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We revisit the Dicke superradiance problem, namely finding the time evolution of the density operator for an initially inverted ensemble of $N$ identical two-level systems (spins), undergoing collective spontaneous decay. We derive a compactly written, easily computable and fully analytical solution, valid for any time during the evolution and for any $N$.

Entanglement in hybrid quantum systems comprised of fundamentally different degrees of freedom, such as light and mechanics is of interest for a wide range of applications in quantum technologies. Here, we propose to engineer bipartite entanglement between traveling acoustic phonons in a Brillouin active solid state system and the accompanying light wave. The effect is achieved by applying optical pump pulses to state-of-the-art waveguides, exciting a Brillouin Stokes process. This pulsed approach, in a system operating in a regime orthogonal to standard optomechanical setups, allows for the generation of entangled photon-phonon pairs, resilient to thermal fluctuations. We propose an experimental platform where readout of the optoacoustics entanglement is done by the simultaneous detection of Stokes and Anti-Stokes photons in a two-pump configuration. The proposed mechanism presents an important feature in that it does not require initial preparation of the quantum ground state of the phonon mode.

Standard cavity cooling of atoms or dielectric particles is based on the action of dispersive optical forces in high-finesse cavities. We investigate here a complementary regime characterized by large cavity losses, resembling the standard Doppler cooling technique. For a single two-level emitter a modification of the cooling rate is obtained from the Purcell enhancement of spontaneous emission in the large cooperativity limit. This mechanism is aimed at cooling of quantum emitters without closed transitions, which is the case for molecular systems, where the Purcell effect can mitigate the loss of population from the cooling cycle. We extend our analytical formulation to the many particle case governed by weak individual coupling but exhibiting collective strong Purcell enhancement to a cavity mode., Comment: 9+5 pages, 7 figures

Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that, under external magnetic field control, stacked layers of quantum metasurfaces can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules., Comment: 6+11 pages, 2+3 figures

We study the photophysics of molecular aggregates from a quantum optics perspective, with emphasis on deriving scaling laws for the fast non-radiative relaxation of collective electronic excitations, referred to as Kasha's rule. Aggregates exhibit an energetically broad manifold of collective states with delocalized electronic excitations originating from near field dipole-dipole exchanges between neighboring monomers. Photo-excitation at optical wavelengths, much larger than the monomer-monomer average separation, addresses almost exclusively symmetric collective states, which for an arrangement known as H-aggregate, show an upward hypsochromic shift. The extremely fast subsequent non-radiative relaxation via intramolecular vibrational modes populates lower energy, subradiant states, resulting in an effective inhibition of fluorescence. Our analytical treatment allows for the derivation of an approximate scaling law of this relaxation process, linear in the number of available low energy vibrational modes and directly proportional to the dipole-dipole interaction strength between neighbouring monomers.

Physical and chemical properties of materials can be modified by a resonant optical mode. Such recent demonstrations have mostly relied on a planar cavity geometry, others have relied on a plasmonic resonator. However, the combination of these two device architectures have remained largely unexplored, especially in the context of maximizing light-matter interactions. Here, we investigate several schemes of electromagnetic field confinement aimed at facilitating the collective coupling of a localized photonic mode to molecular vibrations in the terahertz region. The key aspects are the use of metasurface plasmonic structures combined with standard Fabry-Perot configurations and the deposition of a thin layer of glucose, via a spray coating technique, within a tightly focused electromagnetic mode volume. More importantly, we demonstrate enhanced vacuum Rabi splittings reaching up to 200 GHz when combining plasmonic resonances, photonic cavity modes and low-energy molecular resonances. Furthermore, we demonstrate how a cavity mode can be utilized to enhance the zero-point electric field amplitude of a plasmonic resonator. Our study provides key insight into the design of polaritonic platforms with organic molecules to harvest the unique properties of hybrid light-matter states., Comment: 7 pages (5 Figures) + 7 pages Appendix (5 Figures), updated version

We describe applications of two-dimensional subwavelength quantum emitter arrays as efficient optical elements in the linear regime. For normally incident light, the cooperative optical response, stemming from emitter-emitter dipole exchanges, allows the control of the array's transmission, its resonance frequency, and bandwidth. Operations on fully polarized incident light, such as generic linear and circular polarizers as well as phase retarders can be engineered and described in terms of Jones matrices. Our analytical approach and accompanying numerical simulations identify optimal regimes for such operations and reveal the importance of adjusting the array geometry and of the careful tuning of the external magnetic fields amplitude and direction., Comment: 12 pages main text + 4 Appendix, 8 figures

We propose an adaptive phase technique for the parametric cooling of mechanical resonances. This involves the detection of the mechanical quadratures, followed by a sequence of periodic controllable adjustments of the phase of a parametric modulation. The technique allows the preparation of the quantum ground state with an exponential loss of thermal energy, similarly to the case of cold-damping or cavity self-cooling. Analytical derivations are presented for the cooling rate and final occupancies both in the classical and quantum regimes.

Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom. While vibrations are typically considered detrimental to coherent dynamics, we show that molecular dimers or rings can be operated as platforms for the preparation of long-lived dark superposition states aided by vibrational relaxation. In closed ring configurations, we extend previous predictions for the generation of coherent light from ideal quantum emitters to molecular emitters, quantifying the role of vibronic coupling onto the output intensity and coherence., Comment: 16 pages, 8 figures

Quantum cooperativity is evident in light-matter platforms where quantum emitter ensembles are interfaced with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum. Cooperative effects can find applications, among other areas, in topological quantum optics, in quantum metrology or in quantum information. This tutorial provides a set of theoretical tools to tackle the behavior responsible for the onset of cooperativity by extending open quantum system dynamics methods, such as the master equation and quantum Langevin equations, to electron-photon interactions in strongly coupled and correlated quantum emitter ensembles. The methods are illustrated on a wide range of current research topics such as the design of nanoscale coherent light sources, highly-reflective quantum metasurfaces or low intracavity power superradiant lasers. The analytical approaches are developed for ensembles of identical two-level quantum emitters and then extended to more complex systems where frequency disorder or vibronic couplings are taken into account. The relevance of the approach ranges from atoms in optical lattices to quantum dots or molecular systems in solid-state environments., Comment: 43 pages, 18 figures; revised version; contains some additional material w.r.t. published version

We investigate a one-dimensional quantum emitter chain where transport of excitations and correlations takes place via nearest neighbor, dipole-dipole interactions. In the presence of collective radiative emission, we show that a phase imprinting wavepacket initialization procedure can lead to subradiant transport and can preserve quantum correlations. In the context of cavity mediated transport, where emitters are coupled to a common delocalized optical mode, we analyze the effect of frequency disorder and nonidentical photon-emitter couplings on excitation transport.

We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equations approach, we derive correlation functions and stationary quantities showing strongly modified optical response of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes, in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced vibronic coherence as well as control over vibrational sideband amplitudes. The additional coupling to an infrared cavity allows for the controlled suppression of undesired sidebands, an effect stemming from the Purcell enhancement of vibrational relaxation rates., Comment: [v4]: minor updates to published version

We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, near-field effects and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder alone can already introduce a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS with the level of disorder. Disorder additionally can split a molecular ensemble into donor-type and acceptor-type molecules and the combination of vibronic coupling, dipole-dipole interactions and vibrational relaxation induces an incoherent FRET (F\"{o}rster resonance energy transfer) migration of excitations within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, high-density limit. Overall, this analysis allows to quantify the crucial role played by dark states in cavity quantum electrodynamics with mesoscopic, disordered ensembles.

We investigate the role of time delay in cold-damping optomechanics with multiple mechanical resonances. For instantaneous electronic response, it was recently shown in \textit{Phys. Rev. Lett. \textbf{123}, 203605 (2019)}, that a single feedback loop is sufficient to simultaneously remove thermal noise from many mechanical modes. While the intrinsic delayed response of the electronics can induce single mode and mutual heating between adjacent modes, we propose to counteract such detrimental effects by introducing an additional time delay to the feedback loop. For lossy cavities and broadband feedback, we derive analytical results for the final occupancies of the mechanical modes within the formalism of quantum Langevin equations. For modes that are frequency degenerate collective effects dominate, mimicking behavior similar to Dicke super- and subradiance. These analytical results, corroborated with numerical simulations of both transient and steady state dynamics, allow to find suitable conditions and strategies for efficient single or multimode feedback optomechanics.

We investigate the influence of light-matter interactions on correlated quantum matter by studying the paradigmatic Ising model subject to a quantum Rabi coupling. This type of coupling to a confined, spatially delocalized bosonic light mode, such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As a consequence, the symmetry-broken magnetic state breaks down for strong enough light-mater interactions to a paramagnetic state. The non-local character of the bosonic mode can change the quantum phase transition in a drastic manner, which we analyze quantitatively for the simplest case of a chain geometry (Dicke-Ising chain). The results show a direct transition between a magnetically ordered phase with zero photon density and a magnetically polarized phase with lasing behaviour of the light. Our predictions are equally valid for the dual quantized Ising chain in a conventional transverse magnetic field., Comment: 17 pages, 6 figures

Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations and phonons. In particular, the strong vibronic interaction between electrons and nuclear motion in a molecule resembles the optomechanical radiation pressure Hamiltonian. While molecular vibrations are often in the ground state even at elevated temperatures, one still needs to get a handle on decoherence channels associated with phonons before an efficient quantum optical network based on opto-vibrational interactions in solid-state molecular systems could be realized. As a step towards a better understanding of decoherence in phononic environments, we take here an open quantum system approach to the non-equilibrium dynamics of guest molecules embedded in a crystal, identifying regimes of Markovian versus non-Markovian vibrational relaxation. A stochastic treatment based on quantum Langevin equations predicts collective vibron-vibron dynamics that resembles processes of sub- and superradiance for radiative transitions. This in turn leads to the possibility of decoupling intramolecular vibrations from the phononic bath, allowing for enhanced coherence times of collective vibrations. For molecular polaritonics in strongly confined geometries, we also show that the imprint of opto-vibrational couplings onto the emerging output field results in effective polariton cross-talk rates for finite bath occupancies., Comment: [v2]: revised abstract and introduction, [v3]: corrected rotating frame in Eqs. (31)

We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard cold-damping technique where homodyne read-out of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independently of the number of modes addressed by the feedback as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint towards the design of frequency resolved mechanical resonators where efficient refrigeration is possible via simultaneous cold-damping feedback.

We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The feedback is obtained from a neural network parametrized policy trained via a reinforcement learning strategy to choose the correct sequence of actions from a finite set in order to simultaneously reduce the energy of many modes of vibration. The actions are realized either as optical modulations of the spring constants in the so-called quadratic optomechanical coupling regime or as radiation pressure induced momentum kicks in the linear coupling regime. As a proof of principle we numerically illustrate efficient simultaneous cooling of four independent modes with an overall strong reduction of the total system temperature., Comment: Machine learning in Optomechanics: cooling

We discuss a technique to strongly couple a single target quantum emitter to a cavity mode, which is enabled by virtual excitations of a nearby mesoscopic ensemble of emitters. A collective coupling of the latter to both the cavity and the target emitter induces strong photon non-linearities in addition to polariton formation, in contrast to common schemes for ensemble strong coupling. We demonstrate that strong coupling at the level of a single emitter can be engineered via coherent and dissipative dipolar interactions with the ensemble, and provide realistic parameters for a possible implementation with SiV$^{-}$ defects in diamond. Our scheme can find applications, amongst others, in quantum information processing or in the field of cavity-assisted quantum chemistry., Comment: 13 pages, 6 figures; substantially revised manuscript; see arXiv:1912.12703 for mathematical derivations

We present a general framework for cavity quantum electrodynamics with strongly frequency-dependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photonic-crystal mirrors or with two-dimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard input--output formalism to explicitly include the dynamics of the mirror's internal resonance. We show how to directly extract the interaction tuning parameters from the comparison with classical transfer matrix theory and how to treat the non-Markovian dynamics of the cavity field mode introduced by the mirror's internal resonance. As an application within optomechanics, we illustrate how a non-Markovian Fano cavity possessing a flexible photonic crystal mirror can provide both sideband resolution as well as strong heating suppression in optomechanical cooling. This approach, amenable to a wide range of systems, opens up possibilities for using hybrid frequency-dependent reflectors in cavity quantum electrodynamics for engineering novel forms of light-matter interactions.

We theoretically study prospects and limitations of a new route towards macroscopic scale laser refrigeration based on exciplex-mediated frequency up-conversion in gas filled hollow-core fibres. Using proven quantum optical rate equations we model the dynamics of a dopant-buffer gas mixture filling an optically pumped waveguide. In the particular example of alkali-noble gas mixtures, recent high pressure gas cell setup experiments have shown that efficient kinetic energy extraction cycles appear via the creation of transient exciplex excited electronic bound states. The cooling cycle consists of absorption of lower energy laser photons during collisions followed by blue-shifted spontaneous emission on the atomic line of the alkali atoms. For any arbitrary dopant-buffer gas mixture, we derive scaling laws for cooling power, cooling rates and temperature drops with varying input laser power, dopant and buffer gas concentration, fibre geometry and particularities of the exciplex ground and excited state potential landscapes.

We investigate the interaction between light and molecular systems modeled as quantum emitters coupled to a multitude of vibrational modes via a Holstein-type interaction. We follow a quantum Langevin equations approach that allows for analytical derivations of absorption and fluorescence profiles of molecules driven by classical fields or coupled to quantized optical modes. We retrieve analytical expressions for the modification of the radiative emission branching ratio in the Purcell regime and for the asymmetric cavity transmission associated with dissipative cross-talk between upper and lower polaritons in the strong coupling regime. We also characterize the F\"{o}rster resonance energy transfer process between donor-acceptor molecules mediated by the vacuum or by a cavity mode.

The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole-dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of Pi/2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a second-order approximation accounting for pairwise atom-atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cut-off for the interaction range emerging from the dephasing of different fiber contributions., Comment: 17 pages, 7 figures

Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity $C$, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, $C$ is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)] we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.

Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated Tavis--Cummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems., Comment: 19 pages, 5 figures

The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub- and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.

We study the interplay between charge transport and light-matter interactions in a confined geometry, by considering an open, mesoscopic chain of two-orbital systems resonantly coupled to a single bosonic mode close to its vacuum state. We introduce and benchmark different methods based on self-consistent solutions of non-equilibrium Green's functions and numerical simulations of the quantum master equation, and derive both analytical and numerical results. It is shown that in the dissipative regime where the cavity photon decay rate is the largest parameter, the light-matter coupling is responsible for a steady-state current enhancement scaling with the cooperativity parameter. We further identify different regimes of interest depending on the ratio between the cavity decay rate and the electronic bandwidth. Considering the situation where the lower band has a vanishing bandwidth, we show that for a high-finesse cavity, the properties of the resonant Bloch state in the upper band are transfered to the lower one, giving rise to a delocalized state along the chain. Conversely, in the dissipative regime with low cavity quality factors, we find that the current enhancement is due to a collective decay of populations from the upper to the lower band., Comment: 52 pages, 11 figures

We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for considerable contrast and phase decay, the cavity scenario can exhibit similar behavior at much lower densities., Comment: 8 pages, 4 figures

An array of $N$ closely spaced dipole coupled quantum emitters exhibits super- and subradiance with characteristic tailorable spatial radiation patterns. Optimizing their geometry and distance with respect to the spatial profile of a near resonant optical cavity mode allows to increase the ratio between light scattering into the cavity mode and free space by several orders of magnitude. This leads to a distinct nonlinear particle number scaling of the relative strength of coherent light-matter interactions versus decay. In particular, for subradiant states the collective cooperativity increases much faster than the typical linear $\propto N$ scaling of independent emitters. This extraordinary collective enhancement is manifested both in the intensity and phase profile of the sharp collective emitter antiresonances detectable at the cavity output port via transmission spectroscopy.

We theoretically investigate charge transport through electronic bands of a mesoscopic one-dimensional system, where inter-band transitions are coupled to a confined cavity mode, initially prepared close to its vacuum. This coupling leads to light-matter hybridization where the dressed fermionic bands interact via absorption and emission of dressed cavity-photons. Using a self-consistent non-equilibrium Green's function method, we compute electronic transmissions and cavity photon spectra and demonstrate how light-matter coupling can lead to an enhancement of charge conductivity in the steady-state. We find that depending on cavity loss rate, electronic bandwidth, and coupling strength, the dynamics involves either an individual or a collective response of Bloch states, and explain how this affects the current enhancement. We show that the charge conductivity enhancement can reach orders of magnitudes under experimentally relevant conditions.

We investigate structural resonances in multi-element optical resonators and provide a roadmap for the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of three- and four-mirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced light-matter interactions in the context of cavity quantum electrodynamics and cavity optomechanics.

Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential light shift free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling $1/\sqrt{\tau}$ with $\tau$ being the interrogation time. We employ a technique using decoherence free subspaces first introduced in New J. Phys. \textbf{14}, 043011 (2012) which can restore the scaling with the square root of the inverse particle number $1/\sqrt{N}$. Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.

We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities., Comment: 16 pages, 3 figures

Inherent binary or collective interactions in ensembles of quantum emitters induce a spread in the energy and lifetime of their eigenstates. While this typically causes fast decay and dephasing, in many cases certain special entangled collective states with minimal decay can be found, which possess ideal properties for spectroscopy, precision measurements or information storage. We show that for a specific choice of laser frequency, power and geometry or a suitable configuration of control fields one can efficiently prepare these states. We demonstrate this by studying preparation schemes for strongly subradiant entangled states of a chain of dipole-dipole coupled emitters. The prepared state fidelity and its entanglement depth is further improved via spatial excitation phase engineering or tailored magnetic fields., Comment: 11 pages, 4 figures

Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.

We show that exciton-type transport in certain materials can be dramatically modified by their inclusion in an optical cavity: the modification of the electromagnetic vacuum mode structure introduced by the cavity leads to transport via delocalized polariton modes rather than through tunneling processes in the material itself. This can help overcome exponential suppression of transmission properties as a function of the system size in the case of disorder and other imperfections. We exemplify massive improvement of transmission for excitonic wave-packets through a cavity, as well as enhancement of steady-state exciton currents under incoherent pumping. These results may have implications for experiments of exciton transport in disordered organic materials. We propose that the basic phenomena can be observed in quantum simulators made of Rydberg atoms, cold molecules in optical lattices, as well as in experiments with trapped ions., Comment: 10 pages, 7 figures, [v2]: Updated reference to complementary work arXiv:1409.2514, [v3]: Update to version accepted for publication

We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit superradiant collective decay and dipole-dipole induced frequency shifts, recent results [Ostermann, Ritsch and Genes, Phys. Rev. Lett. \textbf{111}, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an in-depth analysis of this 'protected subspace Ramsey technique' using improved analytical modeling and numerical simulations including larger 3D samples. Surprisingly we find that using sub-radiant states of $N$ particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than $1/\sqrt{N}$. Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth., Comment: 9 pages, 7 figures

We investigate the dynamics of a mechanical resonator in which is embedded an ensemble of two-level systems interacting with an optical cavity field. We show that this hybrid approach to optomechanics allows for enhanced effective interactions between the mechanics and the cavity field, leading for instance to ground state cooling of the mechanics, even in regimes, like the unresolved sideband regime, in which standard radiation pressure cooling would be inefficient., Comment: 9 pages, 4 figures

We investigate the optomechanical photon-phonon coupling of a single light mode propagating through an array of vibrating mechanical elements. As recently shown for the particular case of a periodic array of membranes embedded in a high-finesse optical cavity [A. Xuereb, C. Genes and A. Dantan, Phys. Rev. Lett., \textbf{109}, 223601, (2012)], the intracavity linear optomechanical coupling can be considerably enhanced over the single element value in the so-called \textit{transmissive regime}, where for motionless membranes the whole system is transparent to light. Here, we extend these investigations to quasi-periodic arrays in the presence of engineered spatial defects in the membrane positions. In particular we show that the localization of light modes induced by the defect combined with the access of the transmissive regime window can lead to additional enhancement of the strength of both linear and quadratic optomechanical couplings.

We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring many-body phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective long-range interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely-connected graphs as well as the coherent transfer of excitations between distant elements of optomechanical arrays., Comment: 11 pages, 7 figures

Ramsey interferometry is routinely used in quantum metrology for the most sensitive measurements of optical clock frequencies. Spontaneous decay to the electromagnetic vacuum ultimately limits the interrogation time and thus sets a lower bound to the optimal frequency sensitivity. In dense ensembles of two-level systems the presence of collective effects such as superradiance and dipole-dipole interaction tends to decrease the sensitivity even further. We show that by a redesign of the Ramsey-pulse sequence to include different rotations of individual spins that effectively fold the collective state onto a state close to the center of the Bloch sphere, partial protection from collective decoherence and dephasing is possible. This allows a significant improvement in the sensitivity limit of a clock transition detection scheme over the conventional Ramsey method for interacting systems and even for non-interacting decaying atoms.

We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes., Comment: 14 pages, 14 figures, comments welcome. This is an expanded version of arXiv:1202.6210 with added interpretation and analysis

We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a Fabry-P\'erot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric Fabry-P\'erot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic "optical coalescence" phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics., Comment: 5 pages, 3 figures

This book chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light., Comment: 31 page review paper; to be pulished as a chapter in the forthcoming Springer textbook "Cavity Optomechanics", edited by M. Aspelmeyer, T. Kippenberg, and F. Marquardt. Comments are welcome!

We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solid-state spin qubits, or superconducting devices. We summarize and compare different coupling schemes and describe first experimental implementations. Hybrid mechanical systems enable new approaches to quantum control of mechanical objects, precision sensing, and quantum information processing., Comment: To cite this review, please refer to the published book chapter (see Journal-ref and DOI). This v2 corresponds to the published version

The motion of two distant trapped particles or mechanical oscillators can be strongly coupled by light modes in a high finesse optical resonator. In a two mode ring cavity geometry, trapping, cooling and coupling is implemented by the same modes. While the cosine mode provides for trapping, the sine mode facilitates ground state cooling and mediates non-local interactions. For classical point particles the centre-of-mass mode is strongly damped and the individual momenta get anti-correlated. Surprisingly, quantum fluctuations induce the opposite effect of positively-correlated particle motion, which close to zero temperature generates entanglement. The non-classical correlations and entanglement are dissipation-induced and particularly strong after detection of a scattered photon in the sine mode. This allows for heralded entanglement by post-selection. Entanglement is concurrent with squeezing of the particle distance and relative momenta, while the centre-of-mass observables acquire larger uncertainties., Comment: 7 pages, 8 figures

We investigate the collective optomechanics of an ensemble of scatterers inside a Fabry-Perot resonator and identify an optimized configuration where the ensemble is transmissive, in contrast with the usual reflective optomechanics approach. In this configuration, the optomechanical coupling of a specific collective mechanical mode can be several orders of magnitude larger than the single-element case, and long-range interactions can be generated between the different elements since light permeates throughout the array. This new regime should realistically allow for achieving strong single-photon optomechanical coupling with massive resonators, realizing hybrid quantum interfaces, and exploiting collective long-range interactions in arrays of atoms or mechanical oscillators., Comment: 11 pages, 12 figures