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arXiv:1405.7336 · Physical Review A

Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice

Saubhik Sarkar, S. Langer, Johannes Schachenmayer, Andrew J. Daley

Published Aug 13, 2014• 39 citations
arXivHTMLPDF

Abstract

We investigate the many-body dissipative dynamics of fermionic atoms in an optical lattice in the presence of incoherent light scattering. Deriving and solving a master equation to describe this process microscopically for many particles, we observe contrasting behavior in terms of the robustness against this type of heating for different many-body states. In particular, we find that the magnetic correlations exhibited by a two-component gas in the Mott insulating phase should be particularly robust against decoherence from light scattering, because the decoherence in the lowest band is suppressed by a larger factor than the time scales for effective superexchange interactions that drive coherent dynamics. Furthermore, the derived formalism naturally generalizes to analogous states with $\text{SU}(N)$ symmetry. In contrast, for typical atomic and laser parameters, two-particle correlation functions describing bound dimers for strong attractive interactions exhibit superradiant effects due to the indistinguishability of off-resonant photons scattered by atoms in different internal states. This leads to rapid decay of correlations describing off-diagonal long-range order for these states. Our predictions should be directly measurable in ongoing experiments, providing a basis for characterizing and controlling heating processes in quantum simulation with fermions.

DOI
10.1103/physreva.90.023618

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We investigate the many-body dissipative dynamics of fermionic atoms in an optical lattice in the presence of incoherent light scattering. Deriving and solving a master equation to describe this process microscopically for many particles, we observe contrasting behavior in terms of the robustness against this type of heating for different many-body states. In particular, we find that the magnetic correlations exhibited by a two-component gas in the Mott insulating phase should be particularly robust against decoherence from light scattering, because the decoherence in the lowest band is suppressed by a larger factor than the time scales for effective superexchange interactions that drive coherent dynamics. Furthermore, the derived formalism naturally generalizes to analogous states with SU(N)\text{SU}(N)SU(N) symmetry. In contrast, for typical atomic and laser parameters, two-particle correlation functions describing bound dimers for strong attractive interactions exhibit superradiant effects due to the indistinguishability of off-resonant photons scattered by atoms in different internal states. This leads to rapid decay of correlations describing off-diagonal long-range order for these states. Our predictions should be directly measurable in ongoing experiments, providing a basis for characterizing and controlling heating processes in quantum simulation with fermions.
We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the time scale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based on both perturbation-theory calculations and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for one-dimensional systems by combining time-dependent density-matrix-renormalization-group methods with quantum trajectory techniques.
We show how off-resonant light scattering can provide quantitative information on antiferromagnetic ordering of a two-species fermionic atomic gas in a tightly-confined two-dimensional optical lattice.We analyze the emerging magnetic ordering of atoms in the mean-field and in random phase approximations and show how the many-body static and dynamic correlations, evaluated in the standard Feynman-Dyson perturbation series, can be detected in the scattered light signal.The staggered magnetization reveals itself in the magnetic Bragg peaks of the individual spin components.These magnetic peaks, however, can be considerably suppressed in the absence of a true long-range antiferromagnetic order.The light scattered outside the diffraction orders can be collected by a lens with highly improved signal-to-shot-noise ratio when the diffraction maxima are blocked.The collective and single-particle excitations are identified in the spectrum of the scattered light.We find that the spin-conserving and spin-exchanging atomic transitions convey information on density, longitudinal spin, and transverse spin correlations.The different correlations and scattering processes exhibit characteristic angular distribution profiles for the scattered light, and e.g., the diagnostic signal of transverse spin correlations could be separated from the optical response by the scattering direction, frequency, or polarization.We also analyze the detection accuracy by estimating the number of required measurements, constrained by the heating rate that is determined by inelastic light-scattering events.The imaging technique could be extended to the two-species fermionic states in other regions of the phase diagram where the ground-state properties are still not fully understood.
We investigate the loss of spatial coherence of one-dimensional bosonic gases in optical lattices illuminated by a near-resonant excitation laser. Because the atoms recoil in a random direction after each spontaneous emission, the atomic momentum distribution progressively broadens. Equivalently, the spatial correlation function (the Fourier-conjugate quantity of the momentum distribution) progressively narrows down as more photons are scattered. Here we measure the correlation function of the matter field for fixed distances corresponding to nearest-neighbor (n-n) and next-nearest-neighbor (n-n-n) sites of the optical lattice as a function of time, hereafter called n-n and n-n-n correlators. For strongly interacting lattice gases, we find that the n-n correlator C 1 decays as a power-law at long times, C 1 ∝ 1 / t α , in stark contrast with the exponential decay expected for independent particles. The power-law decay reflects a non-trivial dissipative many-body dynamics, where interactions change drastically the interplay between fluorescence destroying spatial coherence, and coherent tunnelling between neighboring sites restoring spatial coherence at short distances. The observed decay exponent α ≈ 0 . 54 ( 6 ) is in good agreement with the prediction α = 1 / 2 from a dissipative Bose–Hubbard model accounting for the fluorescence-induced decoherence. Furthermore, we find that the n-n correlator C 1 controls the n-n-n correlator C 2 through the relation C 2 ≈ C 1 2 , also in accordance with the dissipative Bose–Hubbard model.
When placing an ultracold atomic gas inside a cavity, the light-matter coupling is enhanced and nonlinear atomic dynamics is generated, offering a promising platform for quantum simulation of models with short- and long-range interactions. Recently, superradiant self-organized phases for ultracold atomic gases inside a cavity, pumped by a blue detuned optical lattice, have been observed. Here, we explore the formation of quantum many-body phases of bosonic atoms inside an optical cavity, subject to transverse blue detuned pumping. We investigate the strongly interacting regime, which can be reached by tuning the s-wave scattering length using external fields. We analyze the interplay between superradiant self-organization with superfluid and Mott insulator phases, without the need of including higher lying bands, as the Wannier functions are dynamically linked to the cavity light via backaction. We observe different kinds of structural phase transitions driven by the light inside the cavity and the interplay with atomic collisions. We observe the mode softening at the critical points in the quantum phase transitions which can be measured in future experiments. We obtain our results within a full self-consistent theoretical framework, the light-matter density matrix renormalization group (DMRG), which employs the computation of light dependent Wannier functions for the full quantum optical lattice in combination with DMRG for the atomic dynamics. The methods introduced here can be used to analyze the effects of strong quantum correlations in strongly interacting light-matter systems.
We analyze the heating of interacting bosonic atoms in an optical lattice due to intensity fluctuations of the lasers forming the lattice. We focus in particular on fluctuations at low frequencies below the band-gap frequency, such that the dynamics is restricted to the lowest band. We derive stochastic equations of motion, and analyze the effects on different many-body states, characterizing heating processes in both strongly and weakly interacting regimes. In the limit where the noise spectrum is flat at low frequencies, we can derive an effective master equation describing the dynamics. We compute heating rates and changes to characteristic correlation functions both in the perturbation theory limit and using a full time-dependent calculation of the stochastic many-body dynamics in one dimension based on time-dependent density-matrix--renormalization-group methods.
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.