C++QED: An object-oriented framework for wave-function simulations of cavity QED systems

We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting quantum dynamics in general. The user is provided with a number of ``elements'', eg pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.Comment: 31 pages, 8 figures, 3 table

Microscopic physics of quantum self-organisation of optical lattices in cavities

We study quantum particles at zero temperature in an optical lattice coupled to a resonant cavity mode. The cavity field substantially modifies the particle dynamics in the lattice, and for strong particle-field coupling leads to a quantum phase with only every second site occupied. We study the growth of this new order out of a homogeneous initial distribution for few particles as the microscopic physics underlying a quantum phase transition. Simulations reveal that the growth dynamics crucially depends on the initial quantum many-body state of the particles and can be monitored via the cavity fluorescence. Studying the relaxation time of the ordering reveals inhibited tunnelling, which indicates that the effective mass of the particles is increased by the interaction with the cavity field. However, the relaxation becomes very quick for large coupling.Comment: 14 pages 6 figure

Fundamental limitation of ultrastrong coupling between light and atoms

In a recent work of ours [Phys. Rev. Lett. 112, 073601 (2014)], we generalized the Power-Zineau-Woolley gauge to describe the electrodynamics of atoms in an arbitrary confined geometry. Here we complement the theory by proposing a tractable form of the polarization field to represent atomic material with well-defined intra-atomic potential. The direct electrostatic dipole-dipole interaction between the atoms is canceled. This theory yields a suitable framework to determine limitations on the light-matter coupling in quantum optical models with discernible atoms. We find that the superradiant criticality is at the border of covalent molecule formation and crystallization.Comment: 6 page

Self-organization of atoms in a cavity field: threshold, bistability and scaling laws

We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on laboratory timescale, a hysteresis masks the mean-field behaviour. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of ``defects'' appear in the organized phase, and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase space density with the atom number is also studied.Comment: submitted to PR

Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is yet an unsettled one. The well-known statement often referred to as the "no-go theorem", asserts that the so-called A-square term, just in the vicinity of the critical point, becomes relevant enough to prevent the system from undergoing a phase transition. At variance with this common belief, in this paper we prove that the Dicke model does give a consistent description of the interaction of light field with the internal excitation of atoms, but in the dipole gauge of quantum electrodynamics. The phase transition cannot be excluded by principle and a spontaneous transverse-electric mean field may appear. We point out that the single-mode approximation is crucial: the proper treatment has to be based on cavity QED, wherefore we present a systematic derivation of the dipole gauge inside a perfect Fabry-P\'erot cavity from first principles. Besides the impact on the debate around the Dicke phase transition, such a cleanup of the theoretical ground of cavity QED is important because currently there are many emerging experimental approaches to reach strong or even ultrastrong coupling between dipoles and photons, which demand a correct treatment of the Dicke model parameters

Prospects for the cavity-assisted laser cooling of molecules

Cooling of molecules via free-space dissipative scattering of photons is thought not to be practicable due to the inherently large number of Raman loss channels available to molecules and the prohibitive expense of building multiple repumping laser systems. The use of an optical cavity to enhance coherent Rayleigh scattering into a decaying cavity mode has been suggested as a potential method to mitigate Raman loss, thereby enabling the laser cooling of molecules to ultracold temperatures. We discuss the possibility of cavity-assisted laser cooling particles without closed transitions, identify conditions necessary to achieve efficient cooling, and suggest solutions given experimental constraints. Specifically, it is shown that cooperativities much greater than unity are required for cooling without loss, and that this could be achieved via the superradiant scattering associated with intracavity self-localization of the molecules. Particular emphasis is given to the polar hydroxyl radical (OH), cold samples of which are readily obtained from Stark deceleration.Comment: 18 pages, 10 figure

Quantum stability of self-organized atomic insulator-like states in optical resonators

We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the mechanical potential emerging from the cavity field spatial mode structure. As in open space, when the optical potential is sufficiently deep, the atomic gas is in the Mott-like state. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity field amplitude. We derive the effective Bose-Hubbard model describing the physics of the system in one dimension and study the crossover between the superfluid -- Mott insulator quantum states. We determine the regions of parameters where the atomic insulator states are stable, and predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.Comment: 13 pages, 6 figures. Replaced with revised version. Accepted for publication in New J. Phys., special issue "Quantum correlations in tailord matter

Transitions in the Horizontal Transport of Vertically Vibrated Granular Layers

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.Comment: 12 pages, 18 figure

Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition

We prove that the observable telegraph signal accompanying the bistability in the photon-blockade-breakdown regime of the driven and lossy Jaynes–Cummings model is the finite-size precursor of what in the thermodynamic limit is a genuine first-order phase transition. We construct a finite-size scaling of the system parameters to a well-defined thermodynamic limit, in which the system remains the same microscopic system, but the telegraph signal becomes macroscopic both in its timescale and intensity. The existence of such a finite-size scaling completes and justifies the classification of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition