stefan Nimmrichter and Klaus Hornberger
Macroscopicity of Mechanical Quantum Superposition States
Phys. Rev. Lett. 110, 160403 (2013), arXiv:1205.3447

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Klaus Hornberger, Stefan Gerlich, Philipp Haslinger, Stefan Nimmrichter and Markus Arndt
Colloquium: Quantum interference of clusters and molecules
Rev. Mod. Phys , , 157 (2012), arXiv:1109.5937

We review recent progress and future prospects of matter wave interferometry with complex organic molecules and inorganic clusters. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. We discuss the theoretical concepts underlying these experiments and the experimental challenges. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. We conclude by investigating the prospects for probing the quantum superposition principle in the limit of high particle mass and complexity.

Thomas Juffmann, Stefan Nimmrichter, Markus Arndt, Herbert Gleiter and Klaus Hornberger
New prospects for de Broglie interferometry
Found. Phys. 42, 98 (2012), arXiv:1009.1569

We consider various effects that are encountered in matter wave interference experiments with massive nanoparticles. The text-book example of far-field interference at a grating is compared with diffraction into the dark field behind an opaque aperture, commonly designated as Poisson's spot or the spot of Arago. Our estimates indicate that both phenomena may still be observed in a mass range exceeding present-day experiments by at least two orders of magnitude. They both require, however, the development of sufficiently cold, intense and coherent cluster beams. While the observation of Poisson's spot offers the advantage of non-dispersiveness and a simple distinction between classical and quantum fringes in the absence of particle wall interactions, van der Waals forces may severely limit the distinguishability between genuine quantum wave diffraction and classically explicable spots already for moderately polarizable objects and diffraction elements as thin as 100 nm.

Stefan Nimmrichter, Klaus Hornberger, Philipp Haslinger and Markus Arndt
Testing spontaneous localization theories with matter-wave interferometry
Phys. Rev. A 83, 043621 (2011), arXiv:1103.1236

We propose to test the theory of continuous spontaneous localization (CSL) in an all-optical time-domain Talbot-Lau interferometer for clusters with masses exceeding 1000000 amu. By assessing the relevant environmental decoherence mechanisms, as well as the growing size of the particles relative to the grating fringes, we argue that it will be feasible to test the quantum superposition principle in a mass range excluded by recent estimates of the CSL effect.

Stefan Nimmrichter, Philipp Haslinger, Klaus Hornberger and Markus Arndt
Concept of an ionizing time-domain matter-wave interferometer
New J. Phys. 13, 075002 (2011), arXiv:1102.3644

We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single photon-absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle-light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot-Lau-like interference effect with a characteristic dependence on the pulse delay time.

Michael Gring, Stefan Gerlich, Sandra Eibenberger, Stefan Nimmrichter, Tarik Berrada, Markus Arndt, Hendrik Ulbricht, Klaus Hornberger, Marcel Müri, Marcel Mayor, Marcus Böckmann and Nikos Doltsinis
Influence of conformational molecular dynamics on matter wave interferometry
Phys. Rev. A 81, 031604(R) (2010), arXiv:1405.4649

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.

Stefan Nimmrichter, Klemens Hammerer, Peter Asenbaum, Helmut Ritsch and Markus Arndt
Master Equation for the Motion of a Polarizable Particle in a Multimode Cavity
New J. Phys. 12, 083003 (2010), arXiv:1004.0807

We derive a master equation for the motion of a polarizable particle weakly interacting with one or several strongly pumped cavity modes. We focus here on massive particles with complex internal structure such as large molecules and clusters, for which we assume a linear scalar polarizability mediating the particle-light interaction. The predicted friction and diffusion coefficients are in good agreement with former semiclassical calculations for atoms and small molecules in weakly pumped cavities, while the current rigorous quantum treatment and numerical assessment sheds a light on the feasibility of experiments that aim at optically manipulating beams of massive molecules with multimode cavities.

Klaus Hornberger, Stefan Gerlich, Hendrik Ulbricht, Lucia Hackermüller, Stefan Nimmrichter, Ilya V. Goldt, Olga Boltalina and Markus Arndt
Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry
New J. Phys. 11, 043032 (2009), arXiv:0902.0234

Kapitza-Dirac-Talbot-Lau interferometry (KDTLI) has recently been established for demonstrating the quantum wave nature of large molecules. A phase space treatment permits us to derive closed equations for the near-field interference pattern, as well as for the Moire-type pattern that would arise if the molecules were to be treated as classical particles. The model provides a simple and elegant way to account for the molecular phase shifts related to the optical dipole potential as well as for the incoherent effect of photon absorption at the second grating. We present experimental results for different molecular masses, polarizabilities and absorption cross sections using fullerenes and fluorofullerenes and discuss the alignment requirements. Our results with C60 and C70, C60F36 and C60F48 verify the theoretical description to a high degree of precision.

Stefan Nimmrichter, Klaus Hornberger, Hendrik Ulbricht and Markus Arndt
Absolute absorption spectroscopy based on molecule interferometry
Phys. Rev. A *7, *, 063607 (2008), arXiv:0811.1141

We propose a new method to measure the absolute photon absorption cross section of neutral molecules in a molecular beam. It is independent of our knowledge of the particle beam density, nor does it rely on photo-induced fragmentation or ionization. The method is based on resolving the recoil resulting from photon absorption by means of near-field matter-wave interference, and it thus applies even to very dilute beams with low optical densities. Our discussion includes the possibility of internal state conversion as well as fluorescence. We assess the influence of various experimental uncertainties and show that the measurement of absolute absorption cross sections is conceivable with high precision and using existing technologies.

Stefan Nimmrichter and Klaus Hornberger
Theory of near-field matter wave interference beyond the eikonal approximation
Phys. Rev. A 78, 023612 (2008), arXiv:0804.3006

A generalized description of Talbot-Lau interference with matter waves is presented, which accounts for arbitrary grating interactions and realistic beam characteristics. The dispersion interaction between the beam particles and the optical elements strongly influences the interference pattern in this near-field effect, and it is known to dominate the fringe visibility if increasingly massive and complex particles are used. We provide a general description of the grating interaction process by combining semiclassical scattering theory with a phase space formulation. It serves to systematically improve the eikonal approximation used so far, and to assess its regime of validity.