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arXiv:1508.05640 · New Journal of Physics

Quantum properties of light scattered from structured many-body phases of ultracold atoms in quantum optical lattices

Santiago F. Caballero-Benítez, Igor B. Mekhov

Published Dec 17, 2015• 23 citations
arXivHTMLPDF

Abstract

Quantum trapping potentials for ultracold gases change the landscape of classical properties of scattered light and matter. The atoms in a quantum many-body correlated phase of matter change the properties of light and vice versa. The properties of both light and matter can be tuned by design and depend on the interplay between long-range (nonlocal) interactions mediated by an optical cavity and short-range processes of the atoms. Moreover, the quantum properties of light get significantly altered by this interplay, leading the light to have nonclassical features. Further, these nonclassical features can be designed and optimised. Introduction and background. Under some of the most extreme experimental conditions of temperature and vacuum, atoms can be controlled by lasers in optical lattices. Beyond controlling the spatial distribution of atoms by light, one can selectively pump at a particular wavelength optimising the interaction with light by several orders of magnitude with additional mirrors. As this occurs, the light in the cavity mediates a true quantum potential that couples all the atoms along the optical lattice, leading to the formation of a quantum optical lattice. The structural arrangement of the atoms can be modified by the light, as photons interact with atoms and vice versa. Main results. In this paper, we concentrate on understanding and showing how the light scattered by the atoms acquires features that are inherently quantum mechanical and originated due to the atomic condensation into a many-body state. The atoms have strong correlations among them as they locally interact and move in the optical lattice in addition to the cavity mediated long-range interaction. We show how one can design and optimise the quantum properties of the scattered light by the atoms, and how it contains information regarding the correlated phases of matter that emerge. Wider Implications. Our results will allow to consider the design of quantum properties of light and the interplay between different energy scales in the system towards the implementation of new quantum simulators, the possibility to optimise these properties for technological applications and ultimately innovate towards possible implementations of quantum system engineering of states.

DOI
10.1088/1367-2630/17/12/123023

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Quantum trapping potentials for ultracold gases change the landscape of classical properties of scattered light and matter. The atoms in a quantum many-body correlated phase of matter change the properties of light and vice versa. The properties of both light and matter can be tuned by design and depend on the interplay between long-range (nonlocal) interactions mediated by an optical cavity and short-range processes of the atoms. Moreover, the quantum properties of light get significantly altered by this interplay, leading the light to have nonclassical features. Further, these nonclassical features can be designed and optimised. Introduction and background. Under some of the most extreme experimental conditions of temperature and vacuum, atoms can be controlled by lasers in optical lattices. Beyond controlling the spatial distribution of atoms by light, one can selectively pump at a particular wavelength optimising the interaction with light by several orders of magnitude with additional mirrors. As this occurs, the light in the cavity mediates a true quantum potential that couples all the atoms along the optical lattice, leading to the formation of a quantum optical lattice. The structural arrangement of the atoms can be modified by the light, as photons interact with atoms and vice versa. Main results. In this paper, we concentrate on understanding and showing how the light scattered by the atoms acquires features that are inherently quantum mechanical and originated due to the atomic condensation into a many-body state. The atoms have strong correlations among them as they locally interact and move in the optical lattice in addition to the cavity mediated long-range interaction. We show how one can design and optimise the quantum properties of the scattered light by the atoms, and how it contains information regarding the correlated phases of matter that emerge. Wider Implications. Our results will allow to consider the design of quantum properties of light and the interplay between different energy scales in the system towards the implementation of new quantum simulators, the possibility to optimise these properties for technological applications and ultimately innovate towards possible implementations of quantum system engineering of states.
We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time possess properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e., infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support nontrivial superfluid states, bosonic dimer, trimer, etc., states, and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.
We show how bond order emerges due to light mediated synthetic interactions in ultracold atoms in optical lattices in an optical cavity. This is a consequence of the competition between both short- and long-range interactions designed by choosing the optical geometry. Light induces effective many-body interactions that modify the landscape of quantum phases supported by the typical Bose–Hubbard model. Using exact diagonalization of small system sizes in one-dimension, we present the many-body quantum phases the system can support via the interplay between the density and bond (or matter–wave coherence) interactions. We find numerical evidence to support that dimer phases due to bond order are analogous to valence bond states. Different possibilities of light-induced atomic interactions are considered that go beyond the typical atomic system with dipolar and other intrinsic interactions. This will broaden the Hamiltonian toolbox available for quantum simulation of condensed matter physics via atomic systems.
Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state.We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced.We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states.In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.
We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. Because of the global coupling between the atoms and the light modes, observing the photons leaking from the cavity allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. Moreover, the detection of the photons perturbs the quantum state of the atoms via the so-called measurement backaction. This effect constitutes an unusual additional dynamical source in a many-body strongly correlated system and it is able to efficiently compete with its intrinsic short-range dynamics. This competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period, without the need of single site addressing. We demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, breakup and protection of strongly interacting fermion pairs. We show that measurement backaction can be exploited for realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves and we demonstrate that such long-range correlations cannot be realized with local addressing. Finally, we describe how to stabilize these emerging phases with the aid of quantum feedback. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems and it is easily extendable to other systems promising for quantum technologies.
Although the study of ultracold quantum gases trapped by light is a prominent direction of modern research, the quantum properties of light were widely neglected in this field. Quantum optics with quantum gases closes this gap and addresses phenomena, where the quantum statistical nature of both light and ultracold matter play equally important roles. First, light can serve as a quantum nondemolition (QND) probe of the quantum dynamics of various ultracold particles from ultracold atomic and molecular gases to nanoparticles and nanomechanical systems. Second, due to dynamic light-matter entanglement, projective measurement-based preparation of the many-body states is possible, where the class of emerging atomic states can be designed via optical geometry. Light scattering constitutes such a quantum measurement with controllable measurement back-action. As in cavity-based spin squeezing, atom number squeezed and Schroedinger cat states can be prepared. Third, trapping atoms inside an optical cavity one creates optical potentials and forces, which are not prescribed but quantized and dynamical variables themselves. Ultimately, cavity QED with quantum gases requires a self-consistent solution for light and particles, which enriches the picture of quantum many-body states of atoms trapped in quantum potentials. This will allow quantum simulations of phenomena related to the physics of phonons, polarons, polaritons and other quantum quasiparticles.