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arXiv:1411.0688 · Physical Review A

Nondestructive selective probing of phononic excitations in a cold Bose gas using impurities

Dominik Hangleiter, Mark T. Mitchison, T. H. Johnson, M. Bruderer, Martin Bodo Plenio, Dieter Jaksch

Published Jan 12, 2015• 39 citations
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Abstract

We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a double-well potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via density-density interactions with the bosons. The system is analogous to a two-level atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are selected in both energy and momentum by adjusting the impurity's potential. We show how to use the detector to observe coherent density waves and to measure temperatures of the Bose gas down to the nanokelvin regime. We analyze how our scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision from a single experimental run.

DOI
10.1103/physreva.91.013611

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We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a double-well potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via density-density interactions with the bosons. The system is analogous to a two-level atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are selected in both energy and momentum by adjusting the impurity's potential. We show how to use the detector to observe coherent density waves and to measure temperatures of the Bose gas down to the nanokelvin regime. We analyze how our scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision from a single experimental run.
We study an impurity atom trapped by an anharmonic potential, immersed within a cold atomic Fermi gas with attractive interactions that realizes the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate. Considering the qubit comprising the lowest two vibrational energy eigenstates of the impurity, we demonstrate that its dynamics probes the equilibrium density fluctuations encoded in the dynamic structure factor of the superfluid. Observing the impurity's evolution is thus shown to facilitate nondestructive measurements of the superfluid order parameter and the contact between collective and single-particle excitation spectra. Our setup constitutes a model of an open quantum system interacting with a thermal reservoir, the latter supporting both bosonic and fermionic excitations that are also coupled to each other.
We study a two-level impurity coupled locally to a quantum gas on an optical lattice.For statedependent interactions between the impurity and the gas, we show that its evolution encodes information on the local excitation spectrum of the gas at the coupling site.Based on this, we design a nondestructive method to probe the system's excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods.We illustrate our findings with numerical simulations for quantum lattice systems, including realistic dephasing noise on the quantum probe, and discuss practical limits on the probe dephasing rate to fully resolve both regular and chaotic spectra.
Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.
We present a nondestructive method to probe a complex quantum system using multiple-impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particular, we show that measurements with two probes reveal the system's nonlocal two-point density correlations, for probe-system contact interactions. We illustrate our findings with analytic and numerical calculations for the Bose-Hubbard model in the weakly and strongly interacting regimes, under conditions relevant to ongoing experiments in cold-atom systems.
Using near-exact numerical simulations, we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas, which allows one to measure properties of the Bose gas nondestructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance, we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the crossover of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas, and the effects on the impurity in both of these strongly interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas.
We present a general and non-invasive probing scheme to perform full momentum-resolved spectroscopy of a cold atomic gas loaded into an optical lattice using a single quantum impurity. The protocol relies on weak collisional interactions and subsequent population measurements of the impurity. By tuning a few controllable external parameters the impurity-lattice interaction can be engineered, and using two sets of measurements, performed with the impurity in two different positions, the full dispersion relation of the superfluid phonons can be reliably extracted.