Schr\"odinger cat state of a Bose-Einstein condensate in a double-well potential

We consider a weakly interacting coherently coupled Bose-Einstein condensate in a double-well potential. We show by means of stochastic simulations that the system could possibly be driven to an entangled macroscopic superposition state or a Schr\"odinger cat state by means of a continuous quantum measurement process.Comment: 6 pages; to be published in memorial volume for Dan Wall

Light propagation beyond the mean-field theory of standard optics

With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around $k^{-1}$, where $k$ is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions

Theoretical formalism for collective electromagnetic response of discrete metamaterial systems

We develop a general formalism to describe the propagation of a near-resonant electromagnetic field in a medium composed of magnetodielectric resonators. As the size and the spatial separation of nanofabricated resonators in a metamaterial array is frequently less than the wavelength, we describe them as discrete scatterers, supporting a single mode of current oscillation represented by a single dynamic variable. We derive a Lagrangian and Hamiltonian formalism for the coupled electromagnetic fields and oscillating currents in the length gauge, obtained by the Power-Zienau-Woolley transformation. The response of each resonator to electromagnetic field is then described by polarization and magnetization densities that, to the lowest order in a multipole expansion, generate electric and magnetic dipole excitations. We derive a closed set of equations for the coherently scattered field and normal mode amplitudes of current oscillations of each resonator both within the rotating wave approximation, in which case the radiative decay rate is much smaller than the resonance frequency, and without such an assumption. The set of equations includes the radiative couplings between a discrete set of resonators mediated by the electromagnetic field, fully incorporating recurrent scattering processes to all orders. By considering an example of a two-dimensional split ring resonator metamaterial array, we show that the system responds cooperatively to near-resonant field, exhibiting collective eigenmodes, resonance frequencies, and radiative linewidths that result from strong radiative interactions between closely-spaced resonators.Comment: 34 pages, 6 figure

Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic Bose-Einstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasi-probability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system, and that these trajectories faithfully represent measurement records of individual experimental runs. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.Comment: 22 pages, 11 figure

Testing quantum superpositions of the gravitational field with Bose-Einstein condensates

We consider the gravity field of a Bose-Einstein condensate in a quantum superposition. The gravity field then is also in a quantum superposition which is in principle observable. Hence we have ``quantum gravity'' far away from the so-called Planck scale

Energetically stable singular vortex cores in an atomic spin-1 Bose-Einstein condensate

We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits energetic hierarchy of length scales resulting from different interaction strengths and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction. We show that in the ferromagnetic phase the resulting stable core structure, despite apparent complexity, can be identified as a single polar core with everywhere nonvanishing axially symmetric density profile. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores.<br/